This function performs dimensionality reduction using various methods including PCA, t-SNE, and UMAP. UMAP runs directly on inputs with 1000 or fewer features (e.g. dense embeddings); PCA pre-reduction applies to wider inputs and to the PCA and t-SNE methods.
Usage
reduce_dimensions(
data_matrix,
method = "PCA",
n_components = 2,
pca_dims = 50,
tsne_perplexity = 30,
tsne_max_iter = 1000,
umap_neighbors = 15,
umap_min_dist = 0.1,
umap_metric = "cosine",
seed = 123,
verbose = TRUE
)Arguments
- data_matrix
A numeric matrix where rows represent documents and columns represent features.
- method
The dimensionality reduction method. Options: "PCA", "t-SNE", "UMAP".
- n_components
The number of components/dimensions to reduce to (default: 2).
- pca_dims
The number of dimensions for PCA preprocessing (default: 50).
- tsne_perplexity
The perplexity parameter for t-SNE (default: 30).
- tsne_max_iter
The maximum number of iterations for t-SNE (default: 1000).
- umap_neighbors
The number of neighbors for UMAP (default: 15).
- umap_min_dist
The minimum distance for UMAP (default: 0.1).
- umap_metric
The metric for UMAP (default: "cosine").
- seed
Random seed for reproducibility (default: 123).
- verbose
Logical, if TRUE, prints progress messages.
Examples
if (interactive()) {
mydata <- TextAnalysisR::SpecialEduTech
united_tbl <- TextAnalysisR::unite_cols(
mydata,
listed_vars = c("title", "keyword", "abstract")
)
tokens <- TextAnalysisR::prep_texts(united_tbl, text_field = "united_texts")
dfm_object <- quanteda::dfm(tokens)
data_matrix <- as.matrix(dfm_object)
pca_result <- TextAnalysisR::reduce_dimensions(
data_matrix,
method = "PCA"
)
print(pca_result)
tsne_result <- TextAnalysisR::reduce_dimensions(
data_matrix,
method = "t-SNE"
)
print(tsne_result)
umap_result <- TextAnalysisR::reduce_dimensions(
data_matrix,
method = "UMAP"
)
print(umap_result)
}
#> Starting dimensionality reduction with method: PCA
#> Performing PCA preprocessing...
#> Returning PCA results...
#> Dimensionality reduction completed in 6.87 seconds
#> $reduced_data
#>
#> docs PC1 PC2
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#> text406 12.75110256 -8.825532129
#> text407 -5.44782438 1.130028680
#> text408 -3.02391564 -0.576904607
#> text409 -6.02672399 -2.502629771
#> text410 -2.98878939 -1.186321829
#> text411 -8.30141034 -3.494301800
#> text412 -6.24011216 -6.837830813
#> text413 -3.27630097 1.009008888
#> text414 -0.68086213 -4.857551559
#> text415 -2.47267801 -5.805899262
#> text416 -7.05104222 -3.650156001
#> text417 0.23811380 1.720561896
#> text418 -3.24238751 -4.198593903
#> text419 -9.94278593 4.253856237
#> text420 7.06007101 -2.075203749
#> text421 -1.29486025 -4.508893636
#> text422 15.63063355 -11.672137060
#> text423 2.23546316 0.767802966
#> text424 8.81579385 4.579919808
#> text425 -3.15904703 3.551881057
#> text426 24.28090669 10.317985405
#> text427 -0.92164103 1.922018294
#> text428 -3.12359030 -0.020942205
#> text429 5.70441364 -1.885436674
#> text430 6.66548373 6.623482721
#> text431 1.34483762 0.088557763
#> text432 -4.28430122 -4.044615132
#> text433 -3.78417822 -0.611038483
#> text434 10.40818428 5.668426906
#> text435 35.45720005 13.424727852
#> text436 1.37346275 -6.803655027
#> text437 12.66513752 -6.568221301
#> text438 11.92758745 -1.830013075
#> text439 2.96124175 2.979352772
#> text440 -3.58732532 4.634128691
#> text441 -4.35133015 -6.859911717
#> text442 3.23186961 -5.608802627
#> text443 -6.93910184 -7.452451120
#> text444 2.78577052 -4.783393036
#> text445 5.84602616 3.989268379
#> text446 -5.57942249 -0.961565342
#> text447 -3.35894195 -5.991487238
#> text448 -6.36153272 -3.266169720
#> text449 -1.86438678 -2.784650025
#> text450 -1.11576991 -2.369483795
#> text451 -8.29020084 -0.082317433
#> text452 -5.77389762 -0.843161820
#> text453 -4.81125066 -2.612842961
#> text454 1.72170580 -1.989878958
#> text455 -0.95818057 -8.592311682
#> text456 -9.52774575 -6.148628582
#> text457 8.61683258 1.153668969
#> text458 11.96227665 4.521625381
#> text459 1.68675604 -0.503189321
#> text460 -5.00923262 -0.265461405
#> text461 -6.66570846 -5.231457178
#> text462 -5.60355732 1.778755314
#> text463 0.89263259 1.136222491
#> text464 -3.10686497 1.001377032
#> text465 -2.81748534 -5.092906535
#> text466 6.32181568 8.093534459
#> text467 -2.44438754 0.387243067
#> text468 -7.37200600 -5.654592038
#> text469 -2.14788834 -5.629791270
#> text470 -1.14364566 -5.324583947
#> text471 -4.46537121 -0.792737531
#> text472 11.48809523 -1.923265999
#> text473 -3.38672828 -3.525152422
#> text474 -5.87444755 -2.260452058
#> text475 4.93076714 1.636914748
#> text476 3.74934940 4.977165373
#> text477 -11.80197161 -1.684517573
#> text478 -0.70486626 2.413410959
#> text479 -6.58511235 -7.914995590
#> text480 -4.80118003 -4.869949065
#> text481 -5.30037603 -6.025407373
#> text482 -1.00171884 -1.310546832
#> text483 -3.71272514 2.542485484
#> text484 -4.13377140 1.460128147
#> text485 -3.30605202 -3.144474065
#> text486 -7.32669382 -4.895869254
#> text487 -3.58131274 -3.586525864
#> text488 6.44221999 1.140693835
#> text489 0.57226488 -1.633038001
#> text490 -7.03180485 -1.309760717
#>
#> $method
#> [1] "PCA"
#>
#> $pca_result
#> Standard deviations (1, .., p=490):
#> [1] 9.243205e+00 4.207211e+00 3.914661e+00 3.640950e+00 3.316587e+00
#> [6] 3.141114e+00 2.852412e+00 2.744243e+00 2.621505e+00 2.531561e+00
#> [11] 2.477948e+00 2.350191e+00 2.280115e+00 2.153115e+00 2.135359e+00
#> [16] 2.073989e+00 2.035517e+00 1.980114e+00 1.904040e+00 1.892190e+00
#> [21] 1.875725e+00 1.799473e+00 1.757500e+00 1.728256e+00 1.708477e+00
#> [26] 1.676742e+00 1.630217e+00 1.623334e+00 1.604087e+00 1.583754e+00
#> [31] 1.567891e+00 1.536249e+00 1.532775e+00 1.520808e+00 1.495698e+00
#> [36] 1.466973e+00 1.451911e+00 1.439230e+00 1.426326e+00 1.408866e+00
#> [41] 1.394070e+00 1.356280e+00 1.355607e+00 1.343218e+00 1.324939e+00
#> [46] 1.317448e+00 1.298042e+00 1.292172e+00 1.290126e+00 1.284486e+00
#> [51] 1.260741e+00 1.252454e+00 1.242871e+00 1.234479e+00 1.221911e+00
#> [56] 1.206628e+00 1.199803e+00 1.195127e+00 1.190011e+00 1.174547e+00
#> [61] 1.171232e+00 1.154458e+00 1.145637e+00 1.135996e+00 1.124914e+00
#> [66] 1.122782e+00 1.116625e+00 1.109650e+00 1.095992e+00 1.094403e+00
#> [71] 1.083500e+00 1.081434e+00 1.073638e+00 1.065964e+00 1.059762e+00
#> [76] 1.047794e+00 1.046608e+00 1.037150e+00 1.030342e+00 1.022820e+00
#> [81] 1.016640e+00 1.010146e+00 1.001855e+00 9.943502e-01 9.920359e-01
#> [86] 9.841591e-01 9.761104e-01 9.732790e-01 9.623114e-01 9.603170e-01
#> [91] 9.559378e-01 9.443870e-01 9.428462e-01 9.410785e-01 9.344836e-01
#> [96] 9.288014e-01 9.271981e-01 9.195127e-01 9.104633e-01 9.076714e-01
#> [101] 9.055111e-01 9.009656e-01 8.940822e-01 8.915336e-01 8.860811e-01
#> [106] 8.783154e-01 8.733380e-01 8.706939e-01 8.655068e-01 8.625876e-01
#> [111] 8.561297e-01 8.521523e-01 8.429825e-01 8.406524e-01 8.389560e-01
#> [116] 8.364509e-01 8.280351e-01 8.254479e-01 8.214640e-01 8.167350e-01
#> [121] 8.132213e-01 8.078696e-01 8.067777e-01 8.007288e-01 7.957929e-01
#> [126] 7.920924e-01 7.888844e-01 7.820410e-01 7.805644e-01 7.768805e-01
#> [131] 7.715894e-01 7.685875e-01 7.664157e-01 7.637809e-01 7.629644e-01
#> [136] 7.571623e-01 7.533174e-01 7.499022e-01 7.485470e-01 7.426886e-01
#> [141] 7.395636e-01 7.355301e-01 7.330848e-01 7.250294e-01 7.219595e-01
#> [146] 7.207059e-01 7.178711e-01 7.134139e-01 7.119358e-01 7.105775e-01
#> [151] 7.072117e-01 7.040330e-01 7.028589e-01 6.992496e-01 6.948058e-01
#> [156] 6.939748e-01 6.892388e-01 6.842039e-01 6.827935e-01 6.813387e-01
#> [161] 6.792254e-01 6.772769e-01 6.720927e-01 6.701258e-01 6.658420e-01
#> [166] 6.623950e-01 6.609654e-01 6.597883e-01 6.573117e-01 6.570087e-01
#> [171] 6.549812e-01 6.485347e-01 6.466902e-01 6.430801e-01 6.392046e-01
#> [176] 6.369904e-01 6.344709e-01 6.313753e-01 6.301461e-01 6.281418e-01
#> [181] 6.267177e-01 6.225714e-01 6.199600e-01 6.185427e-01 6.141035e-01
#> [186] 6.126771e-01 6.096630e-01 6.088156e-01 6.063807e-01 6.036823e-01
#> [191] 6.008063e-01 5.979322e-01 5.965868e-01 5.946803e-01 5.910745e-01
#> [196] 5.881630e-01 5.851488e-01 5.843792e-01 5.832505e-01 5.801898e-01
#> [201] 5.793297e-01 5.776320e-01 5.750328e-01 5.741570e-01 5.726129e-01
#> [206] 5.722598e-01 5.690460e-01 5.653365e-01 5.618373e-01 5.577842e-01
#> [211] 5.563350e-01 5.530227e-01 5.516199e-01 5.506381e-01 5.490014e-01
#> [216] 5.477387e-01 5.470153e-01 5.454412e-01 5.441161e-01 5.401694e-01
#> [221] 5.389369e-01 5.367966e-01 5.332473e-01 5.315658e-01 5.289262e-01
#> [226] 5.276807e-01 5.252845e-01 5.245833e-01 5.209357e-01 5.206105e-01
#> [231] 5.185780e-01 5.158014e-01 5.126761e-01 5.110360e-01 5.095218e-01
#> [236] 5.090777e-01 5.081830e-01 5.054780e-01 5.040159e-01 5.031494e-01
#> [241] 5.007658e-01 4.998503e-01 4.981423e-01 4.946367e-01 4.936244e-01
#> [246] 4.919041e-01 4.901219e-01 4.887549e-01 4.870942e-01 4.855973e-01
#> [251] 4.831134e-01 4.818930e-01 4.807614e-01 4.796236e-01 4.774337e-01
#> [256] 4.756689e-01 4.739295e-01 4.722662e-01 4.716409e-01 4.698954e-01
#> [261] 4.683940e-01 4.666922e-01 4.638996e-01 4.626640e-01 4.606707e-01
#> [266] 4.602921e-01 4.565806e-01 4.551472e-01 4.536993e-01 4.521929e-01
#> [271] 4.512901e-01 4.504168e-01 4.486301e-01 4.481631e-01 4.462478e-01
#> [276] 4.438517e-01 4.433398e-01 4.411723e-01 4.393198e-01 4.379883e-01
#> [281] 4.369864e-01 4.357161e-01 4.335241e-01 4.315384e-01 4.304626e-01
#> [286] 4.299509e-01 4.295972e-01 4.262579e-01 4.251349e-01 4.234177e-01
#> [291] 4.222948e-01 4.210002e-01 4.191833e-01 4.177143e-01 4.160603e-01
#> [296] 4.152285e-01 4.127429e-01 4.116214e-01 4.110062e-01 4.095753e-01
#> [301] 4.090932e-01 4.072502e-01 4.065672e-01 4.042008e-01 4.035206e-01
#> [306] 4.023567e-01 4.017920e-01 4.007671e-01 3.982198e-01 3.976655e-01
#> [311] 3.957143e-01 3.947265e-01 3.935244e-01 3.916946e-01 3.909234e-01
#> [316] 3.900114e-01 3.877642e-01 3.858114e-01 3.847948e-01 3.835150e-01
#> [321] 3.819818e-01 3.813703e-01 3.803031e-01 3.791932e-01 3.779444e-01
#> [326] 3.770000e-01 3.760075e-01 3.751111e-01 3.737653e-01 3.721652e-01
#> [331] 3.718862e-01 3.705055e-01 3.691068e-01 3.674795e-01 3.651444e-01
#> [336] 3.647957e-01 3.633445e-01 3.622535e-01 3.603617e-01 3.600399e-01
#> [341] 3.593517e-01 3.589410e-01 3.572479e-01 3.566297e-01 3.550247e-01
#> [346] 3.531792e-01 3.522962e-01 3.520084e-01 3.504945e-01 3.474721e-01
#> [351] 3.459154e-01 3.446735e-01 3.443787e-01 3.423760e-01 3.416633e-01
#> [356] 3.406604e-01 3.400317e-01 3.391539e-01 3.374578e-01 3.350315e-01
#> [361] 3.347968e-01 3.337742e-01 3.324674e-01 3.315236e-01 3.308446e-01
#> [366] 3.291645e-01 3.281053e-01 3.262903e-01 3.253731e-01 3.242374e-01
#> [371] 3.228902e-01 3.220174e-01 3.211667e-01 3.197456e-01 3.191225e-01
#> [376] 3.185557e-01 3.173933e-01 3.157462e-01 3.147677e-01 3.132461e-01
#> [381] 3.129181e-01 3.121474e-01 3.096893e-01 3.082353e-01 3.073252e-01
#> [386] 3.063280e-01 3.050632e-01 3.046753e-01 3.032957e-01 3.014308e-01
#> [391] 3.006672e-01 2.990869e-01 2.986001e-01 2.965456e-01 2.957026e-01
#> [396] 2.950281e-01 2.936329e-01 2.926258e-01 2.924754e-01 2.913299e-01
#> [401] 2.900980e-01 2.883983e-01 2.875028e-01 2.861673e-01 2.844567e-01
#> [406] 2.840259e-01 2.835168e-01 2.828999e-01 2.824800e-01 2.808992e-01
#> [411] 2.790587e-01 2.781097e-01 2.777240e-01 2.764665e-01 2.759602e-01
#> [416] 2.754744e-01 2.743536e-01 2.726297e-01 2.721738e-01 2.699852e-01
#> [421] 2.694801e-01 2.670432e-01 2.662954e-01 2.650347e-01 2.646827e-01
#> [426] 2.635966e-01 2.617783e-01 2.601196e-01 2.590181e-01 2.574992e-01
#> [431] 2.565837e-01 2.562533e-01 2.544652e-01 2.524027e-01 2.521701e-01
#> [436] 2.508377e-01 2.504753e-01 2.487148e-01 2.476842e-01 2.467597e-01
#> [441] 2.456598e-01 2.448734e-01 2.434520e-01 2.425910e-01 2.412996e-01
#> [446] 2.391077e-01 2.370666e-01 2.353612e-01 2.344336e-01 2.336907e-01
#> [451] 2.314153e-01 2.303490e-01 2.295914e-01 2.288472e-01 2.269513e-01
#> [456] 2.249915e-01 2.245771e-01 2.239882e-01 2.222578e-01 2.211533e-01
#> [461] 2.181852e-01 2.177548e-01 2.168754e-01 2.142710e-01 2.135207e-01
#> [466] 2.109614e-01 2.101698e-01 2.098699e-01 2.083076e-01 2.073489e-01
#> [471] 2.053383e-01 2.032876e-01 1.991847e-01 1.988649e-01 1.963824e-01
#> [476] 1.927598e-01 1.916131e-01 1.903535e-01 1.838843e-01 1.829154e-01
#> [481] 1.813119e-01 1.770114e-01 1.690306e-01 1.657955e-01 1.610450e-01
#> [486] 1.582204e-01 1.515032e-01 1.464400e-01 7.595550e-02 1.445517e-13
#>
#> Rotation (n x k) = (5078 x 50):
#> PC1 PC2 PC3 PC4
#> dyscalculia 8.123147e-03 3.434641e-02 -6.835307e-03 3.620127e-03
#> and 2.905097e-01 -2.284773e-01 -4.524599e-01 4.172579e-01
#> the 7.122090e-01 3.043340e-01 5.670838e-02 -2.755185e-01
#> minicalculator -2.239215e-04 1.429879e-03 -3.287941e-05 2.201319e-04
#> alp -3.358822e-04 2.144819e-03 -4.931911e-05 3.301978e-04
#> program 1.528774e-02 6.624131e-03 5.140127e-02 5.987647e-03
#> arithmetic 1.091652e-03 2.249825e-02 1.421009e-02 1.114105e-02
#> remedial 2.711589e-03 5.546973e-03 1.345337e-03 9.555914e-03
#> teaching 1.378220e-02 -4.057525e-02 -9.719544e-03 -4.299748e-02
#> education 2.133513e-02 -6.931558e-03 -4.982163e-02 7.968249e-02
#> of 4.076348e-01 1.983537e-01 1.636642e-01 -1.371270e-03
#> learning 8.492141e-02 -1.248120e-01 3.402872e-01 4.776740e-01
#> disabled 1.397898e-02 3.751074e-02 6.243532e-02 8.980377e-02
#> children 2.709883e-02 1.077521e-01 -4.778265e-02 5.579009e-02
#> calculators 2.835459e-03 -9.162430e-04 -4.126678e-04 -2.456518e-02
#> study 7.591571e-02 -2.891050e-02 2.862671e-02 -6.110595e-02
#> fractions -2.413915e-03 -1.518366e-02 1.198417e-02 -4.459038e-02
#> difficulties 1.085118e-02 1.534086e-03 5.928954e-03 1.926284e-02
#> calculating 6.742862e-04 -1.018058e-03 -1.380931e-03 -3.825576e-03
#> machines -4.730908e-04 1.381725e-03 -4.351358e-04 -1.069368e-03
#> PC5 PC6 PC7 PC8
#> dyscalculia -8.518113e-03 4.408165e-02 -7.608020e-03 -2.983714e-02
#> and 3.110757e-01 -1.131147e-01 7.146172e-03 3.147001e-01
#> the -8.094097e-02 -5.171942e-02 -3.346250e-01 8.109772e-03
#> minicalculator -5.356746e-04 6.249111e-04 -7.147454e-04 5.728822e-04
#> alp -8.035119e-04 9.373667e-04 -1.072118e-03 8.593234e-04
#> program 3.363432e-02 -4.878602e-02 -1.291003e-02 1.827118e-02
#> arithmetic 8.392728e-03 1.342849e-02 -1.035012e-02 -2.476098e-03
#> remedial -2.670302e-03 1.106635e-02 -1.876078e-02 -4.466639e-03
