Bi-objective Optimization of Biclustering with Binary Data

TL;DR

This paper introduces a bi-objective optimization approach for biclustering with binary data, proposing a heuristic method that outperforms exact solvers in efficiency for large instances.

Contribution

It presents a new integer programming formulation and a heuristic algorithm for bi-objective biclustering, demonstrating improved computational efficiency over exact methods.

Findings

Heuristic achieves near-optimal solutions faster than exact methods.

Exact solver's computational cost increases significantly with data size.

Heuristic provides high-quality solutions with reduced computational expense.

Abstract

Clustering consists of partitioning data objects into subsets called clusters according to some similarity criteria. This paper addresses a generalization called quasi-clustering that allows overlapping of clusters, and which we link to biclustering. Biclustering simultaneously groups the objects and features so that a specific group of objects has a special group of features. In recent years, biclustering has received a lot of attention in several practical applications. In this paper we consider a bi-objective optimization of biclustering problem with binary data. First we present an integer programing formulations for the bi-objective optimization biclustering. Next we propose a constructive heuristic based on the set intersection operation and its efficient implementation for solving a series of mono-objective problems used inside the Epsilon-constraint method (obtained by keeping only one objective function and the other objective function is integrated into constraints). Finally, our experimental results show that using CPLEX solver as an exact algorithm for finding an optimal solution drastically increases the computational cost for large instances, while our proposed heuristic provides very good results and significantly reduces the computational expense.