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Biclustering is a method for detecting homogeneous submatrices in a givenobserved matrix, and it is an effective tool for relational data analysis.Although there are many studies that estimate the underlying biclusterstructure of a matrix, few have enabled us to determine the appropriate numberof biclusters in an observed matrix. Recently, a statistical test on the numberof biclusters has been proposed for a regular-grid bicluster structure, wherewe assume that the latent bicluster structure can be represented by row-columnclustering. However, when the latent bicluster structure does not satisfy suchregular-grid assumption, the previous test requires a larger number ofbiclusters than necessary (i.e., a finer bicluster structure than necessary)for the null hypothesis to be accepted, which is not desirable in terms ofinterpreting the accepted bicluster structure. In this study, we propose a newstatistical test on the number of biclusters that does not require theregular-grid assumption and derive the asymptotic behavior of the proposed teststatistic in both null and alternative cases. We illustrate the effectivenessof the proposed method by applying it to both synthetic and practicalrelational data matrices.

A Goodness-of-fit Test on the Number of Biclusters in a Relational Data Matrix