#> teaching -3.421908e-03 1.972610e-02 2.871404e-02 -6.272162e-02
#> education -8.788030e-02 -1.784698e-01 5.412252e-02 1.046784e-01
#> of -7.490927e-02 1.769726e-01 6.691608e-01 1.858406e-01
#> learning -2.315376e-01 4.949256e-01 -2.456717e-01 4.130822e-02
#> disabled 2.879765e-02 1.494249e-03 5.035938e-03 -2.309148e-03
#> children 4.763912e-02 1.777143e-01 9.782393e-03 -3.981977e-02
#> calculators -1.518972e-02 -1.993583e-02 -1.224997e-02 9.213222e-02
#> study -6.664685e-03 -2.907486e-02 -3.113131e-02 1.697815e-02
#> fractions -1.009165e-02 1.047044e-02 -1.188085e-02 4.672325e-03
#> difficulties -5.088867e-03 4.329691e-02 -2.014528e-02 -1.118554e-03
#> calculating -2.702786e-04 3.294396e-03 4.186318e-04 1.509402e-04
#> machines -3.708257e-04 2.502409e-04 -1.091851e-04 -7.019649e-04
#> PC9 PC10 PC11 PC12
#> dyscalculia -4.837983e-03 -2.108456e-02 2.104386e-02 -1.188665e-03
#> and -1.250335e-01 -8.104706e-02 -1.649360e-01 -2.303596e-01
#> the 1.220980e-01 1.621602e-02 -2.318886e-01 6.943118e-02
#> minicalculator -5.347167e-04 6.643611e-04 -2.288239e-04 2.177146e-05
#> alp -8.020751e-04 9.965417e-04 -3.432358e-04 3.265719e-05
#> program -2.759031e-02 -5.098015e-03 1.498852e-02 3.709115e-02
#> arithmetic -5.444593e-03 -3.267206e-02 3.639029e-03 -1.696330e-02
#> remedial -8.561362e-04 9.510310e-03 8.590700e-03 -2.414216e-02
#> teaching 2.716930e-02 6.508162e-02 -6.924634e-02 1.515410e-02
#> education 1.958923e-01 3.493998e-02 9.877309e-02 8.557598e-02
#> of -8.270446e-02 1.122305e-04 2.419738e-01 -8.357516e-03
#> learning -1.906675e-01 1.730333e-01 -4.515785e-02 8.578301e-03
#> disabled -7.688765e-02 6.399587e-02 3.561697e-02 -8.026518e-02
#> children 7.614519e-03 -1.464911e-01 6.683102e-03 3.308939e-02
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#> machines -1.286009e-03 1.507248e-03 7.511682e-04 2.609605e-04
#> PC13 PC14 PC15 PC16
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#> teaching 1.914065e-02 8.526546e-02 3.275603e-02 -1.129348e-01
#> education 2.306432e-01 1.984019e-01 4.179943e-02 -1.949843e-01
#> of -3.338884e-02 4.808436e-02 -1.333015e-01 1.927593e-02
#> learning 5.187865e-02 8.074989e-02 3.501997e-02 4.556663e-04
#> disabled 3.341848e-02 -2.118448e-02 -1.636755e-02 -1.882455e-02
#> children -3.477076e-02 -1.418761e-01 5.323297e-02 -1.617039e-02
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#> study 4.944313e-02 -3.285463e-03 1.189003e-01 5.427435e-02
#> fractions 5.288890e-04 4.770201e-02 -4.376492e-02 -1.510499e-02
#> difficulties 1.746618e-02 -7.878430e-03 1.021097e-03 3.223167e-02
#> calculating 3.292511e-03 -2.385856e-05 -2.630934e-03 4.559355e-04
#> machines 1.640596e-04 3.590792e-04 1.306054e-03 -2.728334e-04
#> PC17 PC18 PC19 PC20
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#> and -4.469531e-02 -1.461372e-01 1.089681e-01 -2.014383e-02
#> the -3.771500e-02 -9.507035e-02 2.171183e-02 -2.441729e-02
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#> alp 2.873033e-05 -3.949328e-04 1.029711e-03 -1.424099e-03
#> program 2.455291e-02 -3.858448e-03 7.008953e-02 1.976113e-02
#> arithmetic -1.753400e-02 2.450651e-03 1.106956e-02 5.073607e-03
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#> teaching 3.839099e-02 -4.015231e-02 2.829345e-04 4.271296e-02
#> education 3.417267e-01 -4.505579e-02 -7.543353e-02 -1.367413e-01
#> of -5.445737e-02 -1.258619e-02 -7.693603e-02 1.532477e-03
#> learning -8.362836e-02 5.721263e-04 1.007821e-02 -6.009479e-02
#> disabled 2.489228e-02 3.157515e-02 -7.251739e-02 1.735845e-02
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#> study -1.170001e-01 1.050327e-01 -2.145850e-02 6.427163e-02
#> fractions -2.121362e-02 2.105349e-02 -3.718585e-03 4.748787e-03
#> difficulties 6.568750e-03 -6.387987e-03 3.255505e-02 1.613134e-02
#> calculating 3.831660e-03 5.083883e-03 7.044829e-04 5.958202e-03
#> machines 1.688546e-04 -5.112019e-04 4.629020e-04 -3.576136e-04
#> PC21 PC22 PC23 PC24
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#> and 9.762065e-03 -5.885825e-02 8.889584e-02 4.245743e-02
#> the 1.051495e-01 -3.225326e-02 1.349422e-02 1.802594e-02
#> minicalculator 1.964195e-03 -2.131994e-03 1.385813e-04 -6.275872e-04
#> alp 2.946292e-03 -3.197991e-03 2.078720e-04 -9.413807e-04
#> program 1.466349e-03 4.395769e-02 -1.792981e-02 1.326020e-02
#> arithmetic 1.354666e-02 -3.006584e-02 -1.384899e-02 -1.425622e-03
#> remedial -6.181883e-03 9.734426e-03 4.613731e-04 -9.870318e-03
#> teaching 1.106818e-01 9.879710e-03 1.145676e-01 -3.953182e-02
#> education 1.125334e-01 -9.041635e-02 -1.992107e-01 -2.334926e-01
#> of -6.008702e-02 -3.387715e-02 5.911923e-02 -2.014078e-02
#> learning 1.514439e-01 3.708448e-02 2.820422e-02 4.583256e-03
#> disabled 2.680198e-02 -9.652857e-02 -6.894827e-02 5.467862e-02
#> children -6.060316e-02 8.860028e-04 -1.377904e-01 -1.371355e-01
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#> study -3.148589e-02 1.225439e-02 -1.749135e-02 -4.087033e-02
#> fractions -3.034144e-02 -1.403727e-02 -2.943323e-02 7.151391e-03
#> difficulties 1.064511e-02 -2.355987e-02 3.855599e-04 -1.162741e-02
#> calculating 1.998379e-03 -4.223168e-03 2.760354e-03 7.136614e-04
#> machines 2.889324e-03 -4.431027e-04 8.884553e-04 9.560954e-04
#> PC25 PC26 PC27 PC28
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#> and 2.264262e-02 -6.491807e-03 -4.665831e-02 1.436098e-02
#> the 1.754495e-02 3.566124e-02 -3.225968e-02 -8.626582e-02
#> minicalculator 6.994210e-04 -3.672483e-03 2.700182e-03 -9.632841e-05
#> alp 1.049131e-03 -5.508725e-03 4.050273e-03 -1.444926e-04
#> program -4.248708e-02 -2.590701e-02 9.481961e-02 -1.242109e-02
#> arithmetic -1.342879e-03 -1.090353e-02 1.354411e-02 2.450398e-02
#> remedial -2.970011e-03 -1.719701e-02 1.348936e-02 -4.587094e-03
#> teaching -1.610652e-02 -1.900453e-01 -4.925427e-02 -5.876595e-03
#> education 2.660188e-02 -1.225322e-01 1.706633e-01 3.706435e-02
#> of 2.887823e-02 -4.765480e-02 -1.505439e-02 9.042786e-02
#> learning 1.556928e-02 -2.219364e-02 9.285950e-02 -5.790268e-02
#> disabled 1.292210e-03 -1.321961e-01 1.580807e-01 -1.326944e-02
#> children -1.965238e-02 -2.351348e-01 7.413817e-02 -1.153756e-01
#> calculators 5.129810e-02 -7.441841e-02 -2.136648e-02 4.202146e-02
#> study -3.780592e-02 6.062124e-02 -3.819670e-02 1.101956e-01
#> fractions 2.338171e-02 -3.741841e-02 6.102104e-02 6.679489e-03
#> difficulties 3.626243e-02 8.699180e-03 -7.992898e-03 1.885493e-02
#> calculating 2.057408e-03 -8.393343e-03 3.741881e-03 -6.913376e-04
#> machines -3.844806e-04 -3.562887e-03 3.248926e-05 -9.021156e-05
#> PC29 PC30 PC31 PC32
#> dyscalculia 3.876940e-02 8.991376e-02 -6.084627e-02 -4.881428e-02
#> and 1.765885e-02 4.770524e-02 -1.430400e-02 1.781868e-02
#> the 2.916074e-02 -1.600442e-02 1.804129e-02 -6.060371e-03
#> minicalculator -4.513115e-04 3.718926e-04 -1.151210e-03 5.682321e-04
#> alp -6.769673e-04 5.578390e-04 -1.726815e-03 8.523481e-04
#> program 5.429623e-02 3.733585e-03 -9.251954e-02 -1.698877e-02
#> arithmetic 1.998367e-02 4.368260e-03 -3.437296e-02 -1.573146e-02
#> remedial -3.182553e-02 3.329856e-03 8.904330e-03 1.077680e-02
#> teaching -8.150132e-02 -1.782497e-03 -8.633512e-02 4.084443e-02
#> education -8.918831e-02 7.473691e-02 7.363914e-02 -7.123758e-02
#> of 2.340172e-02 -3.054121e-02 3.643771e-02 2.315676e-02
#> learning -3.815753e-02 4.607673e-02 6.928419e-02 -2.725882e-02
#> disabled -1.073352e-02 -1.166162e-01 -2.517423e-02 5.477412e-02
#> children 1.627625e-01 2.610756e-01 -1.582968e-01 1.472748e-01
#> calculators -6.766339e-02 -2.638574e-02 -7.170234e-02 -2.696272e-02
#> study -8.809997e-02 2.652458e-01 -5.404184e-02 -6.899376e-02
#> fractions 7.467116e-02 1.564342e-02 4.141357e-02 3.455449e-02
#> difficulties 4.404004e-02 -5.826459e-03 4.425248e-02 -2.355428e-02
#> calculating 3.470654e-03 -2.277920e-03 -7.080649e-04 -1.432040e-03
#> machines -1.932715e-04 2.121893e-04 -6.271173e-04 -1.120441e-03
#> PC33 PC34 PC35 PC36
#> dyscalculia 6.917357e-05 1.088019e-02 2.167753e-02 -9.013227e-03
#> and 4.557066e-02 4.394395e-02 1.085596e-02 -2.616519e-02
#> the -8.889952e-03 6.368883e-02 -1.075720e-03 -3.113897e-02
#> minicalculator 1.953093e-03 -1.439249e-03 2.939587e-03 5.228419e-04
#> alp 2.929640e-03 -2.158873e-03 4.409381e-03 7.842628e-04
#> program 2.248513e-02 -6.597485e-02 5.064436e-02 -4.924967e-02
#> arithmetic 7.186258e-03 -1.162513e-02 2.551094e-02 1.304531e-02
#> remedial -4.407871e-03 -4.985186e-03 8.784128e-03 -5.724439e-02
#> teaching 4.404603e-02 -1.480893e-01 3.574952e-02 -6.965043e-02
#> education 3.845249e-03 7.015258e-02 -7.409695e-02 -8.734420e-02
#> of 1.128782e-01 -4.856143e-02 1.475448e-02 2.711591e-02
#> learning 2.270686e-02 -6.658835e-03 -1.103335e-01 1.966102e-02
#> disabled 1.794709e-02 4.816807e-02 1.389492e-01 -2.486398e-02
#> children -4.269806e-02 2.007106e-01 8.502947e-02 5.040574e-02
#> calculators -3.449522e-03 -1.056994e-01 -1.584794e-01 2.998063e-02
#> study -1.825014e-02 -9.177706e-02 -1.817223e-02 -3.706466e-04
#> fractions 1.063812e-01 -9.994530e-03 4.644219e-02 1.215488e-02
#> difficulties 4.311647e-03 -2.069499e-02 -1.352601e-02 4.275012e-03
#> calculating -2.003844e-03 -8.214514e-03 -1.804376e-03 9.207620e-03
#> machines 1.155232e-03 -1.669658e-03 3.389054e-03 -2.312018e-03
#> PC37 PC38 PC39 PC40
#> dyscalculia 2.072533e-02 -1.478771e-02 5.165900e-02 3.092463e-02
#> and -3.843449e-02 4.951828e-02 -7.815735e-04 -8.379532e-03
#> the 4.197343e-02 -9.780191e-03 -4.320020e-02 1.609748e-02
#> minicalculator 7.087540e-04 -1.270506e-03 -1.779441e-03 1.155198e-03
#> alp 1.063131e-03 -1.905760e-03 -2.669161e-03 1.732797e-03
#> program -2.160723e-01 -4.171992e-03 -1.175228e-01 -4.999756e-03
#> arithmetic -1.470519e-02 3.617566e-02 -1.819352e-03 2.623219e-02
#> remedial 3.453787e-03 -9.109581e-03 5.924766e-03 2.422498e-02
#> teaching 1.916710e-01 -3.461853e-02 -3.751357e-02 -1.057391e-01
#> education -4.932844e-03 -1.179589e-01 -3.637489e-02 1.206003e-01
#> of -1.663555e-02 6.368757e-03 4.613894e-02 -3.383032e-02
#> learning 8.384851e-02 -4.680325e-02 1.552686e-03 -2.643213e-03
#> disabled 3.122459e-02 8.149829e-03 -8.303884e-02 1.064934e-02
#> children 1.792486e-02 7.807851e-02 5.104469e-02 1.334061e-01
#> calculators 1.752997e-01 2.905935e-02 -8.405635e-02 9.774000e-03
#> study -1.188684e-01 -5.980633e-02 -9.847510e-03 1.431246e-01
#> fractions 1.516880e-03 6.093703e-03 6.485088e-02 -1.060338e-02
#> difficulties -3.067892e-02 3.606136e-02 4.907558e-02 -2.468498e-02
#> calculating 1.912300e-03 2.600555e-03 3.393575e-03 2.872732e-03
#> machines 5.602079e-04 -1.793639e-03 1.860155e-03 -2.611135e-05
#> PC41 PC42 PC43 PC44
#> dyscalculia 1.434474e-03 5.511421e-02 5.045758e-02 7.026059e-03
#> and 1.219027e-02 -1.401024e-02 1.795848e-02 4.428903e-04
#> the -1.274755e-02 -6.780770e-03 -2.008298e-02 -3.465750e-02
#> minicalculator -1.031167e-03 3.235821e-04 -1.955904e-04 7.366261e-04
#> alp -1.546751e-03 4.853731e-04 -2.933856e-04 1.104939e-03
#> program -1.042695e-01 -8.483477e-02 4.282731e-02 -3.921612e-02
#> arithmetic -3.201327e-03 1.075744e-02 3.234436e-02 4.282705e-02
#> remedial 3.166802e-02 -3.165853e-02 4.414795e-03 9.144869e-03
#> teaching -2.736895e-02 -6.757958e-02 8.776898e-02 -1.564869e-02
#> education 7.698236e-02 5.582855e-02 2.863792e-02 5.686179e-02
#> of 2.479063e-03 -1.771518e-03 -2.695033e-02 -1.605157e-02
#> learning -2.313934e-02 1.661877e-02 9.997889e-03 -3.138442e-02
#> disabled -6.470584e-02 5.088572e-02 -4.637900e-02 1.134836e-01
#> children 4.006443e-02 -1.363323e-01 5.951508e-03 -1.273274e-02
#> calculators 1.071678e-01 1.900387e-02 -9.562367e-03 -3.895455e-02
#> study 2.615429e-02 1.338279e-02 1.126025e-01 7.132126e-02
#> fractions 7.544432e-03 -7.593500e-02 8.749519e-03 -3.720069e-02
#> difficulties -4.988628e-02 1.459940e-02 -1.125060e-02 -2.182360e-02
#> calculating 1.775891e-03 -3.588367e-03 1.061837e-02 -2.297128e-04
#> machines 8.773709e-04 -1.525039e-05 -1.313746e-03 9.602678e-04
#> PC45 PC46 PC47 PC48
#> dyscalculia 9.651257e-03 8.267636e-03 -4.714261e-03 -6.824314e-02
#> and 2.289899e-02 2.333510e-03 -1.569669e-02 -1.780171e-02
#> the -1.476324e-02 -1.783537e-02 6.728918e-02 -3.659008e-03
#> minicalculator -9.582784e-04 2.569676e-04 -8.829212e-04 3.095984e-04
#> alp -1.437418e-03 3.854514e-04 -1.324382e-03 4.643976e-04
#> program -2.834847e-02 -1.236971e-03 8.053667e-02 7.336115e-02
#> arithmetic 7.209315e-03 7.659909e-04 7.070788e-04 6.267110e-04
#> remedial 1.035013e-02 2.151504e-02 2.543584e-02 -2.041754e-02
#> teaching 3.806135e-02 1.652133e-01 -6.843776e-02 -1.114837e-01
#> education -3.058875e-02 1.211075e-02 -1.691230e-01 8.225861e-02
#> of 6.855860e-02 1.118669e-03 -3.150436e-02 2.701362e-02
#> learning -3.005010e-02 1.497885e-03 -2.069965e-02 -2.968480e-02
#> disabled -9.114227e-02 -2.108441e-02 3.662867e-02 2.875538e-02
#> children -5.115683e-02 7.333215e-02 -8.029091e-03 1.415032e-01
#> calculators -8.402337e-02 -5.768600e-02 3.966611e-03 7.299160e-02
#> study -5.120298e-02 -8.810153e-02 -1.132366e-01 -6.718208e-02
#> fractions -1.873662e-02 -1.971577e-03 -5.088310e-02 -1.632300e-03
#> difficulties 1.473028e-02 -8.623288e-02 -5.855094e-03 -1.109068e-02
#> calculating 1.024007e-02 -5.995016e-04 8.282165e-03 -1.180926e-03
#> machines 2.830849e-03 4.862742e-04 1.217511e-03 5.168474e-04
#> PC49 PC50
#> dyscalculia 3.283503e-02 -2.212451e-02
#> and -1.002673e-02 -7.135179e-03
#> the -3.201748e-03 -3.201859e-03
#> minicalculator -1.460967e-05 2.488856e-03
#> alp -2.191450e-05 3.733285e-03
#> program 4.001096e-02 -2.070542e-02
#> arithmetic 3.329551e-02 2.573216e-02
#> remedial 3.951300e-02 2.110226e-02
#> teaching -7.700996e-02 8.309827e-03
#> education -1.000201e-02 3.970083e-02
#> of 1.279641e-02 -1.462333e-02
#> learning -1.100013e-03 1.229654e-02
#> disabled -2.287913e-02 3.165276e-02
#> children 6.553890e-02 1.094896e-01
#> calculators 9.214095e-03 -1.041434e-01
#> study -8.360534e-02 1.030065e-01
#> fractions -3.705606e-02 3.335453e-02
#> difficulties -4.741557e-02 -2.976131e-02
#> calculating 1.533855e-03 -4.026449e-03
#> machines -2.156709e-03 2.338337e-03
#> [ reached 'max' / getOption("max.print") -- omitted 5058 rows ]
#>
#> $variance_explained
#> PC1 PC2
#> 0.19119 0.03961
#>
#> $execution_time
#> [1] 6.871363
#>
#> $timestamp
#> [1] "2026-08-14 23:36:42 CDT"
#>
#> $seed
#> [1] 123
#>
#> Starting dimensionality reduction with method: t-SNE
#> Performing PCA preprocessing...
