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t-SNE: KL divergence between joint probabilities in high- and low-dim

Source: R/geron_w4d_native.R
morie_geron_tsne.Rd

High-d affinities: perplexity-calibrated Gaussians, symmetrised p_ij=(p_j|i+p_i|j)/2n. Low-d: Student-t kernel q_ij ~ (1+||yi-yj||^2)^-1. KL(P||Q) minimised by momentum gradient descent.

Usage

morie_geron_tsne(
  X,
  n_components = 2,
  perplexity = 5,
  seed = 0,
  n_iter = 300,
  lr = NULL,
  momentum = 0.8
)

Arguments

X

Data (n, d), n >= 3.

n_components, perplexity, seed, n_iter, lr, momentum

As in Python original.

Value

list with embedding, P, Q, kl, kl_curve, betas, perplexity, estimate, n, method.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_geron_tsne(V)
#> $embedding
#>             [,1]       [,2]
#> [1,]  0.46722577 -2.4130210
#> [2,]  0.94509963 -1.6811166
#> [3,]  0.08223869 -1.2588249
#> [4,]  0.22921690 -0.3766254
#> [5,] -0.01806208  0.4452333
#> [6,] -0.62743788  1.0998626
#> [7,] -0.14085495  1.9281720
#> [8,] -0.94325634  2.2748701
#> 
#> $P
#>             [,1]        [,2]        [,3]        [,4]        [,5]        [,6]
#> [1,] 0.000000000 0.038201807 0.027157826 0.014574913 0.007774085 0.004165839
#> [2,] 0.038201807 0.000000000 0.035423607 0.022368402 0.010728529 0.005232057
#> [3,] 0.027157826 0.035423607 0.000000000 0.036577752 0.019801267 0.008906815
#> [4,] 0.014574913 0.022368402 0.036577752 0.000000000 0.037805597 0.019801267
#> [5,] 0.007774085 0.010728529 0.019801267 0.037805597 0.000000000 0.036577752
#> [6,] 0.004165839 0.005232057 0.008906815 0.019801267 0.036577752 0.000000000
#> [7,] 0.002330051 0.003140869 0.005232057 0.010728529 0.022368402 0.035423607
#> [8,] 0.001474452 0.002330051 0.004165839 0.007774085 0.014574913 0.027157826
#>             [,7]        [,8]
#> [1,] 0.002330051 0.001474452
#> [2,] 0.003140869 0.002330051
#> [3,] 0.005232057 0.004165839
#> [4,] 0.010728529 0.007774085
#> [5,] 0.022368402 0.014574913
#> [6,] 0.035423607 0.027157826
#> [7,] 0.000000000 0.038201807
#> [8,] 0.038201807 0.000000000
#> 
#> $Q
#>             [,1]        [,2]        [,3]        [,4]        [,5]        [,6]
#> [1,] 0.000000000 0.038459134 0.027352114 0.013037959 0.007213489 0.004666443
#> [2,] 0.038459134 0.000000000 0.035282740 0.021107602 0.010519969 0.006053845
#> [3,] 0.027352114 0.035282740 0.000000000 0.037693513 0.017334165 0.009600012
#> [4,] 0.013037959 0.021107602 0.037693513 0.000000000 0.039067027 0.017334165
#> [5,] 0.007213489 0.010519969 0.017334165 0.039067027 0.000000000 0.037693513
#> [6,] 0.004666443 0.006053845 0.009600012 0.017334165 0.037693513 0.000000000
#> [7,] 0.003355990 0.004461566 0.006053845 0.010519969 0.021107602 0.035282740
#> [8,] 0.002717469 0.003355990 0.004666443 0.007213489 0.013037959 0.027352114
#>             [,7]        [,8]
#> [1,] 0.003355990 0.002717469
#> [2,] 0.004461566 0.003355990
#> [3,] 0.006053845 0.004666443
#> [4,] 0.010519969 0.007213489
#> [5,] 0.021107602 0.013037959
#> [6,] 0.035282740 0.027352114
#> [7,] 0.000000000 0.038459134
#> [8,] 0.038459134 0.000000000
#> 
#> $kl
#> [1] 0.003595633
#> 
#> $kl_curve
#>   [1] 0.289613955 0.289587434 0.289391544 0.287773783 0.274695091 0.200134098
#>   [7] 0.068767697 0.017887813 0.010529689 0.013321651 0.017754520 0.024044496
#>  [13] 0.026944979 0.027275464 0.029212698 0.028156649 0.025663059 0.022193415
#>  [19] 0.017212371 0.012116205 0.009836132 0.011538866 0.011663709 0.008320976
#>  [25] 0.005772704 0.005210120 0.005363949 0.005876784 0.006264343 0.005955752
