An SDP-based Branch-and-Cut Algorithm for Biclustering

• URL: http://arxiv.org/abs/2403.11351v1
• Date: Sun, 17 Mar 2024 21:43:19 GMT
• Title: An SDP-based Branch-and-Cut Algorithm for Biclustering
• Authors: Antonio M. Sudoso,
• Abstract summary: We present a tailored branch-and-cut algorithm for biclustering problems. We show that the proposed algorithm can solve instances 20 times larger than those handled by general-purpose solvers.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Biclustering, also called co-clustering, block clustering, or two-way clustering, involves the simultaneous clustering of both the rows and columns of a data matrix into distinct groups, such that the rows and columns within a group display similar patterns. As a model problem for biclustering, we consider the $k$-densest-disjoint biclique problem, whose goal is to identify $k$ disjoint complete bipartite subgraphs (called bicliques) of a given weighted complete bipartite graph such that the sum of their densities is maximized. To address this problem, we present a tailored branch-and-cut algorithm. For the upper bound routine, we consider a semidefinite programming relaxation and propose valid inequalities to strengthen the bound. We solve this relaxation in a cutting-plane fashion using a first-order method. For the lower bound, we design a maximum weight matching rounding procedure that exploits the solution of the relaxation solved at each node. Computational results on both synthetic and real-world instances show that the proposed algorithm can solve instances approximately 20 times larger than those handled by general-purpose solvers.

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