#> Performing t-SNE on PCA results...
#> Read the 490 x 50 data matrix successfully!
#> OpenMP is working. 1 threads.
#> Using no_dims = 2, perplexity = 30.000000, and theta = 0.500000
#> Computing input similarities...
#> Building tree...
#> Done in 0.16 seconds (sparsity = 0.291870)!
#> Learning embedding...
#> Iteration 50: error is 59.599396 (50 iterations in 0.15 seconds)
#> Iteration 100: error is 58.937017 (50 iterations in 0.09 seconds)
#> Iteration 150: error is 59.082314 (50 iterations in 0.09 seconds)
#> Iteration 200: error is 59.081629 (50 iterations in 0.10 seconds)
#> Iteration 250: error is 58.935814 (50 iterations in 0.13 seconds)
#> Iteration 300: error is 1.413887 (50 iterations in 0.07 seconds)
#> Iteration 350: error is 1.331563 (50 iterations in 0.06 seconds)
#> Iteration 400: error is 1.295152 (50 iterations in 0.06 seconds)
#> Iteration 450: error is 1.275665 (50 iterations in 0.05 seconds)
#> Iteration 500: error is 1.258463 (50 iterations in 0.06 seconds)
#> Iteration 550: error is 1.250196 (50 iterations in 0.06 seconds)
#> Iteration 600: error is 1.245667 (50 iterations in 0.05 seconds)
#> Iteration 650: error is 1.242338 (50 iterations in 0.08 seconds)
#> Iteration 700: error is 1.238193 (50 iterations in 0.05 seconds)
#> Iteration 750: error is 1.236570 (50 iterations in 0.04 seconds)
#> Iteration 800: error is 1.235949 (50 iterations in 0.06 seconds)
#> Iteration 850: error is 1.233953 (50 iterations in 0.06 seconds)
#> Iteration 900: error is 1.229892 (50 iterations in 0.05 seconds)
#> Iteration 950: error is 1.228711 (50 iterations in 0.05 seconds)
#> Iteration 1000: error is 1.228196 (50 iterations in 0.05 seconds)
#> Fitting performed in 1.41 seconds.
#> Dimensionality reduction completed in 8.28 seconds
#> $reduced_data
#> [,1] [,2]
#> [1,] 2.96694501 1.59578021
#> [2,] 9.99236823 5.34374728
#> [3,] 10.72473762 2.28386850
#> [4,] 8.40238554 2.61763558
#> [5,] 2.81235667 2.87178149
#> [6,] -2.07560698 -12.85952140
#> [7,] 6.34058626 3.78809082
#> [8,] -3.89198829 -12.27857227
#> [9,] 8.45355429 8.04444515
#> [10,] 10.04630735 3.18971897
#> [11,] -7.99148115 -10.02198963
#> [12,] 3.05614265 1.04175227
#> [13,] 10.66363596 3.48569678
#> [14,] -3.72267663 -13.09727010
#> [15,] -3.78879978 -12.69083328
#> [16,] 3.64532292 6.43477024
#> [17,] 8.78867181 1.27065957
#> [18,] 10.06005770 4.17098917
#> [19,] 9.39889094 8.64454734
#> [20,] 10.19198663 6.72451602
#> [21,] -1.07856661 3.24562587
#> [22,] 8.70497941 2.77703397
#> [23,] 3.10161556 2.37004686
#> [24,] 8.06232052 7.71494360
#> [25,] 7.54105043 1.13435900
#> [26,] -3.93625731 -13.99761228
#> [27,] 8.57306818 6.35282422
#> [28,] 8.32477515 7.39832202
#> [29,] 10.83579742 2.77358540
#> [30,] -0.77886920 -7.47485253
#> [31,] 7.00702923 -1.14069080
#> [32,] 3.87541502 6.42900728
#> [33,] -2.29442981 -12.84450859
#> [34,] 9.80087858 5.69849924
#> [35,] 9.20224845 2.11898232
#> [36,] 8.69508722 1.58984025
#> [37,] 8.36846320 2.64396984
#> [38,] 9.91852255 4.80243342
#> [39,] 9.80993736 6.87796135
#> [40,] 9.69039559 7.96577343
#> [41,] 10.09810807 1.67471750
#> [42,] -7.71740667 -11.68708511
#> [43,] 6.16013590 6.81699345
#> [44,] 0.34754988 -13.90441902
#> [45,] 9.02325798 2.43356379
#> [46,] 3.16340490 0.14608462
#> [47,] 9.85468405 1.40459888
#> [48,] -0.13351326 -8.29415537
#> [49,] -0.53326743 -8.27204516
#> [50,] -5.31549468 3.45720946
#> [51,] 7.79567494 7.65438970
#> [52,] 6.18541152 8.77067302
#> [53,] -8.69734475 -10.12444506
#> [54,] 8.44119941 5.68290879
#> [55,] 1.44255542 0.66710228
#> [56,] 7.52241023 3.88675310
#> [57,] -7.87432692 -8.45224836
#> [58,] 6.64439956 -0.95757709
#> [59,] 12.77073539 1.52379987
#> [60,] 7.76022219 1.33787892
#> [61,] 6.26413711 4.14485451
#> [62,] 9.60537348 2.84490067
#> [63,] 4.49306672 11.19434433
#> [64,] 4.31883913 11.09245229
#> [65,] 4.47764901 11.32503220
#> [66,] -8.56022990 -10.12294123
#> [67,] 10.69223350 1.58842370
#> [68,] 0.87056065 1.23947602
#> [69,] 10.50642830 3.28672853
#> [70,] 7.04559372 4.46169314
#> [71,] 5.20972812 -1.80331724
#> [72,] 8.26823828 2.02386632
#> [73,] 5.33515924 4.61189138
#> [74,] -2.82568273 0.31104501
#> [75,] -3.16092113 0.96312422
#> [76,] 6.58619815 0.33342770
#> [77,] 1.49222021 2.45647792
#> [78,] 9.17380752 5.73337522
#> [79,] 0.58012875 -1.33807685
#> [80,] 11.19384664 1.90169987
#> [81,] 9.84067405 0.28359226
#> [82,] 8.33420851 2.77996739
#> [83,] 6.35291134 3.06783067
#> [84,] -3.92053177 -0.72770156
#> [85,] -0.84921490 -4.92245687
#> [86,] 7.18051440 3.23353163
#> [87,] 6.86605749 2.49013711
#> [88,] 4.68220326 -0.71574260
#> [89,] 4.90419455 11.28312720
#> [90,] -10.65410123 2.88287888
#> [91,] 13.34805670 2.63686469
#> [92,] 2.61768066 1.70135353
#> [93,] 12.44431127 5.16005209
#> [94,] -4.08811220 1.76195435
#> [95,] 6.38725709 2.50347674
#> [96,] 7.64486688 4.21981289
#> [97,] 8.41841606 1.48618138
#> [98,] 5.84102003 5.22993943
#> [99,] 8.48698603 0.64511432
#> [100,] 6.07051972 2.02301870
#> [101,] 4.57176965 2.00907298
#> [102,] -3.96914786 -13.64545248
#> [103,] 6.97080567 2.87610316
#> [104,] -9.06404918 0.82875240
#> [105,] 7.57959485 10.95414329
#> [106,] -1.49006703 0.61722007
#> [107,] 5.41886274 6.85921655
#> [108,] 5.15360831 2.39471495
#> [109,] 7.77585354 2.95790968
#> [110,] 10.10553413 2.80113842
#> [111,] 7.11945745 1.57631097
#> [112,] 6.84461125 4.64653631
#> [113,] -0.33495855 2.03500834
#> [114,] 9.12253061 3.90144635
#> [115,] 8.31027890 2.86403536
#> [116,] -5.14294756 -7.27176761
#> [117,] 0.93540517 -1.00066418
#> [118,] -9.37678730 0.81876967
#> [119,] -2.93904661 -11.72462497
#> [120,] -2.36435258 2.27908933
#> [121,] 6.53996150 7.15502027
#> [122,] 7.85684955 3.60745282
#> [123,] 4.71758325 9.18670351
#> [124,] 7.47054790 2.81292751
#> [125,] -0.78055077 11.47588077
#> [126,] -1.95078367 -0.41130918
#> [127,] 3.89444268 -0.17448432
#> [128,] -0.26445668 -0.51505063
#> [129,] -5.17091139 0.79506299
#> [130,] 7.42512126 3.56301760
#> [131,] 2.10745953 -8.45447605
#> [132,] 2.06042983 -8.43672226
#> [133,] -4.26608005 -8.02670930
#> [134,] -8.92404556 -0.42986399
#> [135,] -8.10809220 -1.20677695
#> [136,] 3.54695974 -0.45373626
#> [137,] -3.07879275 -1.21835884
#> [138,] 0.20766446 -0.07426898
#> [139,] -4.18647231 -11.46497186
#> [140,] -4.59362171 -12.83483986
#> [141,] -6.11314416 2.33956034
#> [142,] -3.19986818 0.87806629
#> [143,] 3.69266134 1.26693107
#> [144,] -8.05550088 -11.57517906
#> [145,] -6.94101397 -9.06676803
#> [146,] 6.43064861 1.32126612
#> [147,] 7.55648262 2.04111285
#> [148,] -5.43040697 -9.32513441
#> [149,] 4.06062405 5.32352999
#> [150,] -6.20980956 2.48229003
#> [151,] -2.18085413 -1.74443581
#> [152,] -4.79143884 1.54743062
#> [153,] -4.60683246 6.10959190
#> [154,] 3.16076774 -3.99919561
#> [155,] 0.74607110 6.08020521
#> [156,] 1.99467050 -2.56839919
#> [157,] 0.43794542 -14.11771963
#> [158,] -2.93989643 -13.50283638
#> [159,] -7.27288600 -8.89839415
#> [160,] 1.42224912 2.92138989
#> [161,] -4.67317206 -2.11455568
#> [162,] -1.00027410 -1.79984252
#> [163,] -3.15599606 -1.38447923
#> [164,] -9.33402582 -0.48308745
#> [165,] -5.97041792 1.75374927
#> [166,] -6.61028273 2.39151260
#> [167,] 6.48000470 1.09392517
#> [168,] -0.95764387 -12.96527134
#> [169,] 5.22138412 -13.38861985
#> [170,] -1.81397034 -11.36201140
#> [171,] -1.18954912 4.27795345
#> [172,] 4.20937913 8.98399307
#> [173,] -5.86075253 -1.98405980
#> [174,] -2.65129886 -10.22985612
#> [175,] -4.32401105 3.28530139
#> [176,] 6.75828930 2.35984195
#> [177,] -1.47843323 -10.60343681
#> [178,] -2.06506700 1.62086675
#> [179,] -7.32021826 -8.71174085
#> [180,] -6.38999488 -1.93700586
#> [181,] 2.99193796 -0.18419918
#> [182,] -12.08357387 -6.69208599
#> [183,] 9.04991397 3.40506729
#> [184,] -1.23352156 2.60742843
#> [185,] 3.46121763 -3.36642182
#> [186,] 4.88832886 3.31793577
#> [187,] 2.33217157 -8.64555369
#> [188,] -8.52192679 -11.91811412
#> [189,] 4.39624846 -6.52028359
#> [190,] -0.50974103 4.20893426
#> [191,] 2.44057173 -12.38595516
#> [192,] 1.73426624 -10.55996879
#> [193,] 5.00209763 -0.28919595
#> [194,] -3.28732595 -3.29632276
#> [195,] -5.48420298 2.08213818
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#> [197,] 2.57677858 0.04217430
#> [198,] -2.33491127 -1.67274753
#> [199,] -2.30624059 -2.50726342
#> [200,] -4.77433183 -8.97945512
#> [201,] 2.09554783 -9.65698633
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#> [203,] -0.99826354 1.43780382
#> [204,] 3.37563046 -14.50720461
#> [205,] -6.90658011 -1.06386823
#> [206,] 7.34719739 10.91791857
#> [207,] 5.48721718 3.66532704
#> [208,] -1.20778145 -8.92356215
#> [209,] -6.16134776 1.96454423
#> [210,] -2.73275027 -4.48418140
#> [211,] -3.21327018 -2.89889010
#> [212,] 0.57413231 8.14015896
#> [213,] -0.07068723 6.71044024
#> [214,] -7.75878257 -2.88628440
#> [215,] 1.82700595 4.58962738
#> [216,] -1.53828575 4.40278113
#> [217,] -1.65340655 -5.81607246
#> [218,] -3.53053224 -1.56091146
#> [219,] 3.05328854 7.61113102
#> [220,] 1.43361367 -4.90205535
#> [221,] -0.54545092 2.50952403
#> [222,] 2.30113650 2.51777566
#> [223,] -6.16146227 12.82930243
#> [224,] -1.03289712 5.94257670
#> [225,] 4.63851580 4.46269919
#> [226,] -2.44473360 -9.52764753
#> [227,] -12.10069812 -6.65633303
#> [228,] -2.17628811 -0.55684099
#> [229,] -2.36494009 -14.87618158
#> [230,] -3.99164727 4.08473375
#> [231,] -3.58641997 1.94440118
#> [232,] 4.00897328 3.51587011
#> [233,] -2.64877483 -4.61042544
#> [234,] -10.57644017 6.79945959
#> [235,] -6.35161278 -6.83199868
#> [236,] 0.93315973 -8.13914365
#> [237,] 2.81725569 4.70543428
#> [238,] -3.08624831 -3.70169046
#> [239,] -2.78553068 -9.22388022
#> [240,] -1.87853973 -13.97917611
#> [241,] 5.02452962 -5.54623670
#> [242,] 5.03249006 -5.10871985
#> [243,] 1.60714080 -0.36615882
#> [244,] -0.72941622 -12.95165037
#> [245,] 5.03607263 -4.34735141
#> [246,] -2.76959771 4.21909516
#> [247,] -4.95975607 -4.07147502
#> [248,] -0.51620257 -13.06318936
#> [249,] 11.05273769 -3.66914025
#> [250,] 1.52863618 -11.42121037
#> [251,] 1.27258635 0.56877288
#> [252,] 3.24810814 10.03549510
#> [253,] -0.09215736 -2.17776247
#> [254,] -1.02794378 11.27038636
#> [255,] -4.93688337 -7.84471933
#> [256,] -0.18063240 7.59497161
#> [257,] 6.15495768 8.87645832
#> [258,] -7.28552446 2.59216487
#> [259,] 3.82272311 -10.55484734
#> [260,] 4.19492520 -10.71328585
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#> [262,] -6.20571857 2.77669100
#> [263,] -7.20903318 6.68520799
#> [264,] 7.48514690 -3.42374999
#> [265,] -1.15022485 -11.96023709
#> [266,] 5.14402230 -9.55687574
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#> [269,] -3.24933088 -4.59964327
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#> [273,] -1.08803477 11.28850742
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#> [288,] 5.24963885 -4.28634772
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#> [326,] 5.29468152 -0.97468887
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#> [329,] -5.99739984 13.01823998
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#> [331,] 0.14609246 0.75101344
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#> [380,] -0.45130572 7.87162844
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#> [382,] 4.04359226 2.78154576
#> [383,] -7.51545564 -2.25288331
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#> [385,] -0.97894251 10.02565867
#> [386,] 6.21990439 -1.87261536
#> [387,] 0.81385543 -3.61608963
#> [388,] 5.53578512 0.32015832
#> [389,] 1.37519419 -1.60225300
#> [390,] 1.80318105 -2.42825913
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#> [392,] -4.69786789 -0.72728524
#> [393,] 2.16572365 -14.22818113
#> [394,] -5.09317801 -3.51904313
#> [395,] -9.63262716 -3.40504482
#> [396,] 10.36798325 -3.22642502
#> [397,] 9.45000470 -2.22812221
#> [398,] -7.03539572 11.67150290
#> [399,] -1.38068699 9.72218682
#> [400,] 0.32260873 -12.67447801
#> [401,] -1.40522451 -6.68395519
#> [402,] 0.06151217 4.08512482
#> [403,] 4.28544878 -11.66424341
#> [404,] 0.76048978 -5.94115369
#> [405,] -10.98177956 6.43564252
#> [406,] 2.00806470 -13.27249453
#> [407,] 0.22195969 5.52532690
#> [408,] -5.74538296 6.64783204
#> [409,] -4.45810269 -0.97642608
#> [410,] -5.54228216 8.21743720
#> [411,] -8.48779509 6.07964733
#> [412,] -8.99782320 6.34320472
#> [413,] -5.50514243 7.81671157
#> [414,] -5.98904134 6.38995527
#> [415,] -4.21669703 7.61557818
#> [416,] 8.11714276 -2.62380913
#> [417,] -0.22549713 6.78498929
#> [418,] -0.44579149 7.88526031
#> [419,] 6.37952526 3.10535077
#> [420,] -2.79760942 -7.36632461
#> [421,] -9.55030368 7.51568758
#> [422,] -5.79111192 -9.96380890
#> [423,] -1.94764060 7.03786954
#> [424,] -0.48929749 -9.59580477
#> [425,] -0.02524895 5.07564743
#> [426,] -1.80448645 -14.05811315
#> [427,] -5.74338539 5.62414627
#> [428,] 5.75459185 11.91206552
#> [429,] -6.98785929 -9.07706552
#> [430,] 0.33534904 -10.10209115
#> [431,] -2.80392367 9.61595474
#> [432,] -5.27340154 9.16334809
#> [433,] -3.46621021 5.48554344
#> [434,] 0.61927119 -11.00960311
#> [435,] -1.16663939 -14.96995649
#> [436,] -7.36246270 11.44506051
#> [437,] 4.94789617 -10.52855246
#> [438,] -2.34248367 -9.60075862
#> [439,] 0.28276015 -9.14913354
#> [440,] 1.79822535 1.46855299
