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rCUR: an R package for CUR matrix decomposition

András Bodor1, István Csabai1*, Michael W Mahoney2 and Norbert Solymosi3

Author affiliations

1 Department of the Physics of Complex Systems, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117, Budapest, Hungary

2 Department of Mathematics, Stanford University, Stanford, CA 94305, USA

3 Department of Animal Hygiene, Herd Health and Veterinary Ethology, Szent István University, István utca, 1078, Budapest, Hungary

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Citation and License

BMC Bioinformatics 2012, 13:103  doi:10.1186/1471-2105-13-103

Published: 17 May 2012

Abstract

Background

Many methods for dimensionality reduction of large data sets such as those generated in microarray studies boil down to the Singular Value Decomposition (SVD). Although singular vectors associated with the largest singular values have strong optimality properties and can often be quite useful as a tool to summarize the data, they are linear combinations of up to all of the data points, and thus it is typically quite hard to interpret those vectors in terms of the application domain from which the data are drawn. Recently, an alternative dimensionality reduction paradigm, CUR matrix decompositions, has been proposed to address this problem and has been applied to genetic and internet data. CUR decompositions are low-rank matrix decompositions that are explicitly expressed in terms of a small number of actual columns and/or actual rows of the data matrix. Since they are constructed from actual data elements, CUR decompositions are interpretable by practitioners of the field from which the data are drawn.

Results

We present an implementation to perform CUR matrix decompositions, in the form of a freely available, open source R-package called rCUR. This package will help users to perform CUR-based analysis on large-scale data, such as those obtained from different high-throughput technologies, in an interactive and exploratory manner. We show two examples that illustrate how CUR-based techniques make it possible to reduce significantly the number of probes, while at the same time maintaining major trends in data and keeping the same classification accuracy.

Conclusions

The package rCUR provides functions for the users to perform CUR-based matrix decompositions in the R environment. In gene expression studies, it gives an additional way of analysis of differential expression and discriminant gene selection based on the use of statistical leverage scores. These scores, which have been used historically in diagnostic regression analysis to identify outliers, can be used by rCUR to identify the most informative data points with respect to which to express the remaining data points.