Sparse random projection matrix with {-1,0,+1} entries

R_ij = +-sqrt(s/d_out) with prob 1/(2s) each (s = 1/density), else 0. Measures realised pairwise-distance distortion.

Usage

morie_geron_sparse_rand_projection(X, d_out, density = NULL, seed = 0)

Arguments

X

Data (n, d_in).

d_out

Target dimension.

density

Optional non-zero fraction in (0,1]; default 1/sqrt(d_in).

seed

LCG seed.

Value

list with X_proj, R, density, s, scale, nnz, max_distortion, mean_distortion, estimate, n, method.

Examples

morie_geron_sparse_rand_projection(X = c(1, 2, 3, 4, 5, 6, 7, 8), d_out = 5L)
#> $X_proj
#>           [,1]      [,2]       [,3]       [,4]      [,5]
#> [1,] 0.4472136 0.4472136 -0.4472136 -0.4472136 0.4472136
#> [2,] 0.8944272 0.8944272 -0.8944272 -0.8944272 0.8944272
#> [3,] 1.3416408 1.3416408 -1.3416408 -1.3416408 1.3416408
#> [4,] 1.7888544 1.7888544 -1.7888544 -1.7888544 1.7888544
#> [5,] 2.2360680 2.2360680 -2.2360680 -2.2360680 2.2360680
#> [6,] 2.6832816 2.6832816 -2.6832816 -2.6832816 2.6832816
#> [7,] 3.1304952 3.1304952 -3.1304952 -3.1304952 3.1304952
#> [8,] 3.5777088 3.5777088 -3.5777088 -3.5777088 3.5777088
#> 
#> $R
#>           [,1]      [,2]       [,3]       [,4]      [,5]
#> [1,] 0.4472136 0.4472136 -0.4472136 -0.4472136 0.4472136
#> 
#> $density
#> [1] 1
#> 
#> $s
#> [1] 1
#> 
#> $scale
#> [1] 0.4472136
#> 
#> $nnz
#> [1] 5
#> 
#> $max_distortion
#> [1] 2.220446e-16
#> 
#> $mean_distortion
#> [1] 8.326673e-17
#> 
#> $estimate
#> [1] 2.220446e-16
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Achlioptas/Li sparse random projection with +/-sqrt(s/d_out) entries"
#>