#> [441,] 0.73162300 8.58609178
#> [442,] 7.52297375 11.11896299
#> [443,] -11.64204180 6.10003936
#> [444,] -4.49471273 10.95051327
#> [445,] 1.78328202 12.51576747
#> [446,] -7.41055724 6.75038583
#> [447,] -7.26779129 8.73918876
#> [448,] 3.33860434 -0.99575332
#> [449,] -4.29702084 3.88567383
#> [450,] -4.07462110 7.53595174
#> [451,] 5.24761396 1.18073491
#> [452,] -4.30084049 6.69784377
#> [453,] -4.61349639 6.95435089
#> [454,] -4.22127075 8.32080073
#> [455,] -8.79362939 -1.35960151
#> [456,] -12.10059680 5.79653230
#> [457,] -1.87891183 -7.96948582
#> [458,] -1.88103020 -8.65645556
#> [459,] -2.50954451 -5.21255865
#> [460,] 3.95888178 6.78306213
#> [461,] 3.54539902 -2.85134858
#> [462,] 1.45701991 4.61121318
#> [463,] -9.63915990 8.09589570
#> [464,] 3.60541937 6.45855121
#> [465,] 4.67997384 -2.52312824
#> [466,] 2.09511036 -9.16605366
#> [467,] 0.03188857 -0.71509035
#> [468,] -8.20693894 4.12795838
#> [469,] -7.32386409 8.70789124
#> [470,] -2.46648384 7.97057832
#> [471,] -4.43306196 0.35761601
#> [472,] -4.36796746 -9.96386509
#> [473,] -5.13020831 8.95928116
#> [474,] -7.96427062 7.07496217
#> [475,] 2.11158429 -6.44582248
#> [476,] 1.57580925 -4.58515505
#> [477,] 9.34215799 -0.91283439
#> [478,] -1.25911040 11.26030305
#> [479,] -7.17384356 11.78852706
#> [480,] -7.13907321 11.68726941
#> [481,] -8.64030246 8.38639959
#> [482,] -3.21348002 5.15328481
#> [483,] -6.76320242 6.49273645
#> [484,] -7.47372513 6.60111958
#> [485,] 2.30932841 -1.06254479
#> [486,] -5.28069213 -0.82650844
#> [487,] -3.74274793 -3.02532602
#> [488,] 0.46900604 -9.84874384
#> [489,] -0.83990021 9.79218213
#> [490,] 3.56407183 -2.79259632
#>
#> $method
#> [1] "t-SNE"
#>
#> $tsne_result
#> $N
#> [1] 490
#>
#> $Y
#> [,1] [,2]
#> [1,] 2.96694501 1.59578021
#> [2,] 9.99236823 5.34374728
#> [3,] 10.72473762 2.28386850
#> [4,] 8.40238554 2.61763558
#> [5,] 2.81235667 2.87178149
#> [6,] -2.07560698 -12.85952140
#> [7,] 6.34058626 3.78809082
#> [8,] -3.89198829 -12.27857227
#> [9,] 8.45355429 8.04444515
#> [10,] 10.04630735 3.18971897
#> [11,] -7.99148115 -10.02198963
#> [12,] 3.05614265 1.04175227
#> [13,] 10.66363596 3.48569678
#> [14,] -3.72267663 -13.09727010
#> [15,] -3.78879978 -12.69083328
#> [16,] 3.64532292 6.43477024
#> [17,] 8.78867181 1.27065957
#> [18,] 10.06005770 4.17098917
#> [19,] 9.39889094 8.64454734
#> [20,] 10.19198663 6.72451602
#> [21,] -1.07856661 3.24562587
#> [22,] 8.70497941 2.77703397
#> [23,] 3.10161556 2.37004686
#> [24,] 8.06232052 7.71494360
#> [25,] 7.54105043 1.13435900
#> [26,] -3.93625731 -13.99761228
#> [27,] 8.57306818 6.35282422
#> [28,] 8.32477515 7.39832202
#> [29,] 10.83579742 2.77358540
#> [30,] -0.77886920 -7.47485253
#> [31,] 7.00702923 -1.14069080
#> [32,] 3.87541502 6.42900728
#> [33,] -2.29442981 -12.84450859
#> [34,] 9.80087858 5.69849924
#> [35,] 9.20224845 2.11898232
#> [36,] 8.69508722 1.58984025
#> [37,] 8.36846320 2.64396984
#> [38,] 9.91852255 4.80243342
#> [39,] 9.80993736 6.87796135
#> [40,] 9.69039559 7.96577343
#> [41,] 10.09810807 1.67471750
#> [42,] -7.71740667 -11.68708511
#> [43,] 6.16013590 6.81699345
#> [44,] 0.34754988 -13.90441902
#> [45,] 9.02325798 2.43356379
#> [46,] 3.16340490 0.14608462
#> [47,] 9.85468405 1.40459888
#> [48,] -0.13351326 -8.29415537
#> [49,] -0.53326743 -8.27204516
#> [50,] -5.31549468 3.45720946
#> [51,] 7.79567494 7.65438970
#> [52,] 6.18541152 8.77067302
#> [53,] -8.69734475 -10.12444506
#> [54,] 8.44119941 5.68290879
#> [55,] 1.44255542 0.66710228
#> [56,] 7.52241023 3.88675310
#> [57,] -7.87432692 -8.45224836
#> [58,] 6.64439956 -0.95757709
#> [59,] 12.77073539 1.52379987
#> [60,] 7.76022219 1.33787892
#> [61,] 6.26413711 4.14485451
#> [62,] 9.60537348 2.84490067
#> [63,] 4.49306672 11.19434433
#> [64,] 4.31883913 11.09245229
#> [65,] 4.47764901 11.32503220
#> [66,] -8.56022990 -10.12294123
#> [67,] 10.69223350 1.58842370
#> [68,] 0.87056065 1.23947602
#> [69,] 10.50642830 3.28672853
#> [70,] 7.04559372 4.46169314
#> [71,] 5.20972812 -1.80331724
#> [72,] 8.26823828 2.02386632
#> [73,] 5.33515924 4.61189138
#> [74,] -2.82568273 0.31104501
#> [75,] -3.16092113 0.96312422
#> [76,] 6.58619815 0.33342770
#> [77,] 1.49222021 2.45647792
#> [78,] 9.17380752 5.73337522
#> [79,] 0.58012875 -1.33807685
#> [80,] 11.19384664 1.90169987
#> [81,] 9.84067405 0.28359226
#> [82,] 8.33420851 2.77996739
#> [83,] 6.35291134 3.06783067
#> [84,] -3.92053177 -0.72770156
#> [85,] -0.84921490 -4.92245687
#> [86,] 7.18051440 3.23353163
#> [87,] 6.86605749 2.49013711
#> [88,] 4.68220326 -0.71574260
#> [89,] 4.90419455 11.28312720
#> [90,] -10.65410123 2.88287888
#> [91,] 13.34805670 2.63686469
#> [92,] 2.61768066 1.70135353
#> [93,] 12.44431127 5.16005209
#> [94,] -4.08811220 1.76195435
#> [95,] 6.38725709 2.50347674
#> [96,] 7.64486688 4.21981289
#> [97,] 8.41841606 1.48618138
#> [98,] 5.84102003 5.22993943
#> [99,] 8.48698603 0.64511432
#> [100,] 6.07051972 2.02301870
#> [101,] 4.57176965 2.00907298
#> [102,] -3.96914786 -13.64545248
#> [103,] 6.97080567 2.87610316
#> [104,] -9.06404918 0.82875240
#> [105,] 7.57959485 10.95414329
#> [106,] -1.49006703 0.61722007
#> [107,] 5.41886274 6.85921655
#> [108,] 5.15360831 2.39471495
#> [109,] 7.77585354 2.95790968
#> [110,] 10.10553413 2.80113842
#> [111,] 7.11945745 1.57631097
#> [112,] 6.84461125 4.64653631
#> [113,] -0.33495855 2.03500834
#> [114,] 9.12253061 3.90144635
#> [115,] 8.31027890 2.86403536
#> [116,] -5.14294756 -7.27176761
#> [117,] 0.93540517 -1.00066418
#> [118,] -9.37678730 0.81876967
#> [119,] -2.93904661 -11.72462497
#> [120,] -2.36435258 2.27908933
#> [121,] 6.53996150 7.15502027
#> [122,] 7.85684955 3.60745282
#> [123,] 4.71758325 9.18670351
#> [124,] 7.47054790 2.81292751
#> [125,] -0.78055077 11.47588077
#> [126,] -1.95078367 -0.41130918
#> [127,] 3.89444268 -0.17448432
#> [128,] -0.26445668 -0.51505063
#> [129,] -5.17091139 0.79506299
#> [130,] 7.42512126 3.56301760
#> [131,] 2.10745953 -8.45447605
#> [132,] 2.06042983 -8.43672226
#> [133,] -4.26608005 -8.02670930
#> [134,] -8.92404556 -0.42986399
#> [135,] -8.10809220 -1.20677695
#> [136,] 3.54695974 -0.45373626
#> [137,] -3.07879275 -1.21835884
#> [138,] 0.20766446 -0.07426898
#> [139,] -4.18647231 -11.46497186
#> [140,] -4.59362171 -12.83483986
#> [141,] -6.11314416 2.33956034
#> [142,] -3.19986818 0.87806629
#> [143,] 3.69266134 1.26693107
#> [144,] -8.05550088 -11.57517906
#> [145,] -6.94101397 -9.06676803
#> [146,] 6.43064861 1.32126612
#> [147,] 7.55648262 2.04111285
#> [148,] -5.43040697 -9.32513441
#> [149,] 4.06062405 5.32352999
#> [150,] -6.20980956 2.48229003
#> [151,] -2.18085413 -1.74443581
#> [152,] -4.79143884 1.54743062
#> [153,] -4.60683246 6.10959190
#> [154,] 3.16076774 -3.99919561
#> [155,] 0.74607110 6.08020521
#> [156,] 1.99467050 -2.56839919
#> [157,] 0.43794542 -14.11771963
#> [158,] -2.93989643 -13.50283638
#> [159,] -7.27288600 -8.89839415
#> [160,] 1.42224912 2.92138989
#> [161,] -4.67317206 -2.11455568
#> [162,] -1.00027410 -1.79984252
#> [163,] -3.15599606 -1.38447923
#> [164,] -9.33402582 -0.48308745
#> [165,] -5.97041792 1.75374927
#> [166,] -6.61028273 2.39151260
#> [167,] 6.48000470 1.09392517
#> [168,] -0.95764387 -12.96527134
#> [169,] 5.22138412 -13.38861985
#> [170,] -1.81397034 -11.36201140
#> [171,] -1.18954912 4.27795345
#> [172,] 4.20937913 8.98399307
#> [173,] -5.86075253 -1.98405980
#> [174,] -2.65129886 -10.22985612
#> [175,] -4.32401105 3.28530139
#> [176,] 6.75828930 2.35984195
#> [177,] -1.47843323 -10.60343681
#> [178,] -2.06506700 1.62086675
#> [179,] -7.32021826 -8.71174085
#> [180,] -6.38999488 -1.93700586
#> [181,] 2.99193796 -0.18419918
#> [182,] -12.08357387 -6.69208599
#> [183,] 9.04991397 3.40506729
#> [184,] -1.23352156 2.60742843
#> [185,] 3.46121763 -3.36642182
#> [186,] 4.88832886 3.31793577
#> [187,] 2.33217157 -8.64555369
#> [188,] -8.52192679 -11.91811412
#> [189,] 4.39624846 -6.52028359
#> [190,] -0.50974103 4.20893426
#> [191,] 2.44057173 -12.38595516
#> [192,] 1.73426624 -10.55996879
#> [193,] 5.00209763 -0.28919595
#> [194,] -3.28732595 -3.29632276
#> [195,] -5.48420298 2.08213818
#> [196,] -1.67240180 -6.82294028
#> [197,] 2.57677858 0.04217430
#> [198,] -2.33491127 -1.67274753
#> [199,] -2.30624059 -2.50726342
#> [200,] -4.77433183 -8.97945512
#> [201,] 2.09554783 -9.65698633
#> [202,] -2.42308781 2.38936041
#> [203,] -0.99826354 1.43780382
#> [204,] 3.37563046 -14.50720461
#> [205,] -6.90658011 -1.06386823
#> [206,] 7.34719739 10.91791857
#> [207,] 5.48721718 3.66532704
#> [208,] -1.20778145 -8.92356215
#> [209,] -6.16134776 1.96454423
#> [210,] -2.73275027 -4.48418140
#> [211,] -3.21327018 -2.89889010
#> [212,] 0.57413231 8.14015896
#> [213,] -0.07068723 6.71044024
#> [214,] -7.75878257 -2.88628440
#> [215,] 1.82700595 4.58962738
#> [216,] -1.53828575 4.40278113
#> [217,] -1.65340655 -5.81607246
#> [218,] -3.53053224 -1.56091146
#> [219,] 3.05328854 7.61113102
#> [220,] 1.43361367 -4.90205535
#> [221,] -0.54545092 2.50952403
#> [222,] 2.30113650 2.51777566
#> [223,] -6.16146227 12.82930243
#> [224,] -1.03289712 5.94257670
#> [225,] 4.63851580 4.46269919
#> [226,] -2.44473360 -9.52764753
#> [227,] -12.10069812 -6.65633303
#> [228,] -2.17628811 -0.55684099
#> [229,] -2.36494009 -14.87618158
#> [230,] -3.99164727 4.08473375
#> [231,] -3.58641997 1.94440118
#> [232,] 4.00897328 3.51587011
#> [233,] -2.64877483 -4.61042544
#> [234,] -10.57644017 6.79945959
#> [235,] -6.35161278 -6.83199868
#> [236,] 0.93315973 -8.13914365
#> [237,] 2.81725569 4.70543428
#> [238,] -3.08624831 -3.70169046
#> [239,] -2.78553068 -9.22388022
#> [240,] -1.87853973 -13.97917611
#> [241,] 5.02452962 -5.54623670
#> [242,] 5.03249006 -5.10871985
#> [243,] 1.60714080 -0.36615882
#> [244,] -0.72941622 -12.95165037
#> [245,] 5.03607263 -4.34735141
#> [246,] -2.76959771 4.21909516
#> [247,] -4.95975607 -4.07147502
#> [248,] -0.51620257 -13.06318936
#> [249,] 11.05273769 -3.66914025
#> [250,] 1.52863618 -11.42121037
#> [251,] 1.27258635 0.56877288
#> [252,] 3.24810814 10.03549510
#> [253,] -0.09215736 -2.17776247
#> [254,] -1.02794378 11.27038636
#> [255,] -4.93688337 -7.84471933
#> [256,] -0.18063240 7.59497161
#> [257,] 6.15495768 8.87645832
#> [258,] -7.28552446 2.59216487
#> [259,] 3.82272311 -10.55484734
#> [260,] 4.19492520 -10.71328585
#> [261,] -9.12446805 0.82265706
#> [262,] -6.20571857 2.77669100
#> [263,] -7.20903318 6.68520799
#> [264,] 7.48514690 -3.42374999
#> [265,] -1.15022485 -11.96023709
#> [266,] 5.14402230 -9.55687574
#> [267,] 5.12184263 -9.64167256
#> [268,] -1.78033988 -4.18476720
#> [269,] -3.24933088 -4.59964327
#> [270,] -4.99230813 -2.99815237
#> [271,] -5.89287373 -1.60196674
#> [272,] 0.42820257 -4.13358730
#> [273,] -1.08803477 11.28850742
#> [274,] -0.87524969 -3.66012367
#> [275,] -0.44221741 -1.43604112
#> [276,] -3.69154758 -1.61878754
#> [277,] -1.76901259 -13.94212583
#> [278,] 1.58959984 -12.62680413
#> [279,] -8.69899201 8.78543024
#> [280,] -3.42326395 6.62011084
#> [281,] 8.91247539 -0.56379042
#> [282,] -3.57550292 -6.55465251
#> [283,] -8.12764497 4.30239165
#> [284,] -12.10606062 -6.64335056
#> [285,] -0.29690279 0.68999499
#> [286,] -3.42044387 1.87876991
#> [287,] 3.25719344 1.56124517
#> [288,] 5.24963885 -4.28634772
#> [289,] 1.42374877 4.98049205
#> [290,] -1.24526402 6.00516830
#> [291,] 5.73242718 3.10797966
#> [292,] 1.94241836 1.03489048
#> [293,] -0.20154069 -9.98666282
#> [294,] -9.87977606 9.13528989
#> [295,] -0.83977498 -0.14420012
#> [296,] -2.21167749 5.38748222
#> [297,] -5.86230497 5.19915486
#> [298,] 10.70315882 -3.49139000
#> [299,] -3.29232823 2.95737811
#> [300,] -8.69357877 9.35406104
#> [301,] -5.00401343 -5.51519526
#> [302,] 2.33087982 5.30990669
#> [303,] -12.10520093 -6.63635324
#> [304,] -5.67368778 8.40688789
#> [305,] -9.36131176 6.34653907
#> [306,] -4.82563152 8.75967987
#> [307,] 0.28255339 -7.13272646
#> [308,] -9.98316491 -0.21928398
#> [309,] 3.00035621 -10.74449113
#> [310,] -1.20054773 -9.59478113
#> [311,] -9.49103607 -2.31658589
#> [312,] -0.27185723 -3.32806169
#> [313,] -3.74054116 -6.52930019
#> [314,] 0.08860962 5.32558077
#> [315,] 0.87096648 1.57384043
#> [316,] 0.36632953 -7.00580896
#> [317,] -3.01181971 -8.03283549
#> [318,] -2.64313813 -11.48640850
#> [319,] -3.06597073 3.29677967
#> [320,] -5.33200391 -0.50433247
#> [321,] 3.20157531 -14.19717419
#> [322,] 10.11364187 -3.26434998
#> [323,] 9.55403397 -2.25809635
#> [324,] 2.99875594 6.49551961
#> [325,] -8.54553694 10.01134869
#> [326,] 5.29468152 -0.97468887
#> [327,] -8.28322809 7.23678360
#> [328,] 8.56638820 11.16277945
#> [329,] -5.99739984 13.01823998
#> [330,] -4.84612201 -10.95412476
#> [331,] 0.14609246 0.75101344
#> [332,] -2.93292352 -3.79194049
#> [333,] 4.22155468 -10.63281544
#> [334,] -1.30919761 -11.90261907
#> [335,] -6.12971663 -8.11444063
#> [336,] -6.22204320 3.03173806
#> [337,] -9.19086617 0.95021091
#> [338,] -4.95422571 8.98320256
#> [339,] -9.51900436 6.45287928
#> [340,] -8.59014217 6.41404253
#> [341,] 10.84475321 -3.67500414
#> [342,] 1.07588447 -7.90682038
#> [343,] 0.04389712 7.22874467
#> [344,] -7.42593466 -5.22019535
#> [345,] -7.43981554 -5.23351018
#> [346,] -1.39832261 -14.74413325
#> [347,] -1.42163865 -1.83575323
#> [348,] 0.70875389 8.20132571
