R: Randomized Singular Value Decomposition (wordspace)

rsvd {wordspace} | R Documentation

## Randomized Singular Value Decomposition (wordspace)

### Description

An implementation of the randomized truncated SVD algorithm of Halko, Martinsson & Tropp (2009).

### Usage

    rsvd(M, n, q = 2, oversampling = 2, transpose = FALSE, verbose = FALSE)

### Arguments

`M` | a dense or sparse numeric matrix
`n` | an integer specifying the desired number of singular components. This argument must be specified and must satisfy `n <= min(nrow(M), ncol(M))`.
`q` | number of power iterations (Halko et al. recommend `q=1` or `q=2`)
`oversampling` | oversampling factor. The rSVD algorithm computes an approximate SVD factorization of rank `n * oversampling`, which is then truncated to the first `n` components.
`transpose` | if `TRUE`, apply the rSVD algorithm to the transpose `t(M)`, which may be more efficient depending on the dimensions of `M`
`verbose` | whether to display progress messages during execution

### Details

This implementation of randomized truncated SVD is based on the randomized PCA algorithm (Halko et al. 2009, p. 9). The discussion in Sec. 4 and 5 of the paper shows that the same algorithm applies to the case where the columns of A are not centered (Algorithm 4.3 + Algorithm 5.1).

### Value

A list with components

`u` | a matrix whose columns contain the first `n` left singular vectors of `M`
`v` | a matrix whose columns contain the first `n` right singular vectors of `M`
`d` | a vector containing the first `n` singular values of `M`

### Author(s)

Stefan Evert (http://purl.org/stefan.evert)

### References

Halko, N., Martinsson, P. G., and Tropp, J. A. (2009). Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions. Technical Report 2009-05, ACM, California Institute of Technology.

### See Also

`svd`, `dsm.projection`, `sparsesvd`

[Package wordspace version 0.2-6 Index]