Regularized Greedy Column Subset Selection

The Column Subset Selection Problem provides a natural framework for unsupervised feature selection. Despite being a hard combinatorial optimization problem, there exist efficient algorithms that provide good approximations. The drawback of the problem formulation is that it incorporates no form of...

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Bibliographic Details
Published in:arXiv.org 2018-04
Main Authors: Ordozgoiti, Bruno, Mozo, Alberto, Jesús García López de Lacalle
Format: Article
Language:English
Subjects:
Adequacy
Combinatorial analysis
Formulations
Greedy algorithms
Lower bounds
Noise sensitivity
Optimization
Regularization
Robustness (mathematics)
Online Access:Get full text
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Summary:The Column Subset Selection Problem provides a natural framework for unsupervised feature selection. Despite being a hard combinatorial optimization problem, there exist efficient algorithms that provide good approximations. The drawback of the problem formulation is that it incorporates no form of regularization, and is therefore very sensitive to noise when presented with scarce data. In this paper we propose a regularized formulation of this problem, and derive a correct greedy algorithm that is similar in efficiency to existing greedy methods for the unregularized problem. We study its adequacy for feature selection and propose suitable formulations. Additionally, we derive a lower bound for the error of the proposed problems. Through various numerical experiments on real and synthetic data, we demonstrate the significantly increased robustness and stability of our method, as well as the improved conditioning of its output, all while remaining efficient for practical use.
ISSN:2331-8422