#> [349,] 2.30793413 3.61579032
#> [350,] -1.98813195 -7.20833386
#> [351,] -1.41358901 -11.62954347
#> [352,] -3.73296349 4.25584324
#> [353,] 2.79844194 8.11704482
#> [354,] 9.46615881 -2.34480807
#> [355,] -3.97860610 -4.92940111
#> [356,] -8.62529579 8.81096287
#> [357,] -8.50814761 9.89012189
#> [358,] 9.91395417 -1.86741140
#> [359,] -5.41554554 -3.12057350
#> [360,] 1.19412062 2.70685335
#> [361,] -3.43105068 -1.35415817
#> [362,] 0.42831668 3.18428678
#> [363,] -2.53611390 -14.93089085
#> [364,] -0.18474542 -10.78144719
#> [365,] 4.52726598 4.42680128
#> [366,] -0.16163204 4.53056394
#> [367,] 0.86175543 -12.52605425
#> [368,] 2.22108216 3.36468042
#> [369,] 1.22505816 10.15802220
#> [370,] -10.90275881 6.46737501
#> [371,] -1.42431845 -3.91672917
#> [372,] -5.87753958 9.24151589
#> [373,] -5.60219606 7.71828486
#> [374,] -5.31002327 7.37460197
#> [375,] -1.52658103 8.74096040
#> [376,] -3.15215678 -5.79221216
#> [377,] 0.28233161 -8.44084003
#> [378,] -2.04325338 3.54345131
#> [379,] 0.28183503 1.06843586
#> [380,] -0.45130572 7.87162844
#> [381,] -1.80999552 10.98925956
#> [382,] 4.04359226 2.78154576
#> [383,] -7.51545564 -2.25288331
#> [384,] -2.49056641 7.38302745
#> [385,] -0.97894251 10.02565867
#> [386,] 6.21990439 -1.87261536
#> [387,] 0.81385543 -3.61608963
#> [388,] 5.53578512 0.32015832
#> [389,] 1.37519419 -1.60225300
#> [390,] 1.80318105 -2.42825913
#> [391,] -2.37130021 7.19618011
#> [392,] -4.69786789 -0.72728524
#> [393,] 2.16572365 -14.22818113
#> [394,] -5.09317801 -3.51904313
#> [395,] -9.63262716 -3.40504482
#> [396,] 10.36798325 -3.22642502
#> [397,] 9.45000470 -2.22812221
#> [398,] -7.03539572 11.67150290
#> [399,] -1.38068699 9.72218682
#> [400,] 0.32260873 -12.67447801
#> [401,] -1.40522451 -6.68395519
#> [402,] 0.06151217 4.08512482
#> [403,] 4.28544878 -11.66424341
#> [404,] 0.76048978 -5.94115369
#> [405,] -10.98177956 6.43564252
#> [406,] 2.00806470 -13.27249453
#> [407,] 0.22195969 5.52532690
#> [408,] -5.74538296 6.64783204
#> [409,] -4.45810269 -0.97642608
#> [410,] -5.54228216 8.21743720
#> [411,] -8.48779509 6.07964733
#> [412,] -8.99782320 6.34320472
#> [413,] -5.50514243 7.81671157
#> [414,] -5.98904134 6.38995527
#> [415,] -4.21669703 7.61557818
#> [416,] 8.11714276 -2.62380913
#> [417,] -0.22549713 6.78498929
#> [418,] -0.44579149 7.88526031
#> [419,] 6.37952526 3.10535077
#> [420,] -2.79760942 -7.36632461
#> [421,] -9.55030368 7.51568758
#> [422,] -5.79111192 -9.96380890
#> [423,] -1.94764060 7.03786954
#> [424,] -0.48929749 -9.59580477
#> [425,] -0.02524895 5.07564743
#> [426,] -1.80448645 -14.05811315
#> [427,] -5.74338539 5.62414627
#> [428,] 5.75459185 11.91206552
#> [429,] -6.98785929 -9.07706552
#> [430,] 0.33534904 -10.10209115
#> [431,] -2.80392367 9.61595474
#> [432,] -5.27340154 9.16334809
#> [433,] -3.46621021 5.48554344
#> [434,] 0.61927119 -11.00960311
#> [435,] -1.16663939 -14.96995649
#> [436,] -7.36246270 11.44506051
#> [437,] 4.94789617 -10.52855246
#> [438,] -2.34248367 -9.60075862
#> [439,] 0.28276015 -9.14913354
#> [440,] 1.79822535 1.46855299
#> [441,] 0.73162300 8.58609178
#> [442,] 7.52297375 11.11896299
#> [443,] -11.64204180 6.10003936
#> [444,] -4.49471273 10.95051327
#> [445,] 1.78328202 12.51576747
#> [446,] -7.41055724 6.75038583
#> [447,] -7.26779129 8.73918876
#> [448,] 3.33860434 -0.99575332
#> [449,] -4.29702084 3.88567383
#> [450,] -4.07462110 7.53595174
#> [451,] 5.24761396 1.18073491
#> [452,] -4.30084049 6.69784377
#> [453,] -4.61349639 6.95435089
#> [454,] -4.22127075 8.32080073
#> [455,] -8.79362939 -1.35960151
#> [456,] -12.10059680 5.79653230
#> [457,] -1.87891183 -7.96948582
#> [458,] -1.88103020 -8.65645556
#> [459,] -2.50954451 -5.21255865
#> [460,] 3.95888178 6.78306213
#> [461,] 3.54539902 -2.85134858
#> [462,] 1.45701991 4.61121318
#> [463,] -9.63915990 8.09589570
#> [464,] 3.60541937 6.45855121
#> [465,] 4.67997384 -2.52312824
#> [466,] 2.09511036 -9.16605366
#> [467,] 0.03188857 -0.71509035
#> [468,] -8.20693894 4.12795838
#> [469,] -7.32386409 8.70789124
#> [470,] -2.46648384 7.97057832
#> [471,] -4.43306196 0.35761601
#> [472,] -4.36796746 -9.96386509
#> [473,] -5.13020831 8.95928116
#> [474,] -7.96427062 7.07496217
#> [475,] 2.11158429 -6.44582248
#> [476,] 1.57580925 -4.58515505
#> [477,] 9.34215799 -0.91283439
#> [478,] -1.25911040 11.26030305
#> [479,] -7.17384356 11.78852706
#> [480,] -7.13907321 11.68726941
#> [481,] -8.64030246 8.38639959
#> [482,] -3.21348002 5.15328481
#> [483,] -6.76320242 6.49273645
#> [484,] -7.47372513 6.60111958
#> [485,] 2.30932841 -1.06254479
#> [486,] -5.28069213 -0.82650844
#> [487,] -3.74274793 -3.02532602
#> [488,] 0.46900604 -9.84874384
#> [489,] -0.83990021 9.79218213
#> [490,] 3.56407183 -2.79259632
#>
#> $costs
#> [1] 2.860131e-03 1.842953e-03 1.664145e-03 5.600132e-04 4.506933e-04
#> [6] 3.464785e-04 8.892214e-04 9.099243e-04 1.694445e-03 1.904657e-03
#> [11] 1.855888e-03 3.191404e-03 6.308873e-04 2.134956e-03 1.563780e-03
#> [16] 4.701250e-03 2.403067e-03 9.287488e-04 2.250947e-03 1.060910e-03
#> [21] 1.859619e-03 1.594868e-03 2.663661e-03 3.813665e-03 3.056491e-03
#> [26] 1.220782e-03 2.696089e-03 3.761405e-03 5.677102e-04 3.523094e-03
#> [31] 1.427559e-03 2.680234e-03 7.642191e-04 1.751297e-03 1.677691e-03
#> [36] 2.300451e-03 4.417259e-06 2.811340e-03 1.400306e-03 3.393958e-03
#> [41] 2.351581e-04 1.001685e-03 3.149290e-03 2.623614e-03 -2.214782e-05
#> [46] 3.773190e-03 3.333184e-04 1.499919e-03 1.821835e-03 1.602129e-03
#> [51] 1.517893e-03 5.218019e-03 2.564493e-03 4.376328e-03 3.452348e-03
#> [56] 6.075730e-04 2.674363e-03 5.724781e-03 4.572505e-03 3.234122e-03
#> [61] 2.036950e-03 2.609058e-04 4.171449e-03 3.449072e-03 1.439993e-03
#> [66] 3.111296e-03 3.091871e-03 9.335851e-03 1.387586e-03 5.443994e-04
#> [71] 4.432602e-03 5.265131e-04 3.028301e-03 4.696648e-03 5.506831e-03
#> [76] 5.638719e-03 1.964485e-03 4.474144e-03 5.018335e-03 7.010075e-04
#> [81] 1.437521e-03 5.756542e-04 1.515399e-03 1.720651e-03 2.259120e-03
#> [86] 1.942356e-03 3.304790e-03 3.373967e-03 2.308557e-03 3.434735e-03
#> [91] 2.740642e-03 6.102558e-03 3.040175e-03 4.973787e-03 2.386348e-04
#> [96] 6.820285e-04 2.768579e-03 1.892465e-03 2.169288e-03 3.367622e-03
#> [101] 1.570955e-03 7.940247e-04 1.871022e-03 3.642413e-03 2.065148e-03
#> [106] 3.261366e-03 3.181595e-03 7.111053e-04 1.262979e-03 1.411855e-03
#> [111] 2.927999e-03 1.251440e-03 2.296640e-03 7.012761e-04 -2.412065e-04
#> [116] 1.535904e-03 1.704795e-03 1.043806e-03 1.543707e-04 5.209924e-03
#> [121] 2.735126e-03 6.724878e-05 6.204007e-03 2.189723e-03 3.301020e-03
#> [126] 3.824486e-03 1.320237e-03 1.097741e-02 2.076253e-03 1.589496e-04
#> [131] 2.080094e-03 2.299795e-03 7.455864e-04 4.792972e-03 4.300483e-03
#> [136] 7.335803e-03 1.151041e-03 1.856066e-03 5.922851e-04 2.278914e-04
#> [141] 3.294677e-03 1.936965e-03 1.132700e-03 3.089976e-03 2.046415e-03
#> [146] 3.338055e-03 4.014838e-03 1.176268e-03 2.604322e-03 9.874806e-04
#> [151] 1.448387e-03 1.371634e-03 4.161753e-03 1.380099e-03 2.956113e-03
#> [156] 8.623345e-04 1.346411e-03 2.293395e-04 2.992595e-03 6.083271e-04
#> [161] 1.266958e-03 8.904510e-04 2.233336e-03 3.315596e-03 7.484914e-04
#> [166] 1.930196e-03 9.514927e-04 2.135669e-03 3.403871e-03 9.655284e-04
#> [171] 1.378655e-03 4.119077e-03 1.678265e-03 8.409754e-04 1.982964e-03
#> [176] 1.492999e-03 1.120192e-03 2.741348e-03 3.610520e-03 1.412603e-03
#> [181] 2.553596e-03 1.687175e-03 6.503207e-04 8.097465e-03 1.231990e-03
#> [186] 2.660496e-03 6.968123e-04 2.320103e-03 2.562604e-03 3.417551e-03
#> [191] 1.321800e-03 2.077475e-03 6.426004e-03 4.341915e-03 1.724133e-03
#> [196] 5.831204e-03 7.386550e-03 5.391129e-04 2.086190e-03 4.474817e-03
#> [201] 6.803746e-04 9.835163e-04 1.392616e-03 2.657539e-03 1.933515e-03
#> [206] 3.989339e-03 5.090242e-03 1.632913e-03 6.980334e-04 4.829069e-03
#> [211] 1.933112e-03 1.390722e-03 6.604730e-03 2.162180e-03 1.378600e-03
#> [216] 4.085751e-03 1.585139e-03 1.008420e-03 1.921757e-03 4.757406e-03
#> [221] 2.806948e-03 2.526293e-03 3.102243e-03 4.972832e-03 3.114789e-03
#> [226] 3.528083e-03 2.405997e-03 1.854728e-03 3.427326e-04 4.308649e-03
#> [231] 1.190064e-02 2.512785e-03 7.359968e-03 2.824443e-03 3.187194e-03
#> [236] 2.662217e-03 1.500520e-03 3.721603e-03 7.605936e-04 1.158855e-03
#> [241] 1.372037e-03 2.024291e-03 3.372337e-03 1.280391e-03 4.563340e-03
#> [246] 2.756985e-03 1.449756e-03 1.751175e-03 1.309821e-03 1.361407e-03
#> [251] 5.415854e-03 2.524577e-03 4.490145e-03 2.891227e-03 3.566303e-03
#> [256] 1.472259e-03 2.575913e-03 1.537507e-03 2.967974e-03 3.775597e-03
#> [261] 1.303162e-03 1.193736e-03 4.699496e-03 2.860729e-03 2.392011e-03
#> [266] 3.891964e-03 2.406813e-03 4.903458e-03 1.442571e-03 1.497944e-03
#> [271] 7.282140e-04 6.381728e-03 1.369099e-03 2.249908e-03 2.907834e-03
#> [276] 5.952222e-04 1.907584e-03 4.424358e-03 5.200594e-03 2.700662e-03
#> [281] 2.681660e-03 4.318418e-03 5.161910e-03 1.798127e-03 3.816967e-04
#> [286] 2.936241e-03 5.582664e-03 1.357444e-03 3.037735e-03 1.730558e-03
#> [291] 1.229671e-03 1.243198e-03 3.669019e-03 1.753953e-03 1.013796e-03
#> [296] 3.122367e-03 3.201179e-03 2.212155e-03 2.007548e-03 2.676167e-03
#> [301] 3.270693e-03 1.284303e-03 1.773435e-03 -3.697313e-05 1.004634e-03
#> [306] 5.014112e-04 3.789639e-03 1.560280e-03 1.402285e-03 3.078953e-03
#> [311] 1.535156e-03 1.567175e-03 3.063087e-03 9.524065e-04 1.246072e-03
#> [316] 2.879768e-03 7.992670e-04 2.781927e-03 5.631044e-03 2.776511e-03
#> [321] 3.430182e-03 5.157502e-03 3.463900e-03 1.209922e-03 3.377832e-03
#> [326] 6.304881e-03 2.223999e-03 3.490662e-03 3.604869e-03 1.060285e-03
#> [331] 6.055450e-03 4.565991e-04 2.600172e-03 1.796621e-03 4.135798e-03
#> [336] 1.270105e-03 1.215416e-03 1.378709e-03 6.333945e-04 1.588464e-03
#> [341] 2.145222e-03 2.295310e-03 1.863399e-03 2.099111e-03 1.929829e-03
#> [346] 6.921839e-04 6.572610e-04 1.755961e-03 1.569796e-03 5.876092e-04
#> [351] 1.471316e-03 4.960982e-03 2.389976e-03 7.596647e-03 1.641302e-03
#> [356] 2.708058e-03 6.112782e-03 1.810433e-03 3.583570e-04 5.268064e-03
#> [361] 1.949176e-03 1.174915e-03 8.025871e-04 1.018167e-03 2.667467e-03
#> [366] 2.602546e-03 4.654195e-03 3.229809e-03 3.531721e-03 3.168238e-03
#> [371] 2.533452e-03 1.198176e-03 6.536984e-04 1.291868e-03 2.041623e-03
#> [376] 2.227540e-03 2.743806e-03 4.434985e-03 5.233703e-03 1.828687e-03
#> [381] 3.021478e-03 1.465825e-03 1.864148e-03 3.161015e-03 1.531564e-03
#> [386] 2.603010e-03 2.777920e-03 2.800250e-03 4.028758e-03 2.042324e-03
#> [391] 3.007173e-03 3.968047e-03 1.490513e-03 1.575071e-03 4.308841e-03
#> [396] 4.339670e-03 3.100883e-03 3.962980e-03 2.491562e-03 2.523633e-04
#> [401] 2.268781e-03 2.686708e-03 2.120619e-03 1.044836e-03 2.859206e-03
#> [406] 2.680500e-03 2.483039e-03 3.760349e-03 1.723454e-03 8.374268e-04
#> [411] 3.236281e-03 9.288383e-04 2.878412e-03 4.222341e-03 1.610359e-03
#> [416] 3.343916e-03 2.576871e-03 1.881999e-03 2.217364e-03 2.530871e-03
#> [421] 1.329949e-03 1.151859e-03 3.539942e-03 9.602873e-04 1.787848e-03
#> [426] 1.049182e-03 4.027010e-03 3.416003e-03 3.830419e-03 2.899390e-03
#> [431] 1.802959e-03 9.633652e-04 2.604538e-03 2.308286e-03 4.304246e-04
#> [436] 1.968660e-03 1.438215e-03 4.001336e-03 5.383207e-03 4.943605e-03
#> [441] 3.498907e-04 1.387581e-03 2.039433e-03 3.190878e-03 3.672587e-03
#> [446] 2.878341e-03 1.286369e-03 8.716000e-04 2.226107e-03 1.646066e-03
#> [451] 1.529187e-03 3.169731e-03 6.218599e-03 7.428387e-04 1.367418e-03
#> [456] 3.364157e-03 4.349729e-03 6.960060e-04 6.150613e-03 5.872998e-04
#> [461] 2.330171e-03 1.049849e-02 1.386883e-03 3.924335e-03 2.291309e-03
#> [466] 1.922799e-03 6.321293e-03 3.193780e-03 2.318224e-03 2.219818e-03
#> [471] 3.402013e-03 2.983945e-03 2.349323e-03 2.368522e-03 2.086347e-03
#> [476] 2.990666e-03 1.074257e-03 3.561375e-03 1.763195e-03 3.611575e-03
#> [481] 2.179819e-03 2.378397e-03 1.461763e-03 1.187729e-03 3.585462e-03
#> [486] 1.900410e-03 9.822531e-04 1.741208e-03 1.253067e-03 2.248268e-03
#>
#> $itercosts
#> [1] 59.599396 58.937017 59.082314 59.081629 58.935814 1.413887 1.331563
#> [8] 1.295152 1.275665 1.258463 1.250196 1.245667 1.242338 1.238193
#> [15] 1.236570 1.235949 1.233953 1.229892 1.228711 1.228196
#>
#> $origD
#> [1] 50
#>
#> $perplexity
#> [1] 30
#>
#> $theta
#> [1] 0.5
#>
#> $max_iter
#> [1] 1000
#>
#> $stop_lying_iter
#> [1] 250
#>
#> $mom_switch_iter
#> [1] 250
#>
#> $momentum
#> [1] 0.5
#>
#> $final_momentum
#> [1] 0.8
#>
#> $eta
#> [1] 200
#>
#> $exaggeration_factor
#> [1] 12
#>
#> attr(,"class")
#> [1] "Rtsne" "list"
#>
#> $pca_result
#> Standard deviations (1, .., p=490):
#> [1] 9.243205e+00 4.207211e+00 3.914661e+00 3.640950e+00 3.316587e+00
#> [6] 3.141114e+00 2.852412e+00 2.744243e+00 2.621505e+00 2.531561e+00
#> [11] 2.477948e+00 2.350191e+00 2.280115e+00 2.153115e+00 2.135359e+00
#> [16] 2.073989e+00 2.035517e+00 1.980114e+00 1.904040e+00 1.892190e+00
#> [21] 1.875725e+00 1.799473e+00 1.757500e+00 1.728256e+00 1.708477e+00
#> [26] 1.676742e+00 1.630217e+00 1.623334e+00 1.604087e+00 1.583754e+00
#> [31] 1.567891e+00 1.536249e+00 1.532775e+00 1.520808e+00 1.495698e+00
#> [36] 1.466973e+00 1.451911e+00 1.439230e+00 1.426326e+00 1.408866e+00
#> [41] 1.394070e+00 1.356280e+00 1.355607e+00 1.343218e+00 1.324939e+00
