ReconstructionError: Calculates the reduced rank reconstruction error

In EESPCA: Eigenvectors from Eigenvalues Sparse Principal Component Analysis (EESPCA)

Calculates the reduced rank reconstruction error

Description

Utility function for computing the squared Frobenius norm of the residual matrix formed by subtracting from X a reduced rank approximation of matrix X generated from the top k principal components contained in matrix V.

Usage

    reconstructionError(X,V,center=TRUE)

Arguments

X	An n-by-p data matrix whose top k principal components are contained the p-by-k matrix V.
V	A p-by-k matrix containing the loadings for the top k principal components of X.
center	If true (the default), X will be mean-centered before the reconstruction error is computed. If the PCs in V were computed via SVD on a mean-centered matrix or via eigen-decomposition of the sample covariance matrix, this should be set to true.

Value

The squared Frobenius norm of the residual matrix.

Examples

    set.seed(1)
    # Simulate 10x5 MVN data matrix
    X=matrix(rnorm(50), nrow=10)
    # Perform PCA
    prcomp.out = prcomp(X)
    # Get rank 2 reconstruction error, which will be the minimum since the first 2 PCs are used
    reconstructionError(X, prcomp.out$rotation[,1:2])
    # Use all PCs to get approximately 0 reconstruction error
    reconstructionError(X, prcomp.out$rotation)    

EESPCA documentation built on June 16, 2022, 1:07 a.m.