#>  [31] 0.005315379 0.004858062 0.004597942 0.004479824 0.004487053 0.004491680
#>  [37] 0.004419850 0.004355561 0.004315258 0.004251111 0.004169484 0.004093012
#>  [43] 0.004044848 0.004030949 0.004024983 0.004003621 0.003969671 0.003935002
#>  [49] 0.003904687 0.003882028 0.003865589 0.003848307 0.003829670 0.003813196
#>  [55] 0.003798022 0.003782716 0.003767982 0.003754109 0.003741171 0.003729802
#>  [61] 0.003719736 0.003710045 0.003700568 0.003691553 0.003683145 0.003675475
#>  [67] 0.003668482 0.003662003 0.003655996 0.003650454 0.003645344 0.003640652
#>  [73] 0.003636340 0.003632359 0.003628715 0.003625414 0.003622418 0.003619695
#>  [79] 0.003617223 0.003614971 0.003612926 0.003611080 0.003609417 0.003607919
#>  [85] 0.003606571 0.003605361 0.003604275 0.003603303 0.003602433 0.003601656
#>  [91] 0.003600961 0.003600342 0.003599792 0.003599302 0.003598868 0.003598483
#>  [97] 0.003598141 0.003597839 0.003597572 0.003597335 0.003597127 0.003596943
#> [103] 0.003596781 0.003596639 0.003596513 0.003596403 0.003596306 0.003596222
#> [109] 0.003596147 0.003596082 0.003596025 0.003595975 0.003595931 0.003595893
#> [115] 0.003595859 0.003595830 0.003595805 0.003595782 0.003595763 0.003595746
#> [121] 0.003595731 0.003595719 0.003595707 0.003595698 0.003595689 0.003595682
#> [127] 0.003595675 0.003595670 0.003595665 0.003595661 0.003595657 0.003595654
#> [133] 0.003595651 0.003595649 0.003595647 0.003595645 0.003595643 0.003595642
#> [139] 0.003595641 0.003595640 0.003595639 0.003595638 0.003595638 0.003595637
#> [145] 0.003595637 0.003595636 0.003595636 0.003595635 0.003595635 0.003595635
#> [151] 0.003595635 0.003595634 0.003595634 0.003595634 0.003595634 0.003595634
#> [157] 0.003595634 0.003595634 0.003595634 0.003595634 0.003595634 0.003595634
#> [163] 0.003595634 0.003595634 0.003595633 0.003595633 0.003595633 0.003595633
#> [169] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [175] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [181] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [187] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [193] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [199] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [205] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [211] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [217] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [223] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [229] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [235] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [241] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [247] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [253] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [259] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [265] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [271] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [277] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [283] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [289] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [295] 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633 0.003595633
#> [301] 0.003595633
#> 
#> $betas
#> [1] 0.06922913 0.10103989 0.17230988 0.23783875 0.23783875 0.17230988 0.10103989
#> [8] 0.06922913
#> 
#> $perplexity
#> [1] 5
#> 
#> $estimate
#> [1] 0.003595633
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "t-SNE: perplexity-calibrated Gaussian P, Student-t Q, KL minimised by gradient descent with momentum"
#>