cov_eigen {sparsediscrim}

Computes the eigenvalue decomposition of the maximum likelihood estimators (MLE) of the covariance matrices for the given data matrix

Description

For the classes given in the vector y, we compute the eigenvalue (spectral) decomposition of the class sample covariance matrices (MLEs) using the data matrix x.

Usage

cov_eigen(x, y, pool = FALSE, fast = FALSE, tol = 1e-06)

Arguments

x

data matrix with n observations and p feature vectors

y

class labels for observations (rows) in x

pool

logical. Should the sample covariance matrices be pooled?

fast

logical. Should the Fast SVD be used? See details.

tol

tolerance value below which the singular values of x are considered zero.

Details

If the fast argument is selected, we utilize the so-called Fast Singular Value Decomposition (SVD) to quickly compute the eigenvalue decomposition. To compute the Fast SVD, we use the corpcor::fast.svd() function, which employs a well-known trick for tall data (large n, small p) and wide data (large p, small n) to compute the SVD corresponding to the nonzero singular values. For more information about the Fast SVD, see corpcor::fast.svd().

Value

a list containing the eigendecomposition for each class. If pool = TRUE, then a single list is returned.

Examples

cov_eigen(x = iris[, -5], y = iris[, 5])
cov_eigen(x = iris[, -5], y = iris[, 5], pool = TRUE)
cov_eigen(x = iris[, -5], y = iris[, 5], pool = TRUE, fast = TRUE)

# Generates a data set having fewer observations than features.
# We apply the Fast SVD to compute the eigendecomposition corresponding to the
# nonzero eigenvalues of the covariance matrices.
set.seed(42)
n <- 5
p <- 20
num_classes <- 3
x <- lapply(seq_len(num_classes), function(k) {
  replicate(p, rnorm(n, mean = k))
})
x <- do.call(rbind, x)
colnames(x) <- paste0("x", 1:ncol(x))
y <- gl(num_classes, n)
cov_eigen(x = x, y = y, fast = TRUE)
cov_eigen(x = x, y = y, pool = TRUE, fast = TRUE)