#> [46] 1.317448e+00 1.298042e+00 1.292172e+00 1.290126e+00 1.284486e+00
#> [51] 1.260741e+00 1.252454e+00 1.242871e+00 1.234479e+00 1.221911e+00
#> [56] 1.206628e+00 1.199803e+00 1.195127e+00 1.190011e+00 1.174547e+00
#> [61] 1.171232e+00 1.154458e+00 1.145637e+00 1.135996e+00 1.124914e+00
#> [66] 1.122782e+00 1.116625e+00 1.109650e+00 1.095992e+00 1.094403e+00
#> [71] 1.083500e+00 1.081434e+00 1.073638e+00 1.065964e+00 1.059762e+00
#> [76] 1.047794e+00 1.046608e+00 1.037150e+00 1.030342e+00 1.022820e+00
#> [81] 1.016640e+00 1.010146e+00 1.001855e+00 9.943502e-01 9.920359e-01
#> [86] 9.841591e-01 9.761104e-01 9.732790e-01 9.623114e-01 9.603170e-01
#> [91] 9.559378e-01 9.443870e-01 9.428462e-01 9.410785e-01 9.344836e-01
#> [96] 9.288014e-01 9.271981e-01 9.195127e-01 9.104633e-01 9.076714e-01
#> [101] 9.055111e-01 9.009656e-01 8.940822e-01 8.915336e-01 8.860811e-01
#> [106] 8.783154e-01 8.733380e-01 8.706939e-01 8.655068e-01 8.625876e-01
#> [111] 8.561297e-01 8.521523e-01 8.429825e-01 8.406524e-01 8.389560e-01
#> [116] 8.364509e-01 8.280351e-01 8.254479e-01 8.214640e-01 8.167350e-01
#> [121] 8.132213e-01 8.078696e-01 8.067777e-01 8.007288e-01 7.957929e-01
#> [126] 7.920924e-01 7.888844e-01 7.820410e-01 7.805644e-01 7.768805e-01
#> [131] 7.715894e-01 7.685875e-01 7.664157e-01 7.637809e-01 7.629644e-01
#> [136] 7.571623e-01 7.533174e-01 7.499022e-01 7.485470e-01 7.426886e-01
#> [141] 7.395636e-01 7.355301e-01 7.330848e-01 7.250294e-01 7.219595e-01
#> [146] 7.207059e-01 7.178711e-01 7.134139e-01 7.119358e-01 7.105775e-01
#> [151] 7.072117e-01 7.040330e-01 7.028589e-01 6.992496e-01 6.948058e-01
#> [156] 6.939748e-01 6.892388e-01 6.842039e-01 6.827935e-01 6.813387e-01
#> [161] 6.792254e-01 6.772769e-01 6.720927e-01 6.701258e-01 6.658420e-01
#> [166] 6.623950e-01 6.609654e-01 6.597883e-01 6.573117e-01 6.570087e-01
#> [171] 6.549812e-01 6.485347e-01 6.466902e-01 6.430801e-01 6.392046e-01
#> [176] 6.369904e-01 6.344709e-01 6.313753e-01 6.301461e-01 6.281418e-01
#> [181] 6.267177e-01 6.225714e-01 6.199600e-01 6.185427e-01 6.141035e-01
#> [186] 6.126771e-01 6.096630e-01 6.088156e-01 6.063807e-01 6.036823e-01
#> [191] 6.008063e-01 5.979322e-01 5.965868e-01 5.946803e-01 5.910745e-01
#> [196] 5.881630e-01 5.851488e-01 5.843792e-01 5.832505e-01 5.801898e-01
#> [201] 5.793297e-01 5.776320e-01 5.750328e-01 5.741570e-01 5.726129e-01
#> [206] 5.722598e-01 5.690460e-01 5.653365e-01 5.618373e-01 5.577842e-01
#> [211] 5.563350e-01 5.530227e-01 5.516199e-01 5.506381e-01 5.490014e-01
#> [216] 5.477387e-01 5.470153e-01 5.454412e-01 5.441161e-01 5.401694e-01
#> [221] 5.389369e-01 5.367966e-01 5.332473e-01 5.315658e-01 5.289262e-01
#> [226] 5.276807e-01 5.252845e-01 5.245833e-01 5.209357e-01 5.206105e-01
#> [231] 5.185780e-01 5.158014e-01 5.126761e-01 5.110360e-01 5.095218e-01
#> [236] 5.090777e-01 5.081830e-01 5.054780e-01 5.040159e-01 5.031494e-01
#> [241] 5.007658e-01 4.998503e-01 4.981423e-01 4.946367e-01 4.936244e-01
#> [246] 4.919041e-01 4.901219e-01 4.887549e-01 4.870942e-01 4.855973e-01
#> [251] 4.831134e-01 4.818930e-01 4.807614e-01 4.796236e-01 4.774337e-01
#> [256] 4.756689e-01 4.739295e-01 4.722662e-01 4.716409e-01 4.698954e-01
#> [261] 4.683940e-01 4.666922e-01 4.638996e-01 4.626640e-01 4.606707e-01
#> [266] 4.602921e-01 4.565806e-01 4.551472e-01 4.536993e-01 4.521929e-01
#> [271] 4.512901e-01 4.504168e-01 4.486301e-01 4.481631e-01 4.462478e-01
#> [276] 4.438517e-01 4.433398e-01 4.411723e-01 4.393198e-01 4.379883e-01
#> [281] 4.369864e-01 4.357161e-01 4.335241e-01 4.315384e-01 4.304626e-01
#> [286] 4.299509e-01 4.295972e-01 4.262579e-01 4.251349e-01 4.234177e-01
#> [291] 4.222948e-01 4.210002e-01 4.191833e-01 4.177143e-01 4.160603e-01
#> [296] 4.152285e-01 4.127429e-01 4.116214e-01 4.110062e-01 4.095753e-01
#> [301] 4.090932e-01 4.072502e-01 4.065672e-01 4.042008e-01 4.035206e-01
#> [306] 4.023567e-01 4.017920e-01 4.007671e-01 3.982198e-01 3.976655e-01
#> [311] 3.957143e-01 3.947265e-01 3.935244e-01 3.916946e-01 3.909234e-01
#> [316] 3.900114e-01 3.877642e-01 3.858114e-01 3.847948e-01 3.835150e-01
#> [321] 3.819818e-01 3.813703e-01 3.803031e-01 3.791932e-01 3.779444e-01
#> [326] 3.770000e-01 3.760075e-01 3.751111e-01 3.737653e-01 3.721652e-01
#> [331] 3.718862e-01 3.705055e-01 3.691068e-01 3.674795e-01 3.651444e-01
#> [336] 3.647957e-01 3.633445e-01 3.622535e-01 3.603617e-01 3.600399e-01
#> [341] 3.593517e-01 3.589410e-01 3.572479e-01 3.566297e-01 3.550247e-01
#> [346] 3.531792e-01 3.522962e-01 3.520084e-01 3.504945e-01 3.474721e-01
#> [351] 3.459154e-01 3.446735e-01 3.443787e-01 3.423760e-01 3.416633e-01
#> [356] 3.406604e-01 3.400317e-01 3.391539e-01 3.374578e-01 3.350315e-01
#> [361] 3.347968e-01 3.337742e-01 3.324674e-01 3.315236e-01 3.308446e-01
#> [366] 3.291645e-01 3.281053e-01 3.262903e-01 3.253731e-01 3.242374e-01
#> [371] 3.228902e-01 3.220174e-01 3.211667e-01 3.197456e-01 3.191225e-01
#> [376] 3.185557e-01 3.173933e-01 3.157462e-01 3.147677e-01 3.132461e-01
#> [381] 3.129181e-01 3.121474e-01 3.096893e-01 3.082353e-01 3.073252e-01
#> [386] 3.063280e-01 3.050632e-01 3.046753e-01 3.032957e-01 3.014308e-01
#> [391] 3.006672e-01 2.990869e-01 2.986001e-01 2.965456e-01 2.957026e-01
#> [396] 2.950281e-01 2.936329e-01 2.926258e-01 2.924754e-01 2.913299e-01
#> [401] 2.900980e-01 2.883983e-01 2.875028e-01 2.861673e-01 2.844567e-01
#> [406] 2.840259e-01 2.835168e-01 2.828999e-01 2.824800e-01 2.808992e-01
#> [411] 2.790587e-01 2.781097e-01 2.777240e-01 2.764665e-01 2.759602e-01
#> [416] 2.754744e-01 2.743536e-01 2.726297e-01 2.721738e-01 2.699852e-01
#> [421] 2.694801e-01 2.670432e-01 2.662954e-01 2.650347e-01 2.646827e-01
#> [426] 2.635966e-01 2.617783e-01 2.601196e-01 2.590181e-01 2.574992e-01
#> [431] 2.565837e-01 2.562533e-01 2.544652e-01 2.524027e-01 2.521701e-01
#> [436] 2.508377e-01 2.504753e-01 2.487148e-01 2.476842e-01 2.467597e-01
#> [441] 2.456598e-01 2.448734e-01 2.434520e-01 2.425910e-01 2.412996e-01
#> [446] 2.391077e-01 2.370666e-01 2.353612e-01 2.344336e-01 2.336907e-01
#> [451] 2.314153e-01 2.303490e-01 2.295914e-01 2.288472e-01 2.269513e-01
#> [456] 2.249915e-01 2.245771e-01 2.239882e-01 2.222578e-01 2.211533e-01
#> [461] 2.181852e-01 2.177548e-01 2.168754e-01 2.142710e-01 2.135207e-01
#> [466] 2.109614e-01 2.101698e-01 2.098699e-01 2.083076e-01 2.073489e-01
#> [471] 2.053383e-01 2.032876e-01 1.991847e-01 1.988649e-01 1.963824e-01
#> [476] 1.927598e-01 1.916131e-01 1.903535e-01 1.838843e-01 1.829154e-01
#> [481] 1.813119e-01 1.770114e-01 1.690306e-01 1.657955e-01 1.610450e-01
#> [486] 1.582204e-01 1.515032e-01 1.464400e-01 7.595550e-02 1.445517e-13
#>
#> Rotation (n x k) = (5078 x 50):
#> PC1 PC2 PC3 PC4
#> dyscalculia 8.123147e-03 3.434641e-02 -6.835307e-03 3.620127e-03
#> and 2.905097e-01 -2.284773e-01 -4.524599e-01 4.172579e-01
#> the 7.122090e-01 3.043340e-01 5.670838e-02 -2.755185e-01
#> minicalculator -2.239215e-04 1.429879e-03 -3.287941e-05 2.201319e-04
#> alp -3.358822e-04 2.144819e-03 -4.931911e-05 3.301978e-04
#> program 1.528774e-02 6.624131e-03 5.140127e-02 5.987647e-03
#> arithmetic 1.091652e-03 2.249825e-02 1.421009e-02 1.114105e-02
#> remedial 2.711589e-03 5.546973e-03 1.345337e-03 9.555914e-03
#> teaching 1.378220e-02 -4.057525e-02 -9.719544e-03 -4.299748e-02
#> education 2.133513e-02 -6.931558e-03 -4.982163e-02 7.968249e-02
#> of 4.076348e-01 1.983537e-01 1.636642e-01 -1.371270e-03
#> learning 8.492141e-02 -1.248120e-01 3.402872e-01 4.776740e-01
#> disabled 1.397898e-02 3.751074e-02 6.243532e-02 8.980377e-02
#> children 2.709883e-02 1.077521e-01 -4.778265e-02 5.579009e-02
#> calculators 2.835459e-03 -9.162430e-04 -4.126678e-04 -2.456518e-02
#> study 7.591571e-02 -2.891050e-02 2.862671e-02 -6.110595e-02
#> fractions -2.413915e-03 -1.518366e-02 1.198417e-02 -4.459038e-02
#> difficulties 1.085118e-02 1.534086e-03 5.928954e-03 1.926284e-02
#> calculating 6.742862e-04 -1.018058e-03 -1.380931e-03 -3.825576e-03
#> machines -4.730908e-04 1.381725e-03 -4.351358e-04 -1.069368e-03
#> PC5 PC6 PC7 PC8
#> dyscalculia -8.518113e-03 4.408165e-02 -7.608020e-03 -2.983714e-02
#> and 3.110757e-01 -1.131147e-01 7.146172e-03 3.147001e-01
#> the -8.094097e-02 -5.171942e-02 -3.346250e-01 8.109772e-03
#> minicalculator -5.356746e-04 6.249111e-04 -7.147454e-04 5.728822e-04
#> alp -8.035119e-04 9.373667e-04 -1.072118e-03 8.593234e-04
#> program 3.363432e-02 -4.878602e-02 -1.291003e-02 1.827118e-02
#> arithmetic 8.392728e-03 1.342849e-02 -1.035012e-02 -2.476098e-03
#> remedial -2.670302e-03 1.106635e-02 -1.876078e-02 -4.466639e-03
#> teaching -3.421908e-03 1.972610e-02 2.871404e-02 -6.272162e-02
#> education -8.788030e-02 -1.784698e-01 5.412252e-02 1.046784e-01
#> of -7.490927e-02 1.769726e-01 6.691608e-01 1.858406e-01
#> learning -2.315376e-01 4.949256e-01 -2.456717e-01 4.130822e-02
#> disabled 2.879765e-02 1.494249e-03 5.035938e-03 -2.309148e-03
#> children 4.763912e-02 1.777143e-01 9.782393e-03 -3.981977e-02
#> calculators -1.518972e-02 -1.993583e-02 -1.224997e-02 9.213222e-02
#> study -6.664685e-03 -2.907486e-02 -3.113131e-02 1.697815e-02
#> fractions -1.009165e-02 1.047044e-02 -1.188085e-02 4.672325e-03
#> difficulties -5.088867e-03 4.329691e-02 -2.014528e-02 -1.118554e-03
#> calculating -2.702786e-04 3.294396e-03 4.186318e-04 1.509402e-04
#> machines -3.708257e-04 2.502409e-04 -1.091851e-04 -7.019649e-04
#> PC9 PC10 PC11 PC12
#> dyscalculia -4.837983e-03 -2.108456e-02 2.104386e-02 -1.188665e-03
#> and -1.250335e-01 -8.104706e-02 -1.649360e-01 -2.303596e-01
#> the 1.220980e-01 1.621602e-02 -2.318886e-01 6.943118e-02
#> minicalculator -5.347167e-04 6.643611e-04 -2.288239e-04 2.177146e-05
#> alp -8.020751e-04 9.965417e-04 -3.432358e-04 3.265719e-05
#> program -2.759031e-02 -5.098015e-03 1.498852e-02 3.709115e-02
#> arithmetic -5.444593e-03 -3.267206e-02 3.639029e-03 -1.696330e-02
#> remedial -8.561362e-04 9.510310e-03 8.590700e-03 -2.414216e-02
#> teaching 2.716930e-02 6.508162e-02 -6.924634e-02 1.515410e-02
#> education 1.958923e-01 3.493998e-02 9.877309e-02 8.557598e-02
#> of -8.270446e-02 1.122305e-04 2.419738e-01 -8.357516e-03
#> learning -1.906675e-01 1.730333e-01 -4.515785e-02 8.578301e-03
#> disabled -7.688765e-02 6.399587e-02 3.561697e-02 -8.026518e-02
#> children 7.614519e-03 -1.464911e-01 6.683102e-03 3.308939e-02
#> calculators -2.033577e-04 -8.253252e-03 1.893240e-02 -1.433354e-02
#> study -8.057784e-02 2.837616e-02 3.846932e-02 9.160346e-03
#> fractions -3.488343e-03 -1.249577e-02 -2.388512e-03 -4.511306e-02
#> difficulties 1.989564e-02 -5.363615e-03 2.033541e-02 -5.359926e-03
#> calculating -1.292133e-03 -4.819486e-03 -4.599656e-03 7.454358e-05
#> machines -1.286009e-03 1.507248e-03 7.511682e-04 2.609605e-04
#> PC13 PC14 PC15 PC16
#> dyscalculia -9.826865e-03 -1.139473e-02 2.375906e-02 -2.041144e-04
#> and 1.186116e-01 4.975345e-02 -5.924944e-02 1.960956e-02
#> the 1.741669e-02 -1.527181e-02 3.948965e-02 -5.319925e-02
#> minicalculator -4.453942e-04 9.468749e-04 -6.154501e-04 -5.153859e-04
#> alp -6.680913e-04 1.420312e-03 -9.231752e-04 -7.730788e-04
#> program 3.612009e-03 -9.036126e-04 -1.775656e-02 3.065474e-02
#> arithmetic -1.557782e-02 -1.209143e-02 -5.681527e-04 -6.456692e-03
#> remedial 4.456661e-03 3.027971e-02 -2.320228e-03 1.047919e-06
#> teaching 1.914065e-02 8.526546e-02 3.275603e-02 -1.129348e-01
#> education 2.306432e-01 1.984019e-01 4.179943e-02 -1.949843e-01
#> of -3.338884e-02 4.808436e-02 -1.333015e-01 1.927593e-02
#> learning 5.187865e-02 8.074989e-02 3.501997e-02 4.556663e-04
#> disabled 3.341848e-02 -2.118448e-02 -1.636755e-02 -1.882455e-02
#> children -3.477076e-02 -1.418761e-01 5.323297e-02 -1.617039e-02
#> calculators 5.169591e-03 -7.053637e-02 2.107054e-02 8.397619e-03
#> study 4.944313e-02 -3.285463e-03 1.189003e-01 5.427435e-02
#> fractions 5.288890e-04 4.770201e-02 -4.376492e-02 -1.510499e-02
#> difficulties 1.746618e-02 -7.878430e-03 1.021097e-03 3.223167e-02
#> calculating 3.292511e-03 -2.385856e-05 -2.630934e-03 4.559355e-04
#> machines 1.640596e-04 3.590792e-04 1.306054e-03 -2.728334e-04
#> PC17 PC18 PC19 PC20
#> dyscalculia -4.484598e-02 -1.002895e-02 5.931592e-02 3.168805e-02
#> and -4.469531e-02 -1.461372e-01 1.089681e-01 -2.014383e-02
#> the -3.771500e-02 -9.507035e-02 2.171183e-02 -2.441729e-02
#> minicalculator 1.915356e-05 -2.632885e-04 6.864738e-04 -9.493996e-04
#> alp 2.873033e-05 -3.949328e-04 1.029711e-03 -1.424099e-03
#> program 2.455291e-02 -3.858448e-03 7.008953e-02 1.976113e-02
#> arithmetic -1.753400e-02 2.450651e-03 1.106956e-02 5.073607e-03
#> remedial -2.523095e-03 1.151749e-02 7.045528e-03 -9.775209e-03
#> teaching 3.839099e-02 -4.015231e-02 2.829345e-04 4.271296e-02
#> education 3.417267e-01 -4.505579e-02 -7.543353e-02 -1.367413e-01
#> of -5.445737e-02 -1.258619e-02 -7.693603e-02 1.532477e-03
#> learning -8.362836e-02 5.721263e-04 1.007821e-02 -6.009479e-02
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#> PC37 PC38 PC39 PC40
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#> [ reached 'max' / getOption("max.print") -- omitted 5058 rows ]
#>
#> $perplexity
#> [1] 30
#>
#> $execution_time
#> [1] 8.279726
#>
#> $timestamp
#> [1] "2026-08-14 23:36:51 CDT"
#>
#> $seed
#> [1] 123
#>
#> Starting dimensionality reduction with method: UMAP
#> Performing PCA preprocessing...
