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Finding large average submatrices in high dimensional data. (English) Zbl 1196.62087

Summary: 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.) 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 data sets. 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. Software is available at https://genome.unc.edu/las/.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62P10 Applications of statistics to biology and medical sciences; meta analysis
92D10 Genetics and epigenetics
65C60 Computational problems in statistics (MSC2010)

Software:

KEGG; COSA; LAS

References:

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