Gaussian random projection (Geron Ch 8, morie.fn grgrp)

Z = X R with R_ij ~ N(0, 1/d) drawn from the reference LCG and reshaped ROW-MAJOR into (n, d). achieved_variance is the ddof = 1 variance, matching the payload (not the ddof = 0 summary line).

Usage

morie_geron_gaussian_random_projection(X, d, seed = 0)

Arguments

X

(m, n) data.

d

Target dimension.

seed

LCG seed.

Value

List with projected, R, target_variance, achieved_variance, mean_distance_ratio, max_distance_ratio.

Examples

morie_geron_gaussian_random_projection(X = c(1, 2, 3, 4, 5, 6, 7, 8), d = 5L)
#> $projected
#>          [,1]       [,2]      [,3]     [,4]      [,5]
#> [1,] 8.070968 -0.2746068 0.9530029 4.098278 -5.865283
#> 
#> $R
#>             [,1]        [,2]        [,3]        [,4]        [,5]
#> [1,] -0.13566488  0.74769595 -0.13922765 -0.24540484 -0.44615930
#> [2,] -0.42860982 -0.41649364 -0.50368374 -0.45339372 -0.25596568
#> [3,] -0.02353098 -0.30057333  0.33163607 -0.29194708 -1.40790811
#> [4,] -0.13086211 -0.14052006  0.34428118 -0.38021065 -0.48812465
#> [5,] -0.49045795 -0.13154572  0.01075495  0.60505234 -0.12829530
#> [6,]  1.31871292 -0.06200600 -0.05278134  0.37585615  0.41880015
#> [7,]  0.64781232  0.09075158 -0.45056334  0.44021359 -0.04194005
#> [8,] -0.04209747  0.20862354  0.39305272 -0.08934243 -0.03858922
#> 
#> $target_variance
#> [1] 0.2
#> 
#> $achieved_variance
#> [1] 0.2103512
#> 
#> $mean_distance_ratio
#> NULL
#> 
#> $max_distance_ratio
#> NULL
#> 
#> $d
#> [1] 5
#> 
#> $seed
#> [1] 0
#> 
#> $estimate
#>          [,1]       [,2]      [,3]     [,4]      [,5]
#> [1,] 8.070968 -0.2746068 0.9530029 4.098278 -5.865283
#> 
#> $n
#> [1] 1
#>