Robust Sparse Hyperplane Classifiers: Application to Uncertain Molecular Profiling Data

Bhattacharyya, C and Grate, LR and Jordan, MI and Ghaoui, El L and Mian, IS (2004) Robust Sparse Hyperplane Classifiers: Application to Uncertain Molecular Profiling Data. In: Journal of Computational Biology, 11 (6). pp. 1073-1089.

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Abstract

Molecular profiling studies can generate abundance measurements for thousands of transcripts, proteins, metabolites, or other species in, for example, normal and tumor tissue samples. Treating such measurements as features and the samples as labeled data points, sparse hyperplanes provide a statistical methodology for classifying data points into one of two categories (classification and prediction) and defining a small subset of discriminatory features (relevant feature identification). However, this and other extant classification methods address only implicitly the issue of observed data being a combination of underlying signals and noise. Recently, robust optimization has emerged as a powerful framework for handling uncertain data explicitly. Here, ideas from this field are exploited to develop robust sparse hyperplanes, i.e., classification and relevant feature identification algorithms that are resilient to variation in the data. Specifically, each data point is associated with an explicit data uncertainty model in the form of an ellipsoid parameterized by a center and covariance matrix. The task of learning a robust sparse hyperplane from such data is formulated as a second order cone program (SOCP). Gaussian and distribution-free data uncertainty models are shown to yield SOCPs that are equivalent to the SCOP based on ellipsoidal uncertainty. The real-world utility of robust sparse hyperplanes is demonstrated via retrospective analysis of breast cancer related transcript profiles. Data-dependent heuristics are used to compute the parameters of each ellipsoidal data uncertainty model. The generalization performance of a specific implementation, designated "robust LIKNON," is better than its nominal counterpart. Finally, the strengths and limitations of robust sparse hyperplanes are discussed.

Item Type:	Journal Article
Publication:	Journal of Computational Biology
Publisher:	Mary Ann Liebert
Additional Information:	The copyright for this article belongs to Mary Ann Liebert Publishers.
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	09 Mar 2005
Last Modified:	20 Jan 2012 06:28
URI:	http://eprints.iisc.ac.in/id/eprint/2865

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