CUR: Function to perform CUR matrix decomposition

In rCUR: CUR decomposition package

Description

By the function the CUR matrix decomposition can be done obtaining a CURobj-class object

Usage

CUR(A, c=dim(A)[2], r=dim(A)[1], k=NULL, sv=NULL,
     method="random", alpha=1, weighted=FALSE, beta=4,
     matrix.return=TRUE, error.return=FALSE)

Arguments

A	a matrix for decomposition with m rows and n columns
c	column number to be selected from matrix A. Default: all columns, in this case column selection is skipped.
r	row number to be selected from matrix A. Default: all rows, in this case row selection is skipped.
k	rank parameter with perhaps k << min(m,n). Default: if not supplied, singular values accounting for 80% of the sum of the singular values is selected.
sv	the singular value decomposition of A. It is the most expensive part of the computation, so it can be supplied, if already available. Default: svd is computed on the fly.
method	the method, used, to select the rows. Possible values are random the original method in [Mahoney and Drineas], rows and columns are selected randomly, with the probability of selection proportional to the leverage score exact.num.random like random, but it is guaranteed, that exactly r rows and c columns are selected top.scores the rows and columns with the highest leverage scores are returned deterministically ortho.top.scores those rows and columns are selected, where the linear combination of the leverage score and orthogonality to the subspace of previously selected items is maximal. See parameter alpha. highest.ranks rows and columns with the highest rank of leverage score for some rank parameter are selected. Every possible value is tried up to the value of k. k must be larger than 1.
alpha	if method="ortho.top.scores", the coefficent of orthogonality in the linear combination. alpha=0 is equivalent to method="top.scores". The coefficent of the leverage score is always 1. Default: 1. Should be positive.
weighted	if true, leverage scores are computed with weighting by the singular values. In this case k should be set to its default value. Not used, if method=highest.ranks. Best used whith method=top.scores. See parameter beta. Default: FALSE.
beta	if weighted=TRUE, leverage scores are computed with weighting of the singular values raised to the power of beta. Default: 4.
matrix.return	if TRUE, the matrices C, U, R are returned. If matrix.return is FALSE, U is not computed, which can be expensive, if r and c are large. Default: TRUE.
error.return	if true, the Frobenius norm of the difference between the original matrix and the CUR approximation is returned. Effective only if matrix.return is TRUE. Default: FALSE.

Value

The function produces an object of CURobj-class.

References

Mahoney M. W. and Drineas P. (2009) CUR matrix decompositions for improved data analysis. PNAS, 106(3):697-702

Andras Bodor, Istvan Csabai, Michael W Mahoney and Norbert Solymosi rCUR:an R package for CUR matrix decomposition BMC Bioinformatics 2012, 13:103 doi:10.1186/1471-2105-13-103

The development was initially based on the Matlab code of Christos Boutsidis:
http://www.cs.rpi.edu/~boutsc/files/AlgorithmCUR.m

Examples

data(STTm)
CUR.results <- CUR(STTm, 31, 12, 3)

Example output

Loading required package: MASS
Loading required package: Matrix
Loading required package: lattice

rCUR documentation built on May 2, 2019, 2:21 a.m.