A goodness-of-fit test on the number of biclusters in a relational data matrix

Chihiro Watanabe () and Taiji Suzuki
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Chihiro Watanabe: The University of Tokyo
Taiji Suzuki: The University of Tokyo

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 6, No 5, 979-1009

Abstract: Abstract Biclustering is a method for detecting homogeneous submatrices in a given matrix. Although there are many studies that estimate the underlying bicluster structure of a matrix, few have enabled us to determine the appropriate number of biclusters. Recently, a statistical test on the number of biclusters has been proposed for a regular-grid bicluster structure. However, when the latent bicluster structure does not satisfy such regular-grid assumption, the previous test requires a larger number of biclusters than necessary for the null hypothesis to be accepted, which is not desirable in terms of interpreting the accepted structure. In this study, we propose a new statistical test on the number of biclusters that does not require the regular-grid assumption and derive the asymptotic behavior of the proposed test statistic in both null and alternative cases. We illustrate the effectiveness of the proposed method by applying it to both synthetic and practical data matrices.

Keywords: Biclustering; Submatrix detection; Goodness-of-fit test; Random matrix theory (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10463-023-00869-3

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