factEN (MATLAB)

This MATLAB package includes the implementation of the low-rank matrix approximation algorithm using elastic-net regularization (factEN). 

Elastic-Net Regularization of Singular Values for Robust Subspace Learning

• Article:
  • Eunwoo Kim, Minsik Lee, and Songhwai Oh, "Elastic-Net Regularization of Singular Values for Robust Subspace Learning," in Proc. of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Jun. 2015.
  • Eunwoo Kim, Minsik Lee, and Songhwai Oh, "Robust Elastic-Net Subspace Representation," IEEE Transactions on Image Processing, vol. 25, no. 9, pp. 4245-4259, Sep. 2016.
• Abstract: Learning a low-dimensional structure plays an important role in computer vision. Recently, a new family of methods, such as l1 minimization and robust principal component analysis, has been proposed for low-rank matrix approximation problems and shown to be robust against outliers and missing data. But these methods often require heavy computational load and can fail to find a solution when highly corrupted data are presented. In this paper, an elastic-net regularization based low-rank matrix factorization method for subspace learning is proposed. The proposed method finds a robust solution efficiently by enforcing a strong convex constraint to improve the algorithm’s stability while maintaining the low-rank property of the solution.  It is shown that any stationary point of the proposed algorithm satisfies the Karush-Kuhn-Tucker optimality conditions. The proposed method is applied to a number of low-rank matrix approximation problems to demonstrate its efficiency in the presence of heavy corruptions and to show its effectiveness and robustness compared to the existing methods.

• Bibtex entry: 

@inproceedings {kim:factEN:cvpr15,
  author    = {Eunwoo Kim and Minsik Lee and Songhwai Oh},
  title     = {Elastic-Net Regularization of Singular Values for Robust Subspace Learning}, 
  bocktitle = {Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
  month     = {June},
  year      = {2015}
}

@ARTICLE {kim:factEN:tip16
  author  = {Eunwoo Kim and Minsik Lee and Songhwai Oh},
  title   = {Robust Elastic-Net Subspace Representation}, 
  journal = {IEEE Transactions on Image Processing},
  volume  = {25},
  number  = {9},
  pages   = {4245--4259},
  month   = {Sep},
  year    = {2016}
}

DEMO

This example is provided in demo.m. There are three steps written below.

1. Generate a synthetic data matrix.
2. Insert missing entries or outliers to the data matrix.
3. Run factEN for approximating the noisy matrix.

Download

This software is made available for free for non-commercial use. The software must not be modified or distributed without prior permission of the author. Please send your request to webmaster@rllab.snu.ac.kr. In your email, please include your name and institution. By submitting this request you agree to be bound by this license.