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:
  • 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}


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.


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@cpslab.snu.ac.kr. In your email, please include your name and institution. By submitting this request you agree to be bound by this license.