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Fraction of Variance Explained

Source: R/main.R
fraction_variance_explained.Rd

Computes the sum of marginal component variances divided by \(tr(\Sigma)\). This equals the variance explained by projection onto the span of U when the columns of U are orthonormal; otherwise it is the normalized sparse-PCA objective.

Usage

fraction_variance_explained(C, U)

Arguments

C

A matrix. The correlation or covariance matrix (p x p).

U

A matrix. The matrix containing the r PCs (p x r).

Value

A float.

Examples

TestMat <- cor(mtcars)
mspcares <- mspca(TestMat, r = 2, ks = c(4, 4), verbose = FALSE)
fraction_variance_explained(TestMat, mspcares$x_best)
#> [1] 0.6023322