Robust formulations for clustering-based large-scale classification

Jagarlapudi, Saketha Nath and Ben-Tal, Aharon and Bhattacharyya, Chiranjib (2013) Robust formulations for clustering-based large-scale classification. In: Optimization and Engineering, 14 (2). pp. 225-250.

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Abstract

Chebyshev-inequality-based convex relaxations of Chance-Constrained Programs (CCPs) are shown to be useful for learning classifiers on massive datasets. In particular, an algorithm that integrates efficient clustering procedures and CCP approaches for computing classifiers on large datasets is proposed. The key idea is to identify high density regions or clusters from individual class conditional densities and then use a CCP formulation to learn a classifier on the clusters. The CCP formulation ensures that most of the data points in a cluster are correctly classified by employing a Chebyshev-inequality-based convex relaxation. This relaxation is heavily dependent on the second-order statistics. However, this formulation and in general such relaxations that depend on the second-order moments are susceptible to moment estimation errors. One of the contributions of the paper is to propose several formulations that are robust to such errors. In particular a generic way of making such formulations robust to moment estimation errors is illustrated using two novel confidence sets. An important contribution is to show that when either of the confidence sets is employed, for the special case of a spherical normal distribution of clusters, the robust variant of the formulation can be posed as a second-order cone program. Empirical results show that the robust formulations achieve accuracies comparable to that with true moments, even when moment estimates are erroneous. Results also illustrate the benefits of employing the proposed methodology for robust classification of large-scale datasets.

Item Type:	Journal Article
Publication:	Optimization and Engineering
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer.
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	18 Jul 2013 06:57
Last Modified:	18 Jul 2013 06:57
URI:	http://eprints.iisc.ac.in/id/eprint/46862

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