R/spectrum-shift.R

In acabassi/klic: Kernel Learning Integrative Clustering

#' Spectrum shift
#'
#' Make a symmetric matrix positive semi-definite.
#' @param kernelMatrix symmetric matrix
#' @param coeff Coefficient by which the minimum eigenvalue is multiplied when
#' shifting the eigenvalues, in order to avoid numeric problems. Default is 1.2.
#' @param shift Value of the constant added to the diagonal, if known a priori.
#' Default is NULL.
#' @param verbose Boolean flag: if TRUE, information about the shift is printed
#' to screen. Default is FALSE.
#' @return This function returns the matrix \code{kernelMatrix} after applying
#' the required spectrum shift.
#' @author Alessandra Cabassi \email{alessandra.cabassi@mrc-bsu.cam.ac.uk}
#' @examples
#' # Load one dataset with 300 observations, 2 variables, 6 clusters
#' data <- as.matrix(read.csv(system.file("extdata", "dataset1.csv",
#' package = "klic"), row.names = 1))
#'
#' # Compute consensus clustering with K=4 clusters
#' cm <- coca::consensusCluster(data, 4)
#'
#' # Shift eigenvalues of the matrix by a constant: (min eigenvalue) * (coeff)
#' km <- spectrumShift(cm, coeff = 1.05)
#' @export

spectrumShift = function(kernelMatrix,
                         coeff = 1.2,
                         shift = NULL,
                         verbose = FALSE) {


    if (!isSymmetric(kernelMatrix))
        stop("The kernel matrix must be symmetric!")

    N <- dim(kernelMatrix)[1]

    if (is.null(shift)) {
        # Get smallest eigenvalue
        min_eig <- eigen(kernelMatrix, symmetric = TRUE)$values[N]

        if (min_eig < 0) {

            if (verbose)
                cat("The smallest eigenvalue is negative:", min_eig, "\n")

            kernelMatrix <- kernelMatrix + diag(dim(kernelMatrix)[1]) *
                abs(min_eig * coeff)
            kernelMatrix <- kernelMatrix/kernelMatrix[1, 1]  # Rescale

            if (verbose)
                cat("Shifting by a coefficient:  ", abs(min_eig * coeff), "\n")

            new_min_eig <- eigen(kernelMatrix)$values[N]

            if (verbose)
                cat("The smallest eigenvalue is now: ", new_min_eig, "\n")
        }
    } else {
        kernelMatrix <- kernelMatrix + diag(dim(kernelMatrix)[1]) * shift
        kernelMatrix <- kernelMatrix/kernelMatrix[1, 1]  # Rescale

        if (verbose)
            cat("Shifting by a coefficient:  ", shift, "\n")

        new_min_eig <- eigen(kernelMatrix)$values[N]

        if (verbose)
            cat("The smallest eigenvalue is now: ", new_min_eig, "\n")
    }

    kernelMatrix
}