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

arXiv: https://arxiv.org/abs/2102.11658 · HTML: https://mlsanity.com/paper/2102.11658/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 66 references that are in the map.
- First posted on arXiv 23 Feb 2021.

## Builds on (most cited first, 15 of 15)

- [Reducibility and Computational Lower Bounds for Problems with Planted Sparse Structure](https://mlsanity.com/paper/1806.07508/) (2018)
- [Tensor Clustering with Planted Structures: Statistical Optimality and Computational Limits](https://mlsanity.com/paper/2005.10743/) (2020)
- [Statistical-Computational Tradeoffs in Planted Problems and Submatrix Localization with a Growing Number of Clusters and Submatrices](https://mlsanity.com/paper/1402.1267/) (2014)
- [A goodness-of-fit test for stochastic block models](https://mlsanity.com/paper/1412.4857/) (2014)
- [Information Limits for Recovering a Hidden Community](https://mlsanity.com/paper/1509.07859/) (2015)
- [Automatic Yara Rule Generation Using Biclustering](https://mlsanity.com/paper/2009.03779/) (2020)
- [Hypothesis Testing for Automated Community Detection in Networks](https://mlsanity.com/paper/1311.2694/) (2013)
- [Universality of Computational Lower Bounds for Submatrix Detection](https://mlsanity.com/paper/1902.06916/) (2019)
- [Computational and Statistical Boundaries for Submatrix Localization in a Large Noisy Matrix](https://mlsanity.com/paper/1502.01988/) (2015)
- [Using Maximum Entry-Wise Deviation to Test the Goodness-of-Fit for Stochastic Block Models](https://mlsanity.com/paper/1703.06558/) (2017)
- [Submatrix localization via message passing](https://mlsanity.com/paper/1510.09219/) (2015)
- [Goodness-of-fit Test for Latent Block Models](https://mlsanity.com/paper/1906.03886/) (2019)
- [Exact ICL maximization in a non-stationary time extension of the latent block model for dynamic networks](https://mlsanity.com/paper/1506.04138/) (2015)
- [Fast L1-NMF for Multiple Parametric Model Estimation](https://mlsanity.com/paper/1610.05712/) (2016)
- [Distribution-Free, Size Adaptive Submatrix Detection with Acceleration](https://mlsanity.com/paper/1804.10887/) (2018)

## Abstract (arXiv)

Biclustering is a method for detecting homogeneous submatrices in a given observed matrix, and it is an effective tool for relational data analysis. 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 in an observed matrix. Recently, a statistical test on the number of biclusters has been proposed for a regular-grid bicluster structure, where we assume that the latent bicluster structure can be represented by row-column clustering. However, when the latent bicluster structure does not satisfy such regular-grid assumption, the previous test requires a larger number of biclusters than necessary (i.e., a finer bicluster structure than necessary) for the null hypothesis to be accepted, which is not desirable in terms of interpreting the accepted bicluster 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 relational data matrices.