Kernel PCA with polynomial kernel (Geron Ch 7, morie.fn hmkppl)

Usage

morie_geron_kernel_pca_poly(
  X,
  n_components,
  degree = 3,
  gamma = NULL,
  coef0 = 1
)

Arguments

X: Data.
n_components: Components.
degree: Degree.
gamma: Scale.
coef0: Offset.

Value

List with X_projected, eigenvalues, alphas, K, feature_space_dim, estimate, n, method.

Examples

morie_geron_kernel_pca_poly(X = c(1, 2, 3, 4, 5, 6, 7, 8), n_components = 5L)
#> $X_projected
#>            [,1]       [,2]        [,3]          [,4]          [,5]
#> [1,] -166.37659  8.7818387  0.45823973  1.416345e-06  0.000000e+00
#> [2,] -158.42278  4.8672362 -0.18421977 -7.197821e-07 -2.097289e-06
#> [3,] -138.01581  0.1208676 -0.35020502  1.137720e-06  8.210860e-07
#> [4,]  -99.28526 -4.2296520 -0.21628187  1.509220e-06 -8.640186e-07
#> [5,]  -36.36073 -6.9567073  0.04098381  1.044845e-06 -3.644795e-07
#> [6,]   56.62821 -6.8326832  0.24502618  3.947192e-07 -5.183536e-07
#> [7,]  185.55197 -2.6299644  0.21927938  2.089690e-07 -9.576647e-07
#> [8,]  356.28098  6.8790643 -0.21282245  1.137720e-06 -3.113343e-07
#> 
#> $eigenvalues
#> [1] 2.475794e+05 2.680348e+02 5.684363e-01 8.681853e-12 7.234917e-12
#> 
#> $alphas
#>               [,1]          [,2]        [,3]      [,4]       [,5]
#> [1,] -0.0006720131  0.0327637982  0.80614084 163138.60       0.00
#> [2,] -0.0006398868  0.0181589700 -0.32408163 -82906.50 -289884.29
#> [3,] -0.0005574608  0.0004509399 -0.61608488 131045.76  113489.35
#> [4,] -0.0004010239 -0.0157802334 -0.38048567 173836.22 -119423.44
#> [5,] -0.0001468649 -0.0259544911  0.07209921 120348.15  -50377.85
#> [6,]  0.0002287275 -0.0254917746  0.43105300  45464.86  -71646.10
#> [7,]  0.0007494645 -0.0098120251  0.38575892  24069.63 -132367.07
#> [8,]  0.0014390574  0.0256648161 -0.37439981 131045.76  -43032.19
#> 
#> $K
#>      [,1] [,2]  [,3]  [,4]  [,5]   [,6]   [,7]   [,8]
#> [1,]    8   27    64   125   216    343    512    729
#> [2,]   27  125   343   729  1331   2197   3375   4913
#> [3,]   64  343  1000  2197  4096   6859  10648  15625
#> [4,]  125  729  2197  4913  9261  15625  24389  35937
#> [5,]  216 1331  4096  9261 17576  29791  46656  68921
#> [6,]  343 2197  6859 15625 29791  50653  79507 117649
#> [7,]  512 3375 10648 24389 46656  79507 125000 185193
#> [8,]  729 4913 15625 35937 68921 117649 185193 274625
#> 
#> $K_centered
#>          [,1]     [,2]     [,3]     [,4]     [,5]    [,6]     [,7]     [,8]
#> [1,]  27758.5  26400.5  22963.5  16481.5   5988.5 -9481.5 -30894.5 -59216.5
#> [2,]  26400.5  25121.5  21865.5  15708.5   5726.5 -9004.5 -29408.5 -56409.5
#> [3,]  22963.5  21865.5  19048.5  13702.5   5017.5 -7816.5 -25609.5 -49171.5
#> [4,]  16481.5  15708.5  13702.5   9875.5   3639.5 -5593.5 -18411.5 -35402.5
#> [5,]   5988.5   5726.5   5017.5   3639.5   1370.5 -2011.5  -6728.5 -13002.5
#> [6,]  -9481.5  -9004.5  -7816.5  -5593.5  -2011.5  3253.5  10525.5  20128.5
#> [7,] -30894.5 -29408.5 -25609.5 -18411.5  -6728.5 10525.5  34436.5  66090.5
#> [8,] -59216.5 -56409.5 -49171.5 -35402.5 -13002.5 20128.5  66090.5 126983.5
#> 
#> $feature_space_dim
#> [1] 4
#> 
#> $degree
#> [1] 3
#> 
#> $gamma
#> [1] 1
#> 
#> $coef0
#> [1] 1
#> 
#> $estimate
#> [1] 247579.4
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Kernel PCA (polynomial kernel)"
#>