#> Performing UMAP on PCA results...
#> Dimensionality reduction completed in 9.12 seconds
#> $reduced_data
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#>
#> $method
#> [1] "UMAP"
#>
#> $umap_result
#> umap embedding of 490 items in 2 dimensions
#> object components: layout, data, knn, config
#>
#> $pca_result
#> Standard deviations (1, .., p=490):
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#> [6] 3.141114e+00 2.852412e+00 2.744243e+00 2.621505e+00 2.531561e+00
#> [11] 2.477948e+00 2.350191e+00 2.280115e+00 2.153115e+00 2.135359e+00
#> [16] 2.073989e+00 2.035517e+00 1.980114e+00 1.904040e+00 1.892190e+00
#> [21] 1.875725e+00 1.799473e+00 1.757500e+00 1.728256e+00 1.708477e+00
#> [26] 1.676742e+00 1.630217e+00 1.623334e+00 1.604087e+00 1.583754e+00
#> [31] 1.567891e+00 1.536249e+00 1.532775e+00 1.520808e+00 1.495698e+00
#> [36] 1.466973e+00 1.451911e+00 1.439230e+00 1.426326e+00 1.408866e+00
#> [41] 1.394070e+00 1.356280e+00 1.355607e+00 1.343218e+00 1.324939e+00
#> [46] 1.317448e+00 1.298042e+00 1.292172e+00 1.290126e+00 1.284486e+00
#> [51] 1.260741e+00 1.252454e+00 1.242871e+00 1.234479e+00 1.221911e+00
#> [56] 1.206628e+00 1.199803e+00 1.195127e+00 1.190011e+00 1.174547e+00
#> [61] 1.171232e+00 1.154458e+00 1.145637e+00 1.135996e+00 1.124914e+00
#> [66] 1.122782e+00 1.116625e+00 1.109650e+00 1.095992e+00 1.094403e+00
#> [71] 1.083500e+00 1.081434e+00 1.073638e+00 1.065964e+00 1.059762e+00
#> [76] 1.047794e+00 1.046608e+00 1.037150e+00 1.030342e+00 1.022820e+00
#> [81] 1.016640e+00 1.010146e+00 1.001855e+00 9.943502e-01 9.920359e-01
#> [86] 9.841591e-01 9.761104e-01 9.732790e-01 9.623114e-01 9.603170e-01
#> [91] 9.559378e-01 9.443870e-01 9.428462e-01 9.410785e-01 9.344836e-01
#> [96] 9.288014e-01 9.271981e-01 9.195127e-01 9.104633e-01 9.076714e-01
#> [101] 9.055111e-01 9.009656e-01 8.940822e-01 8.915336e-01 8.860811e-01
#> [106] 8.783154e-01 8.733380e-01 8.706939e-01 8.655068e-01 8.625876e-01
#> [111] 8.561297e-01 8.521523e-01 8.429825e-01 8.406524e-01 8.389560e-01
#> [116] 8.364509e-01 8.280351e-01 8.254479e-01 8.214640e-01 8.167350e-01
#> [121] 8.132213e-01 8.078696e-01 8.067777e-01 8.007288e-01 7.957929e-01
#> [126] 7.920924e-01 7.888844e-01 7.820410e-01 7.805644e-01 7.768805e-01
#> [131] 7.715894e-01 7.685875e-01 7.664157e-01 7.637809e-01 7.629644e-01
#> [136] 7.571623e-01 7.533174e-01 7.499022e-01 7.485470e-01 7.426886e-01
#> [141] 7.395636e-01 7.355301e-01 7.330848e-01 7.250294e-01 7.219595e-01
#> [146] 7.207059e-01 7.178711e-01 7.134139e-01 7.119358e-01 7.105775e-01
#> [151] 7.072117e-01 7.040330e-01 7.028589e-01 6.992496e-01 6.948058e-01
#> [156] 6.939748e-01 6.892388e-01 6.842039e-01 6.827935e-01 6.813387e-01
#> [161] 6.792254e-01 6.772769e-01 6.720927e-01 6.701258e-01 6.658420e-01
#> [166] 6.623950e-01 6.609654e-01 6.597883e-01 6.573117e-01 6.570087e-01
#> [171] 6.549812e-01 6.485347e-01 6.466902e-01 6.430801e-01 6.392046e-01
#> [176] 6.369904e-01 6.344709e-01 6.313753e-01 6.301461e-01 6.281418e-01
#> [181] 6.267177e-01 6.225714e-01 6.199600e-01 6.185427e-01 6.141035e-01
#> [186] 6.126771e-01 6.096630e-01 6.088156e-01 6.063807e-01 6.036823e-01
#> [191] 6.008063e-01 5.979322e-01 5.965868e-01 5.946803e-01 5.910745e-01
#> [196] 5.881630e-01 5.851488e-01 5.843792e-01 5.832505e-01 5.801898e-01
#> [201] 5.793297e-01 5.776320e-01 5.750328e-01 5.741570e-01 5.726129e-01
#> [206] 5.722598e-01 5.690460e-01 5.653365e-01 5.618373e-01 5.577842e-01
#> [211] 5.563350e-01 5.530227e-01 5.516199e-01 5.506381e-01 5.490014e-01
#> [216] 5.477387e-01 5.470153e-01 5.454412e-01 5.441161e-01 5.401694e-01
#> [221] 5.389369e-01 5.367966e-01 5.332473e-01 5.315658e-01 5.289262e-01
#> [226] 5.276807e-01 5.252845e-01 5.245833e-01 5.209357e-01 5.206105e-01
#> [231] 5.185780e-01 5.158014e-01 5.126761e-01 5.110360e-01 5.095218e-01
#> [236] 5.090777e-01 5.081830e-01 5.054780e-01 5.040159e-01 5.031494e-01
#> [241] 5.007658e-01 4.998503e-01 4.981423e-01 4.946367e-01 4.936244e-01
#> [246] 4.919041e-01 4.901219e-01 4.887549e-01 4.870942e-01 4.855973e-01
#> [251] 4.831134e-01 4.818930e-01 4.807614e-01 4.796236e-01 4.774337e-01
#> [256] 4.756689e-01 4.739295e-01 4.722662e-01 4.716409e-01 4.698954e-01
#> [261] 4.683940e-01 4.666922e-01 4.638996e-01 4.626640e-01 4.606707e-01
#> [266] 4.602921e-01 4.565806e-01 4.551472e-01 4.536993e-01 4.521929e-01
#> [271] 4.512901e-01 4.504168e-01 4.486301e-01 4.481631e-01 4.462478e-01
#> [276] 4.438517e-01 4.433398e-01 4.411723e-01 4.393198e-01 4.379883e-01
#> [281] 4.369864e-01 4.357161e-01 4.335241e-01 4.315384e-01 4.304626e-01
#> [286] 4.299509e-01 4.295972e-01 4.262579e-01 4.251349e-01 4.234177e-01
#> [291] 4.222948e-01 4.210002e-01 4.191833e-01 4.177143e-01 4.160603e-01
#> [296] 4.152285e-01 4.127429e-01 4.116214e-01 4.110062e-01 4.095753e-01
#> [301] 4.090932e-01 4.072502e-01 4.065672e-01 4.042008e-01 4.035206e-01
#> [306] 4.023567e-01 4.017920e-01 4.007671e-01 3.982198e-01 3.976655e-01
#> [311] 3.957143e-01 3.947265e-01 3.935244e-01 3.916946e-01 3.909234e-01
#> [316] 3.900114e-01 3.877642e-01 3.858114e-01 3.847948e-01 3.835150e-01
#> [321] 3.819818e-01 3.813703e-01 3.803031e-01 3.791932e-01 3.779444e-01
#> [326] 3.770000e-01 3.760075e-01 3.751111e-01 3.737653e-01 3.721652e-01
#> [331] 3.718862e-01 3.705055e-01 3.691068e-01 3.674795e-01 3.651444e-01
#> [336] 3.647957e-01 3.633445e-01 3.622535e-01 3.603617e-01 3.600399e-01
#> [341] 3.593517e-01 3.589410e-01 3.572479e-01 3.566297e-01 3.550247e-01
#> [346] 3.531792e-01 3.522962e-01 3.520084e-01 3.504945e-01 3.474721e-01
#> [351] 3.459154e-01 3.446735e-01 3.443787e-01 3.423760e-01 3.416633e-01
#> [356] 3.406604e-01 3.400317e-01 3.391539e-01 3.374578e-01 3.350315e-01
#> [361] 3.347968e-01 3.337742e-01 3.324674e-01 3.315236e-01 3.308446e-01
#> [366] 3.291645e-01 3.281053e-01 3.262903e-01 3.253731e-01 3.242374e-01
#> [371] 3.228902e-01 3.220174e-01 3.211667e-01 3.197456e-01 3.191225e-01
#> [376] 3.185557e-01 3.173933e-01 3.157462e-01 3.147677e-01 3.132461e-01
#> [381] 3.129181e-01 3.121474e-01 3.096893e-01 3.082353e-01 3.073252e-01
#> [386] 3.063280e-01 3.050632e-01 3.046753e-01 3.032957e-01 3.014308e-01
#> [391] 3.006672e-01 2.990869e-01 2.986001e-01 2.965456e-01 2.957026e-01
#> [396] 2.950281e-01 2.936329e-01 2.926258e-01 2.924754e-01 2.913299e-01
#> [401] 2.900980e-01 2.883983e-01 2.875028e-01 2.861673e-01 2.844567e-01
#> [406] 2.840259e-01 2.835168e-01 2.828999e-01 2.824800e-01 2.808992e-01
#> [411] 2.790587e-01 2.781097e-01 2.777240e-01 2.764665e-01 2.759602e-01
#> [416] 2.754744e-01 2.743536e-01 2.726297e-01 2.721738e-01 2.699852e-01
#> [421] 2.694801e-01 2.670432e-01 2.662954e-01 2.650347e-01 2.646827e-01
#> [426] 2.635966e-01 2.617783e-01 2.601196e-01 2.590181e-01 2.574992e-01
#> [431] 2.565837e-01 2.562533e-01 2.544652e-01 2.524027e-01 2.521701e-01
#> [436] 2.508377e-01 2.504753e-01 2.487148e-01 2.476842e-01 2.467597e-01
#> [441] 2.456598e-01 2.448734e-01 2.434520e-01 2.425910e-01 2.412996e-01
#> [446] 2.391077e-01 2.370666e-01 2.353612e-01 2.344336e-01 2.336907e-01
#> [451] 2.314153e-01 2.303490e-01 2.295914e-01 2.288472e-01 2.269513e-01
#> [456] 2.249915e-01 2.245771e-01 2.239882e-01 2.222578e-01 2.211533e-01
#> [461] 2.181852e-01 2.177548e-01 2.168754e-01 2.142710e-01 2.135207e-01
#> [466] 2.109614e-01 2.101698e-01 2.098699e-01 2.083076e-01 2.073489e-01
#> [471] 2.053383e-01 2.032876e-01 1.991847e-01 1.988649e-01 1.963824e-01
#> [476] 1.927598e-01 1.916131e-01 1.903535e-01 1.838843e-01 1.829154e-01
#> [481] 1.813119e-01 1.770114e-01 1.690306e-01 1.657955e-01 1.610450e-01
#> [486] 1.582204e-01 1.515032e-01 1.464400e-01 7.595550e-02 1.445517e-13
#>
#> Rotation (n x k) = (5078 x 50):
#> PC1 PC2 PC3 PC4
#> dyscalculia 8.123147e-03 3.434641e-02 -6.835307e-03 3.620127e-03
#> and 2.905097e-01 -2.284773e-01 -4.524599e-01 4.172579e-01
#> the 7.122090e-01 3.043340e-01 5.670838e-02 -2.755185e-01
#> minicalculator -2.239215e-04 1.429879e-03 -3.287941e-05 2.201319e-04
#> alp -3.358822e-04 2.144819e-03 -4.931911e-05 3.301978e-04
#> program 1.528774e-02 6.624131e-03 5.140127e-02 5.987647e-03
#> arithmetic 1.091652e-03 2.249825e-02 1.421009e-02 1.114105e-02
#> remedial 2.711589e-03 5.546973e-03 1.345337e-03 9.555914e-03
#> teaching 1.378220e-02 -4.057525e-02 -9.719544e-03 -4.299748e-02
#> education 2.133513e-02 -6.931558e-03 -4.982163e-02 7.968249e-02
#> of 4.076348e-01 1.983537e-01 1.636642e-01 -1.371270e-03
#> learning 8.492141e-02 -1.248120e-01 3.402872e-01 4.776740e-01
#> disabled 1.397898e-02 3.751074e-02 6.243532e-02 8.980377e-02
#> children 2.709883e-02 1.077521e-01 -4.778265e-02 5.579009e-02
#> calculators 2.835459e-03 -9.162430e-04 -4.126678e-04 -2.456518e-02
#> study 7.591571e-02 -2.891050e-02 2.862671e-02 -6.110595e-02
#> fractions -2.413915e-03 -1.518366e-02 1.198417e-02 -4.459038e-02
#> difficulties 1.085118e-02 1.534086e-03 5.928954e-03 1.926284e-02
#> calculating 6.742862e-04 -1.018058e-03 -1.380931e-03 -3.825576e-03
#> machines -4.730908e-04 1.381725e-03 -4.351358e-04 -1.069368e-03
#> PC5 PC6 PC7 PC8
#> dyscalculia -8.518113e-03 4.408165e-02 -7.608020e-03 -2.983714e-02
#> and 3.110757e-01 -1.131147e-01 7.146172e-03 3.147001e-01
#> the -8.094097e-02 -5.171942e-02 -3.346250e-01 8.109772e-03
#> minicalculator -5.356746e-04 6.249111e-04 -7.147454e-04 5.728822e-04
#> alp -8.035119e-04 9.373667e-04 -1.072118e-03 8.593234e-04
#> program 3.363432e-02 -4.878602e-02 -1.291003e-02 1.827118e-02
#> arithmetic 8.392728e-03 1.342849e-02 -1.035012e-02 -2.476098e-03
#> remedial -2.670302e-03 1.106635e-02 -1.876078e-02 -4.466639e-03
#> teaching -3.421908e-03 1.972610e-02 2.871404e-02 -6.272162e-02
#> education -8.788030e-02 -1.784698e-01 5.412252e-02 1.046784e-01
#> of -7.490927e-02 1.769726e-01 6.691608e-01 1.858406e-01
#> learning -2.315376e-01 4.949256e-01 -2.456717e-01 4.130822e-02
#> disabled 2.879765e-02 1.494249e-03 5.035938e-03 -2.309148e-03
#> children 4.763912e-02 1.777143e-01 9.782393e-03 -3.981977e-02
#> calculators -1.518972e-02 -1.993583e-02 -1.224997e-02 9.213222e-02
#> study -6.664685e-03 -2.907486e-02 -3.113131e-02 1.697815e-02
#> fractions -1.009165e-02 1.047044e-02 -1.188085e-02 4.672325e-03
#> difficulties -5.088867e-03 4.329691e-02 -2.014528e-02 -1.118554e-03
#> calculating -2.702786e-04 3.294396e-03 4.186318e-04 1.509402e-04
#> machines -3.708257e-04 2.502409e-04 -1.091851e-04 -7.019649e-04
#> PC9 PC10 PC11 PC12
#> dyscalculia -4.837983e-03 -2.108456e-02 2.104386e-02 -1.188665e-03
#> and -1.250335e-01 -8.104706e-02 -1.649360e-01 -2.303596e-01
#> the 1.220980e-01 1.621602e-02 -2.318886e-01 6.943118e-02
#> minicalculator -5.347167e-04 6.643611e-04 -2.288239e-04 2.177146e-05
#> alp -8.020751e-04 9.965417e-04 -3.432358e-04 3.265719e-05
#> program -2.759031e-02 -5.098015e-03 1.498852e-02 3.709115e-02
#> arithmetic -5.444593e-03 -3.267206e-02 3.639029e-03 -1.696330e-02
#> remedial -8.561362e-04 9.510310e-03 8.590700e-03 -2.414216e-02
#> teaching 2.716930e-02 6.508162e-02 -6.924634e-02 1.515410e-02
#> education 1.958923e-01 3.493998e-02 9.877309e-02 8.557598e-02
#> of -8.270446e-02 1.122305e-04 2.419738e-01 -8.357516e-03
#> learning -1.906675e-01 1.730333e-01 -4.515785e-02 8.578301e-03
#> disabled -7.688765e-02 6.399587e-02 3.561697e-02 -8.026518e-02
#> children 7.614519e-03 -1.464911e-01 6.683102e-03 3.308939e-02
#> calculators -2.033577e-04 -8.253252e-03 1.893240e-02 -1.433354e-02
#> study -8.057784e-02 2.837616e-02 3.846932e-02 9.160346e-03
#> fractions -3.488343e-03 -1.249577e-02 -2.388512e-03 -4.511306e-02
#> difficulties 1.989564e-02 -5.363615e-03 2.033541e-02 -5.359926e-03
#> calculating -1.292133e-03 -4.819486e-03 -4.599656e-03 7.454358e-05
#> machines -1.286009e-03 1.507248e-03 7.511682e-04 2.609605e-04
#> PC13 PC14 PC15 PC16
#> dyscalculia -9.826865e-03 -1.139473e-02 2.375906e-02 -2.041144e-04
#> and 1.186116e-01 4.975345e-02 -5.924944e-02 1.960956e-02
#> the 1.741669e-02 -1.527181e-02 3.948965e-02 -5.319925e-02
#> minicalculator -4.453942e-04 9.468749e-04 -6.154501e-04 -5.153859e-04
#> alp -6.680913e-04 1.420312e-03 -9.231752e-04 -7.730788e-04
#> program 3.612009e-03 -9.036126e-04 -1.775656e-02 3.065474e-02
#> arithmetic -1.557782e-02 -1.209143e-02 -5.681527e-04 -6.456692e-03
#> remedial 4.456661e-03 3.027971e-02 -2.320228e-03 1.047919e-06
#> teaching 1.914065e-02 8.526546e-02 3.275603e-02 -1.129348e-01
#> education 2.306432e-01 1.984019e-01 4.179943e-02 -1.949843e-01
#> of -3.338884e-02 4.808436e-02 -1.333015e-01 1.927593e-02
#> learning 5.187865e-02 8.074989e-02 3.501997e-02 4.556663e-04
