Fast and Consistent Algorithm for the Latent Block Model

TL;DR

This paper introduces a fast, consistent algorithm called Largest Gaps for clustering in the latent block model, leveraging marginals for binary data when the number of blocks is small, and includes a model selection method with proven consistency.

Contribution

The paper proposes a novel, efficient clustering algorithm based on marginals for the latent block model, with a consistent model selection approach, simplifying complex estimation tasks.

Findings

The Largest Gaps algorithm performs well with small block numbers.

Marginals provide accurate parameter and classification estimates.

The model selection method is proven to be consistent.

Abstract

The latent block model is used to simultaneously rank the rows and columns of a matrix to reveal a block structure. The algorithms used for estimation are often time consuming. However, recent work shows that the log-likelihood ratios are equivalent under the complete and observed (with unknown labels) models and the groups posterior distribution to converge as the size of the data increases to a Dirac mass located at the actual groups configuration. Based on these observations, the algorithm $Largest$ $Gaps$ is proposed in this paper to perform clustering using only the marginals of the matrix, when the number of blocks is very small with respect to the size of the whole matrix in the case of binary data. In addition, a model selection method is incorporated with a proof of its consistency. Thus, this paper shows that studying simplistic configurations (few blocks compared to the size of the matrix or very contrasting blocks) with complex algorithms is useless since the marginals already give very good parameter and classification estimates.