yukara-ikemiya / online-rpca

Online Robust PCA

Batch and Online Robust PCA (Robust Principal Component Analysis) implementation and examples (Python).

Robust PCA based on Principal Component Pursuit (RPCA-PCP) is the most popular RPCA algorithm which decomposes the observed matrix M into a low-rank matrix L and a sparse matrix S by solving Principal Component Pursuit:

\min ||L||_* + \lambda ||S||_1

s.t. L + S = M

where ||.||_* is a nuclear norm, ||.||_1 is L1-norm.

See the paper for details

What is inside?

Folder rpca contains various batch and online Robust PCA algorithms.

• pcp.py: Robust PCA based on Principal Component Pursuit (RPCA-PCP). Reference: Candes, Emmanuel J., et al. "Robust principal component analysis." Journal of the ACM (JACM) 58.3 (2011): 11.

• spca.py: Stable Principal Component Pursuit (Zhou et al., 2009). This implementation uses the Accelerated Proximal Gradient method with a fixed mu_iter. Reference: Zhou, Zihan, et al. "Stable principal component pursuit." Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on. IEEE, 2010.

• spca2.py: Stable Principal Component Pursuit (Zhou et al., 2009). This implementation uses the Accelerated Proximal Gradient method with a decreasing mu_iter. Reference: Zhou, Zihan, et al. "Stable principal component pursuit." Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on. IEEE, 2010.

• stoc_rpca.py: Online Robust PCA via Stochastic Optimization (Feng, Xu and Yan, 2013). Reference: Feng, Jiashi, Huan Xu, and Shuicheng Yan. "Online robust pca via stochastic optimization."" Advances in Neural Information Processing Systems. 2013.

• omwrpca.py: Online Moving Window Robust PCA.

• omwrpca_cp.py: Online Moving Window Robust PCA with Change Point Detection. A novel online robust principal component analysis algorithm which can track both slowly changing and abruptly changed subspace. The algorithm is also able to automatically discover change points of the underlying low-rank subspace.

Folder simulation contains code to reproduce all simulation studies of the paper Xiao, Wei, et al. "Online Robust Principal Component Analysis with Change Point Detection" arXiv (2017).

Folder example/survillance contains ipython notebooks to apply the online rpca algorithms for real-world video survillance data (separating foreground from background in the video). Before running the corresponding ipython notebooks, please first download the video data from http://perception.i2r.a-star.edu.sg/bk_model/bk_index.html.

Citation

If you use this package in any way, please cite the following preprint.

@article{xiao2017online,
  title={Online Robust Principal Component Analysis with Change Point Detection},
  author={Xiao, Wei and Huang, Xiaolin and Silva, Jorge and Emrani, Saba and Chaudhuri, Arin},
  journal={arXiv preprint arXiv:1702.05698},
  year={2017}
}

Contacts

Wei Xiao [e-mail]