csi-class function

Class "csi"

The reduced Cholesky decomposition object class

Objects from the Class

Objects can be created by calls of the form new("csi", ...). or by calling the csi function.

Slots

• .Data:: Object of class "matrix" contains the decomposed matrix
• pivots:: Object of class "vector" contains the pivots performed
• diagresidues:: Object of class "vector" contains the diagonial residues
• maxresiduals:: Object of class "vector" contains the maximum residues
• predgain: Object of class "vector" contains the predicted gain before adding each column
• truegain: Object of class "vector" contains the actual gain after adding each column
• Q: Object of class "matrix" contains Q from the QR decomposition of the kernel matrix
• R: Object of class "matrix" contains R from the QR decomposition of the kernel matrix

Extends

Class "matrix", directly.

Methods

• diagresidues: signature(object = "csi"): returns the diagonial residues
• maxresiduals: signature(object = "csi"): returns the maximum residues
• pivots: signature(object = "csi"): returns the pivots performed
• predgain: signature(object = "csi"): returns the predicted gain before adding each column
• truegain: signature(object = "csi"): returns the actual gain after adding each column
• Q: signature(object = "csi"): returns Q from the QR decomposition of the kernel matrix
• R: signature(object = "csi"): returns R from the QR decomposition of the kernel matrix

Author(s)

Alexandros Karatzoglou

alexandros.karatzoglou@ci.tuwien.ac.at

See Also

csi, inchol-class

Examples

data(iris)

## create multidimensional y matrix
yind <- t(matrix(1:3,3,150))
ymat <- matrix(0, 150, 3)
ymat[yind==as.integer(iris[,5])] <- 1

datamatrix <- as.matrix(iris[,-5])
# initialize kernel function
rbf <- rbfdot(sigma=0.1)
rbf
Z <- csi(datamatrix,ymat, kernel=rbf, rank = 30)
dim(Z)
pivots(Z)
# calculate kernel matrix
K <- crossprod(t(Z))
# difference between approximated and real kernel matrix
(K - kernelMatrix(kernel=rbf, datamatrix))[6,]