PCA projection (Geron Ch 8, morie.fn grpcap)

Centre, SVD, project on the first d right singular vectors; each component's sign is pinned so its largest-magnitude entry is positive, which makes the projection deterministic across BLAS builds.

Usage

morie_geron_pca_projection(X, d)

Arguments

X

(m, n) data.

d

Components in [1, min(m, n)].

Value

List with projection, components, explained_variance, explained_variance_ratio, cumulative_ratio, singular_values, mean.

Examples

set.seed(1)
X <- matrix(rnorm(60), 20, 3)
morie_geron_pca_projection(X, d = 2)
#> $projection
#>              [,1]        [,2]
#>  [1,] -1.20311026  0.14697593
#>  [2,] -0.64135876  0.60345441
#>  [3,] -0.43153112 -0.68200222
#>  [4,]  2.23152391 -0.53036199
#>  [5,] -0.67984221  0.61927611
#>  [6,] -1.07147782 -0.65265268
#>  [7,]  0.39343239  0.07377909
#>  [8,]  1.49156333 -0.74974222
#>  [9,]  0.38416277 -0.06292519
#> [10,] -0.17822269 -0.08668523
#> [11,]  0.24740569  1.87193333
#> [12,] -0.20196965  0.12600241
#> [13,] -0.64650888 -0.27888789
#> [14,] -2.20507848 -1.56176383
#> [15,]  2.03530942 -0.47339198
#> [16,]  1.01763148 -0.60829051
#> [17,] -0.18183249 -0.38219753
#> [18,] -0.08436412  0.56858669
#> [19,]  0.02496970  1.20080648
#> [20,] -0.30070221  0.85808684
#> 
#> $components
#>           [,1]       [,2]        [,3]
#> [1,] 0.6565885 -0.5519002  0.51409893
#> [2,] 0.6779490  0.7305700 -0.08156353
#> 
#> $explained_variance
#> [1] 1.1518689 0.6210151
#> 
#> $explained_variance_ratio
#> [1] 0.5121781 0.2761341
#> 
#> $cumulative_ratio
#> [1] 0.5121781 0.7883122
#> 
#> $singular_values
#> [1] 4.678195 3.435009
#> 
#> $mean
#> [1]  0.190523876 -0.006471519  0.138796773
#> 
#> $estimate
#>              [,1]        [,2]
#>  [1,] -1.20311026  0.14697593
#>  [2,] -0.64135876  0.60345441
#>  [3,] -0.43153112 -0.68200222
#>  [4,]  2.23152391 -0.53036199
#>  [5,] -0.67984221  0.61927611
#>  [6,] -1.07147782 -0.65265268
#>  [7,]  0.39343239  0.07377909
#>  [8,]  1.49156333 -0.74974222
#>  [9,]  0.38416277 -0.06292519
#> [10,] -0.17822269 -0.08668523
#> [11,]  0.24740569  1.87193333
#> [12,] -0.20196965  0.12600241
#> [13,] -0.64650888 -0.27888789
#> [14,] -2.20507848 -1.56176383
#> [15,]  2.03530942 -0.47339198
#> [16,]  1.01763148 -0.60829051
#> [17,] -0.18183249 -0.38219753
#> [18,] -0.08436412  0.56858669
#> [19,]  0.02496970  1.20080648
#> [20,] -0.30070221  0.85808684
#> 
#> $n
#> [1] 20
#>