#> disabled 3.341848e-02 -2.118448e-02 -1.636755e-02 -1.882455e-02
#> children -3.477076e-02 -1.418761e-01 5.323297e-02 -1.617039e-02
#> calculators 5.169591e-03 -7.053637e-02 2.107054e-02 8.397619e-03
#> study 4.944313e-02 -3.285463e-03 1.189003e-01 5.427435e-02
#> fractions 5.288890e-04 4.770201e-02 -4.376492e-02 -1.510499e-02
#> difficulties 1.746618e-02 -7.878430e-03 1.021097e-03 3.223167e-02
#> calculating 3.292511e-03 -2.385856e-05 -2.630934e-03 4.559355e-04
#> machines 1.640596e-04 3.590792e-04 1.306054e-03 -2.728334e-04
#> PC17 PC18 PC19 PC20
#> dyscalculia -4.484598e-02 -1.002895e-02 5.931592e-02 3.168805e-02
#> and -4.469531e-02 -1.461372e-01 1.089681e-01 -2.014383e-02
#> the -3.771500e-02 -9.507035e-02 2.171183e-02 -2.441729e-02
#> minicalculator 1.915356e-05 -2.632885e-04 6.864738e-04 -9.493996e-04
#> alp 2.873033e-05 -3.949328e-04 1.029711e-03 -1.424099e-03
#> program 2.455291e-02 -3.858448e-03 7.008953e-02 1.976113e-02
#> arithmetic -1.753400e-02 2.450651e-03 1.106956e-02 5.073607e-03
#> remedial -2.523095e-03 1.151749e-02 7.045528e-03 -9.775209e-03
#> teaching 3.839099e-02 -4.015231e-02 2.829345e-04 4.271296e-02
#> education 3.417267e-01 -4.505579e-02 -7.543353e-02 -1.367413e-01
#> of -5.445737e-02 -1.258619e-02 -7.693603e-02 1.532477e-03
#> learning -8.362836e-02 5.721263e-04 1.007821e-02 -6.009479e-02
#> disabled 2.489228e-02 3.157515e-02 -7.251739e-02 1.735845e-02
#> children -4.833142e-02 8.741470e-02 7.931680e-02 -7.796518e-02
#> calculators 6.205399e-02 2.328751e-02 3.133844e-02 -2.939797e-02
#> study -1.170001e-01 1.050327e-01 -2.145850e-02 6.427163e-02
#> fractions -2.121362e-02 2.105349e-02 -3.718585e-03 4.748787e-03
#> difficulties 6.568750e-03 -6.387987e-03 3.255505e-02 1.613134e-02
#> calculating 3.831660e-03 5.083883e-03 7.044829e-04 5.958202e-03
#> machines 1.688546e-04 -5.112019e-04 4.629020e-04 -3.576136e-04
#> PC21 PC22 PC23 PC24
#> dyscalculia -1.575124e-02 4.765171e-02 1.676304e-02 -1.270040e-02
#> and 9.762065e-03 -5.885825e-02 8.889584e-02 4.245743e-02
#> the 1.051495e-01 -3.225326e-02 1.349422e-02 1.802594e-02
#> minicalculator 1.964195e-03 -2.131994e-03 1.385813e-04 -6.275872e-04
#> alp 2.946292e-03 -3.197991e-03 2.078720e-04 -9.413807e-04
#> program 1.466349e-03 4.395769e-02 -1.792981e-02 1.326020e-02
#> arithmetic 1.354666e-02 -3.006584e-02 -1.384899e-02 -1.425622e-03
#> remedial -6.181883e-03 9.734426e-03 4.613731e-04 -9.870318e-03
#> teaching 1.106818e-01 9.879710e-03 1.145676e-01 -3.953182e-02
#> education 1.125334e-01 -9.041635e-02 -1.992107e-01 -2.334926e-01
#> of -6.008702e-02 -3.387715e-02 5.911923e-02 -2.014078e-02
#> learning 1.514439e-01 3.708448e-02 2.820422e-02 4.583256e-03
#> disabled 2.680198e-02 -9.652857e-02 -6.894827e-02 5.467862e-02
#> children -6.060316e-02 8.860028e-04 -1.377904e-01 -1.371355e-01
#> calculators -6.021286e-02 -2.500866e-02 2.253316e-02 6.139321e-02
#> study -3.148589e-02 1.225439e-02 -1.749135e-02 -4.087033e-02
#> fractions -3.034144e-02 -1.403727e-02 -2.943323e-02 7.151391e-03
#> difficulties 1.064511e-02 -2.355987e-02 3.855599e-04 -1.162741e-02
#> calculating 1.998379e-03 -4.223168e-03 2.760354e-03 7.136614e-04
#> machines 2.889324e-03 -4.431027e-04 8.884553e-04 9.560954e-04
#> PC25 PC26 PC27 PC28
#> dyscalculia -2.831547e-02 -2.450996e-02 1.947569e-02 -1.079038e-03
#> and 2.264262e-02 -6.491807e-03 -4.665831e-02 1.436098e-02
#> the 1.754495e-02 3.566124e-02 -3.225968e-02 -8.626582e-02
#> minicalculator 6.994210e-04 -3.672483e-03 2.700182e-03 -9.632841e-05
#> alp 1.049131e-03 -5.508725e-03 4.050273e-03 -1.444926e-04
#> program -4.248708e-02 -2.590701e-02 9.481961e-02 -1.242109e-02
#> arithmetic -1.342879e-03 -1.090353e-02 1.354411e-02 2.450398e-02
#> remedial -2.970011e-03 -1.719701e-02 1.348936e-02 -4.587094e-03
#> teaching -1.610652e-02 -1.900453e-01 -4.925427e-02 -5.876595e-03
#> education 2.660188e-02 -1.225322e-01 1.706633e-01 3.706435e-02
#> of 2.887823e-02 -4.765480e-02 -1.505439e-02 9.042786e-02
#> learning 1.556928e-02 -2.219364e-02 9.285950e-02 -5.790268e-02
#> disabled 1.292210e-03 -1.321961e-01 1.580807e-01 -1.326944e-02
#> children -1.965238e-02 -2.351348e-01 7.413817e-02 -1.153756e-01
#> calculators 5.129810e-02 -7.441841e-02 -2.136648e-02 4.202146e-02
#> study -3.780592e-02 6.062124e-02 -3.819670e-02 1.101956e-01
#> fractions 2.338171e-02 -3.741841e-02 6.102104e-02 6.679489e-03
#> difficulties 3.626243e-02 8.699180e-03 -7.992898e-03 1.885493e-02
#> calculating 2.057408e-03 -8.393343e-03 3.741881e-03 -6.913376e-04
#> machines -3.844806e-04 -3.562887e-03 3.248926e-05 -9.021156e-05
#> PC29 PC30 PC31 PC32
#> dyscalculia 3.876940e-02 8.991376e-02 -6.084627e-02 -4.881428e-02
#> and 1.765885e-02 4.770524e-02 -1.430400e-02 1.781868e-02
#> the 2.916074e-02 -1.600442e-02 1.804129e-02 -6.060371e-03
#> minicalculator -4.513115e-04 3.718926e-04 -1.151210e-03 5.682321e-04
#> alp -6.769673e-04 5.578390e-04 -1.726815e-03 8.523481e-04
#> program 5.429623e-02 3.733585e-03 -9.251954e-02 -1.698877e-02
#> arithmetic 1.998367e-02 4.368260e-03 -3.437296e-02 -1.573146e-02
#> remedial -3.182553e-02 3.329856e-03 8.904330e-03 1.077680e-02
#> teaching -8.150132e-02 -1.782497e-03 -8.633512e-02 4.084443e-02
#> education -8.918831e-02 7.473691e-02 7.363914e-02 -7.123758e-02
#> of 2.340172e-02 -3.054121e-02 3.643771e-02 2.315676e-02
#> learning -3.815753e-02 4.607673e-02 6.928419e-02 -2.725882e-02
#> disabled -1.073352e-02 -1.166162e-01 -2.517423e-02 5.477412e-02
#> children 1.627625e-01 2.610756e-01 -1.582968e-01 1.472748e-01
#> calculators -6.766339e-02 -2.638574e-02 -7.170234e-02 -2.696272e-02
#> study -8.809997e-02 2.652458e-01 -5.404184e-02 -6.899376e-02
#> fractions 7.467116e-02 1.564342e-02 4.141357e-02 3.455449e-02
#> difficulties 4.404004e-02 -5.826459e-03 4.425248e-02 -2.355428e-02
#> calculating 3.470654e-03 -2.277920e-03 -7.080649e-04 -1.432040e-03
#> machines -1.932715e-04 2.121893e-04 -6.271173e-04 -1.120441e-03
#> PC33 PC34 PC35 PC36
#> dyscalculia 6.917357e-05 1.088019e-02 2.167753e-02 -9.013227e-03
#> and 4.557066e-02 4.394395e-02 1.085596e-02 -2.616519e-02
#> the -8.889952e-03 6.368883e-02 -1.075720e-03 -3.113897e-02
#> minicalculator 1.953093e-03 -1.439249e-03 2.939587e-03 5.228419e-04
#> alp 2.929640e-03 -2.158873e-03 4.409381e-03 7.842628e-04
#> program 2.248513e-02 -6.597485e-02 5.064436e-02 -4.924967e-02
#> arithmetic 7.186258e-03 -1.162513e-02 2.551094e-02 1.304531e-02
#> remedial -4.407871e-03 -4.985186e-03 8.784128e-03 -5.724439e-02
#> teaching 4.404603e-02 -1.480893e-01 3.574952e-02 -6.965043e-02
#> education 3.845249e-03 7.015258e-02 -7.409695e-02 -8.734420e-02
#> of 1.128782e-01 -4.856143e-02 1.475448e-02 2.711591e-02
#> learning 2.270686e-02 -6.658835e-03 -1.103335e-01 1.966102e-02
#> disabled 1.794709e-02 4.816807e-02 1.389492e-01 -2.486398e-02
#> children -4.269806e-02 2.007106e-01 8.502947e-02 5.040574e-02
#> calculators -3.449522e-03 -1.056994e-01 -1.584794e-01 2.998063e-02
#> study -1.825014e-02 -9.177706e-02 -1.817223e-02 -3.706466e-04
#> fractions 1.063812e-01 -9.994530e-03 4.644219e-02 1.215488e-02
#> difficulties 4.311647e-03 -2.069499e-02 -1.352601e-02 4.275012e-03
#> calculating -2.003844e-03 -8.214514e-03 -1.804376e-03 9.207620e-03
#> machines 1.155232e-03 -1.669658e-03 3.389054e-03 -2.312018e-03
#> PC37 PC38 PC39 PC40
#> dyscalculia 2.072533e-02 -1.478771e-02 5.165900e-02 3.092463e-02
#> and -3.843449e-02 4.951828e-02 -7.815735e-04 -8.379532e-03
#> the 4.197343e-02 -9.780191e-03 -4.320020e-02 1.609748e-02
#> minicalculator 7.087540e-04 -1.270506e-03 -1.779441e-03 1.155198e-03
#> alp 1.063131e-03 -1.905760e-03 -2.669161e-03 1.732797e-03
#> program -2.160723e-01 -4.171992e-03 -1.175228e-01 -4.999756e-03
#> arithmetic -1.470519e-02 3.617566e-02 -1.819352e-03 2.623219e-02
#> remedial 3.453787e-03 -9.109581e-03 5.924766e-03 2.422498e-02
#> teaching 1.916710e-01 -3.461853e-02 -3.751357e-02 -1.057391e-01
#> education -4.932844e-03 -1.179589e-01 -3.637489e-02 1.206003e-01
#> of -1.663555e-02 6.368757e-03 4.613894e-02 -3.383032e-02
#> learning 8.384851e-02 -4.680325e-02 1.552686e-03 -2.643213e-03
#> disabled 3.122459e-02 8.149829e-03 -8.303884e-02 1.064934e-02
#> children 1.792486e-02 7.807851e-02 5.104469e-02 1.334061e-01
#> calculators 1.752997e-01 2.905935e-02 -8.405635e-02 9.774000e-03
#> study -1.188684e-01 -5.980633e-02 -9.847510e-03 1.431246e-01
#> fractions 1.516880e-03 6.093703e-03 6.485088e-02 -1.060338e-02
#> difficulties -3.067892e-02 3.606136e-02 4.907558e-02 -2.468498e-02
#> calculating 1.912300e-03 2.600555e-03 3.393575e-03 2.872732e-03
#> machines 5.602079e-04 -1.793639e-03 1.860155e-03 -2.611135e-05
#> PC41 PC42 PC43 PC44
#> dyscalculia 1.434474e-03 5.511421e-02 5.045758e-02 7.026059e-03
#> and 1.219027e-02 -1.401024e-02 1.795848e-02 4.428903e-04
#> the -1.274755e-02 -6.780770e-03 -2.008298e-02 -3.465750e-02
#> minicalculator -1.031167e-03 3.235821e-04 -1.955904e-04 7.366261e-04
#> alp -1.546751e-03 4.853731e-04 -2.933856e-04 1.104939e-03
#> program -1.042695e-01 -8.483477e-02 4.282731e-02 -3.921612e-02
#> arithmetic -3.201327e-03 1.075744e-02 3.234436e-02 4.282705e-02
#> remedial 3.166802e-02 -3.165853e-02 4.414795e-03 9.144869e-03
#> teaching -2.736895e-02 -6.757958e-02 8.776898e-02 -1.564869e-02
#> education 7.698236e-02 5.582855e-02 2.863792e-02 5.686179e-02
#> of 2.479063e-03 -1.771518e-03 -2.695033e-02 -1.605157e-02
#> learning -2.313934e-02 1.661877e-02 9.997889e-03 -3.138442e-02
#> disabled -6.470584e-02 5.088572e-02 -4.637900e-02 1.134836e-01
#> children 4.006443e-02 -1.363323e-01 5.951508e-03 -1.273274e-02
#> calculators 1.071678e-01 1.900387e-02 -9.562367e-03 -3.895455e-02
#> study 2.615429e-02 1.338279e-02 1.126025e-01 7.132126e-02
#> fractions 7.544432e-03 -7.593500e-02 8.749519e-03 -3.720069e-02
#> difficulties -4.988628e-02 1.459940e-02 -1.125060e-02 -2.182360e-02
#> calculating 1.775891e-03 -3.588367e-03 1.061837e-02 -2.297128e-04
#> machines 8.773709e-04 -1.525039e-05 -1.313746e-03 9.602678e-04
#> PC45 PC46 PC47 PC48
#> dyscalculia 9.651257e-03 8.267636e-03 -4.714261e-03 -6.824314e-02
#> and 2.289899e-02 2.333510e-03 -1.569669e-02 -1.780171e-02
#> the -1.476324e-02 -1.783537e-02 6.728918e-02 -3.659008e-03
#> minicalculator -9.582784e-04 2.569676e-04 -8.829212e-04 3.095984e-04
#> alp -1.437418e-03 3.854514e-04 -1.324382e-03 4.643976e-04
#> program -2.834847e-02 -1.236971e-03 8.053667e-02 7.336115e-02
#> arithmetic 7.209315e-03 7.659909e-04 7.070788e-04 6.267110e-04
#> remedial 1.035013e-02 2.151504e-02 2.543584e-02 -2.041754e-02
#> teaching 3.806135e-02 1.652133e-01 -6.843776e-02 -1.114837e-01
#> education -3.058875e-02 1.211075e-02 -1.691230e-01 8.225861e-02
#> of 6.855860e-02 1.118669e-03 -3.150436e-02 2.701362e-02
#> learning -3.005010e-02 1.497885e-03 -2.069965e-02 -2.968480e-02
#> disabled -9.114227e-02 -2.108441e-02 3.662867e-02 2.875538e-02
#> children -5.115683e-02 7.333215e-02 -8.029091e-03 1.415032e-01
#> calculators -8.402337e-02 -5.768600e-02 3.966611e-03 7.299160e-02
#> study -5.120298e-02 -8.810153e-02 -1.132366e-01 -6.718208e-02
#> fractions -1.873662e-02 -1.971577e-03 -5.088310e-02 -1.632300e-03
#> difficulties 1.473028e-02 -8.623288e-02 -5.855094e-03 -1.109068e-02
#> calculating 1.024007e-02 -5.995016e-04 8.282165e-03 -1.180926e-03
#> machines 2.830849e-03 4.862742e-04 1.217511e-03 5.168474e-04
#> PC49 PC50
#> dyscalculia 3.283503e-02 -2.212451e-02
#> and -1.002673e-02 -7.135179e-03
#> the -3.201748e-03 -3.201859e-03
#> minicalculator -1.460967e-05 2.488856e-03
#> alp -2.191450e-05 3.733285e-03
#> program 4.001096e-02 -2.070542e-02
#> arithmetic 3.329551e-02 2.573216e-02
#> remedial 3.951300e-02 2.110226e-02
#> teaching -7.700996e-02 8.309827e-03
#> education -1.000201e-02 3.970083e-02
#> of 1.279641e-02 -1.462333e-02
#> learning -1.100013e-03 1.229654e-02
#> disabled -2.287913e-02 3.165276e-02
#> children 6.553890e-02 1.094896e-01
#> calculators 9.214095e-03 -1.041434e-01
#> study -8.360534e-02 1.030065e-01
#> fractions -3.705606e-02 3.335453e-02
#> difficulties -4.741557e-02 -2.976131e-02
#> calculating 1.533855e-03 -4.026449e-03
#> machines -2.156709e-03 2.338337e-03
#> [ reached 'max' / getOption("max.print") -- omitted 5058 rows ]
#>
#> $umap_params
#> $umap_params$n_neighbors
#> [1] 15
#>
#> $umap_params$min_dist
#> [1] 0.1
#>
#> $umap_params$metric
#> [1] "cosine"
#>
#>
#> $execution_time
#> [1] 9.122437
#>
#> $timestamp
#> [1] "2026-08-14 23:37:00 CDT"
#>
#> $seed
#> [1] 123
#>