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

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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.

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Notes

  1. By its nature, non-rejection of a null hypothesis in a statistical test does not mean the positive acceptance of it, and this is also the case when selecting the number of biclusters with the proposed test. However, we prioritize simplicity and use the term “accepted” to mean “not rejected” throughout this paper.

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Acknowledgements

We would like to thank Editage (www.editage.com) for English language editing.

Funding

This work was supported by JSPS KAKENHI (18H03201 and 20H00576), Fujitsu Laboratories Ltd., and JST CREST.

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Authors and Affiliations

  1. Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Chihiro Watanabe & Taiji Suzuki

  2. Center for Advanced Intelligence Project (AIP), RIKEN, Tokyo, Japan

    Taiji Suzuki

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  1. Chihiro Watanabe
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Correspondence to Chihiro Watanabe.

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Watanabe, C., Suzuki, T. A goodness-of-fit test on the number of biclusters in a relational data matrix. Ann Inst Stat Math 75, 979–1009 (2023). https://doi.org/10.1007/s10463-023-00869-3

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