Open Access
September 2009 Finding large average submatrices in high dimensional data
Andrey A. Shabalin, Victor J. Weigman, Charles M. Perou, Andrew B. Nobel
Ann. Appl. Stat. 3(3): 985-1012 (September 2009). DOI: 10.1214/09-AOAS239


The search for sample-variable associations is an important problem in the exploratory analysis of high dimensional data. Biclustering methods search for sample-variable associations in the form of distinguished submatrices of the data matrix. (The rows and columns of a submatrix need not be contiguous.) In this paper we propose and evaluate a statistically motivated biclustering procedure (LAS) that finds large average submatrices within a given real-valued data matrix. The procedure operates in an iterative-residual fashion, and is driven by a Bonferroni-based significance score that effectively trades off between submatrix size and average value. We examine the performance and potential utility of LAS, and compare it with a number of existing methods, through an extensive three-part validation study using two gene expression datasets. The validation study examines quantitative properties of biclusters, biological and clinical assessments using auxiliary information, and classification of disease subtypes using bicluster membership. In addition, we carry out a simulation study to assess the effectiveness and noise sensitivity of the LAS search procedure. These results suggest that LAS is an effective exploratory tool for the discovery of biologically relevant structures in high dimensional data.

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Andrey A. Shabalin. Victor J. Weigman. Charles M. Perou. Andrew B. Nobel. "Finding large average submatrices in high dimensional data." Ann. Appl. Stat. 3 (3) 985 - 1012, September 2009.


Published: September 2009
First available in Project Euclid: 5 October 2009

zbMATH: 1196.62087
MathSciNet: MR2750383
Digital Object Identifier: 10.1214/09-AOAS239

Keywords: Biclustering , breast cancer , ‎classification‎ , gene expression , lung cancer , microarray

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.3 • No. 3 • September 2009
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