Jointly Clustering Rows and Columns of Binary Matrices: Algorithms and Trade-offs

TL;DR

This paper addresses the problem of exactly recovering row and column clusters in binary matrices with noise, proposing algorithms with different complexities and analyzing the trade-offs between observations, computational time, and accuracy.

Contribution

It introduces three algorithms for joint clustering of binary matrices, analyzes their observation requirements, and explores the trade-offs between computational complexity and data availability.

Findings

Derived a lower bound on observations needed for exact recovery

Compared three algorithms with different running times and data requirements

Showed smooth trade-offs between computational complexity and data volume

Abstract

In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many applications, which exhibit both row and column cluster structure, and our goal is to exactly recover the underlying row and column clusters by observing only a small fraction of noisy entries. We first derive a lower bound on the minimum number of observations needed for exact cluster recovery. Then, we propose three algorithms with different running time and compare the number of observations needed by them for successful cluster recovery. Our analytical results show smooth time-data trade-offs: one can gradually reduce the computational complexity when increasingly more observations are available.