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.
- Generate a synthetic data matrix.
- Insert missing entries or outliers to the data matrix.
- 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.