Bayesian extreme components analysis

Authors:
Yutian Chen;Max Welling
Affiliations:
Bren School of Information and Computer Science, University of California, Irvine;Bren School of Information and Computer Science, University of California, Irvine
Venue:
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Year:
2009

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Abstract

Extreme Components Analysis (XCA) is a statistical method based on a single eigenvalue decomposition to recover the optimal combination of principal and minor components in the data. Unfortunately, minor components are notoriously sensitive to overfitting when the number of data items is small relative to the number of attributes. We present a Bayesian extension of XCA by introducing a conjugate prior for the parameters of the XCA model. This Bayesian-XCA is shown to outperform plain vanilla XCA as well as Bayesian-PCA and XCA based on a frequentist correction to the sample spectrum. Moreover, we show that minor components are only picked when they represent genuine constraints in the data, even for very small sample sizes. An extension to mixtures of Bayesian XCA models is also explored.