rpca-package: RobustPCA: Decompose a Matrix into Low-Rank and Sparse...

In 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: This package was not yet installed at build time.

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:

minimize ||L||_{*} + lambda ||S||_{1}

subject to 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

rpca documentation built on May 2, 2019, 6:01 a.m.