Principal component compression of a marker matrix

Formula: Q = X'X/(n-1) on scaled columns; W the eigenvectors of Q; PC = X W; keep the first k columns

Usage

Pcadim(X, k = NULL)

Arguments

X

One record per row.

k

Number of components retained; None keeps all.

Value

List with scores, loadings, eigenvalues, compressed, prop_variance, cum_variance, k, n, p.

References

Montesinos Lopez, Montesinos Lopez and Crossa (2022), Multivariate Statistical Machine Learning Methods for Genomic Prediction, Springer, doi:10.1007/978-3-030-89010-0. Chapter 2, Sect. 2.8 pp. 63-64. DEFECT FOUND: neither shared core sign-fixes its eigenvectors, so morie.fn._gp_core.pca_compress and the R morie_pca return loadings and scores that differ by a column sign; the three-way parity harness caught it. The sign is fixed HERE, in the same way morie.fn._tail1core.eigsym does it – the largest-magnitude entry of every loading column is made positive – rather than in the shared cores, which this slice must not edit. With that, a repeated eigenvalue leaves its loadings determined only up to a rotation within the eigenspace and is not a stable quantity in either language.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Pcadim(V)
#> $scores
#>            [,1]
#> [1,] -1.4288690
#> [2,] -1.0206207
#> [3,] -0.6123724
#> [4,] -0.2041241
#> [5,]  0.2041241
#> [6,]  0.6123724
#> [7,]  1.0206207
#> [8,]  1.4288690
#> 
#> $loadings
#>      [,1]
#> [1,]    1
#> 
#> $eigenvalues
#> [1] 1
#> 
#> $compressed
#>            [,1]
#> [1,] -1.4288690
#> [2,] -1.0206207
#> [3,] -0.6123724
#> [4,] -0.2041241
#> [5,]  0.2041241
#> [6,]  0.6123724
#> [7,]  1.0206207
#> [8,]  1.4288690
#> 
#> $prop_variance
#> [1] 1
#> 
#> $cum_variance
#> [1] 1
#> 
#> $k
#> [1] 1
#> 
#> $n
#> [1] 8
#> 
#> $p
#> [1] 1
#> 
#> $method
#> [1] "PCA compression, MVSML Sect. 2.8"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"