rpca-package {rpca}

RobustPCA: Decompose a Matrix into Low-Rank and Sparse Components

Description

Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Candes, E. J., Li, X., Ma, Y., & Wright, J. (2011). Robust principal component analysis?. Journal of the ACM (JACM), 58(3), 11. prove that we can recover each component individually under some suitable assumptions. It is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the L1 norm. This package implements this decomposition algorithm resulting with Robust PCA approach.

Details

Index of help topics:

F2norm                  Frobenius norm of a matrix
rpca                    Decompose a matrix into a low-rank component
                        and a sparse component by solving Principal
                        Components Pursuit
rpca-package            RobustPCA: Decompose a Matrix into Low-Rank and
                        Sparse Components
thresh.l1               Shrinkage operator
thresh.nuclear          Thresholding operator

This package contains rpca function, which decomposes a rectangular matrix M into a low-rank component, and a sparse component, by solving a convex program called Principal Component Pursuit:

\textrm{minimize}\quad \|L\|_{*} + \lambda \|S\|_{1}

\textrm{subject to}\quad L+S = M

where \|L\|_{*} is the nuclear norm of L (sum of singular values).

Note

Use citation("rpca") to cite this R package.

Author(s)

Maciek Sykulski [aut, cre]

Maintainer: Maciek Sykulski <[e-mail]>

References

Candès, E. J., Li, X., Ma, Y., & Wright, J. (2011). Robust principal component analysis?. Journal of the ACM (JACM), 58(3), 11.

Yuan, X., & Yang, J. (2009). Sparse and low-rank matrix decomposition via alternating direction methods. preprint, 12.

See Also

rpca