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UMAP: uniform manifold approximation, preserves local and some global structure

Source: R/geron_w4d_native.R
morie_geron_umap.Rd

Smoothed-kNN fuzzy graph (rho = nearest-neighbour distance, sigma solved by binary search to hit log2(k)), fuzzy union W = A+A'-A.A', low-d kernel v = 1/(1+a*d^2b) fitted via morie_geron_fit_ab, exact fuzzy cross-entropy minimised by gradient descent (gradient clipped at norm 4).

Usage

morie_geron_umap(
  X,
  n_components = 2,
  n_neighbors = 3,
  min_dist = 0.1,
  seed = 0,
  n_iter = 300,
  lr = 0.1
)

Arguments

X

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

n_components, n_neighbors, min_dist, seed, n_iter, lr

As in Python original.

Value

list with embedding, graph, directed_graph, a, b, ab_sse, cross_entropy, ce_curve, rho, sigma, estimate, n, method.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_geron_umap(V)
#> $embedding
#>             [,1]       [,2]
#> [1,]  0.39145394 -1.6863766
#> [2,]  0.35532731 -1.5371211
#> [3,]  0.22843760 -1.0128870
#> [4,]  0.02705371 -0.1809059
#> [5,] -0.17278766  0.6446648
#> [6,] -0.37418892  1.4766417
#> [7,] -0.50109518  2.0008718
#> [8,] -0.53722714  2.1501260
#> 
#> $graph
#>           [,1] [,2]      [,3]      [,4]      [,5]      [,6] [,7]      [,8]
#> [1,] 0.0000000    1 0.4137583 0.1711959 0.0000000 0.0000000    0 0.0000000
#> [2,] 1.0000000    0 1.0000000 0.0000000 0.0000000 0.0000000    0 0.0000000
#> [3,] 0.4137583    1 0.0000000 1.0000000 0.0000000 0.0000000    0 0.0000000
#> [4,] 0.1711959    0 1.0000000 0.0000000 1.0000000 0.0000000    0 0.0000000
#> [5,] 0.0000000    0 0.0000000 1.0000000 0.0000000 1.0000000    0 0.1711959
#> [6,] 0.0000000    0 0.0000000 0.0000000 1.0000000 0.0000000    1 0.4137583
#> [7,] 0.0000000    0 0.0000000 0.0000000 0.0000000 1.0000000    0 1.0000000
#> [8,] 0.0000000    0 0.0000000 0.0000000 0.1711959 0.4137583    1 0.0000000
#> 
#> $directed_graph
#>      [,1] [,2]      [,3]      [,4]      [,5]      [,6] [,7] [,8]
#> [1,]    0    1 0.4137583 0.1711959 0.0000000 0.0000000    0    0
#> [2,]    1    0 1.0000000 0.0000000 0.0000000 0.0000000    0    0
#> [3,]    0    1 0.0000000 1.0000000 0.0000000 0.0000000    0    0
#> [4,]    0    0 1.0000000 0.0000000 1.0000000 0.0000000    0    0
#> [5,]    0    0 0.0000000 1.0000000 0.0000000 1.0000000    0    0
#> [6,]    0    0 0.0000000 0.0000000 1.0000000 0.0000000    1    0
#> [7,]    0    0 0.0000000 0.0000000 0.0000000 1.0000000    0    1
#> [8,]    0    0 0.0000000 0.0000000 0.1711959 0.4137583    1    0
#> 
#> $a
#> [1] 1.568312
#> 
#> $b
#> [1] 0.9
#> 
#> $ab_sse
#> [1] 0.07906359
#> 
#> $cross_entropy
#> [1] 11.1504
#> 
#> $ce_curve
#>   [1] 40.04817 29.87440 26.42030 24.71214 23.14175 21.64202 20.20387 18.82474
#>   [9] 17.65408 16.91084 16.47269 16.10762 15.76033 15.41438 15.05941 14.68821
#>  [17] 14.29595 13.88059 13.44488 13.00015 12.57151 12.19829 11.91652 11.72803
#>  [25] 11.60366 11.51744 11.45550 11.40982 11.37512 11.34789 11.32589 11.30765
#>  [33] 11.29221 11.27893 11.26734 11.25712 11.24803 11.23989 11.23257 11.22594
#>  [41] 11.21992 11.21443 11.20942 11.20483 11.20062 11.19676 11.19321 11.18994
#>  [49] 11.18693 11.18416 11.18160 11.17924 11.17706 11.17505 11.17319 11.17147
#>  [57] 11.16989 11.16842 11.16706 11.16581 11.16466 11.16358 11.16260 11.16168
#>  [65] 11.16083 11.16005 11.15933 11.15866 11.15804 11.15747 11.15694 11.15645
#>  [73] 11.15600 11.15558 11.15519 11.15483 11.15450 11.15420 11.15391 11.15365
#>  [81] 11.15341 11.15318 11.15298 11.15278 11.15261 11.15244 11.15229 11.15215
#>  [89] 11.15202 11.15190 11.15179 11.15168 11.15159 11.15150 11.15142 11.15134
#>  [97] 11.15127 11.15121 11.15115 11.15109 11.15104 11.15099 11.15095 11.15091
#> [105] 11.15087 11.15084 11.15080 11.15077 11.15075 11.15072 11.15070 11.15068
#> [113] 11.15066 11.15064 11.15062 11.15060 11.15059 11.15057 11.15056 11.15055
#> [121] 11.15054 11.15053 11.15052 11.15051 11.15050 11.15049 11.15049 11.15048
#> [129] 11.15047 11.15047 11.15046 11.15046 11.15046 11.15045 11.15045 11.15044
#> [137] 11.15044 11.15044 11.15043 11.15043 11.15043 11.15043 11.15043 11.15042
#> [145] 11.15042 11.15042 11.15042 11.15042 11.15042 11.15041 11.15041 11.15041
#> [153] 11.15041 11.15041 11.15041 11.15041 11.15041 11.15041 11.15041 11.15041
#> [161] 11.15041 11.15041 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [169] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [177] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [185] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [193] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [201] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [209] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [217] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [225] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [233] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [241] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [249] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [257] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [265] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [273] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [281] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [289] 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040 11.15040
#> [297] 11.15040 11.15040 11.15040 11.15040 11.15040
#> 
#> $rho
#> [1] 1 1 1 1 1 1 1 1
#> 
#> $sigma
#> [1] 1.133179e+00 5.421011e-20 5.421011e-20 5.421011e-20 5.421011e-20
#> [6] 5.421011e-20 5.421011e-20 1.133179e+00
#> 
#> $estimate
#> [1] 11.1504
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "UMAP: smoothed kNN fuzzy graph, fitted (a, b) low-d kernel, exact fuzzy cross-entropy by gradient descent"
#>