An Efficient Algorithm for Convex Biclustering

Jie Chen and Joe Suzuki
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Jie Chen: Graduate School of Engineering Science, Osaka University, Osaka 560-0043, Japan
Joe Suzuki: Graduate School of Engineering Science, Osaka University, Osaka 560-0043, Japan

Mathematics, 2021, vol. 9, issue 23, 1-18

Abstract: We consider biclustering that clusters both samples and features and propose efficient convex biclustering procedures. The convex biclustering algorithm (COBRA) procedure solves twice the standard convex clustering problem that contains a non-differentiable function optimization. We instead convert the original optimization problem to a differentiable one and improve another approach based on the augmented Lagrangian method (ALM). Our proposed method combines the basic procedures in the ALM with the accelerated gradient descent method (Nesterov’s accelerated gradient method), which can attain O ( 1 / k 2 ) convergence rate. It only uses first-order gradient information, and the efficiency is not influenced by the tuning parameter λ so much. This advantage allows users to quickly iterate among the various tuning parameters λ and explore the resulting changes in the biclustering solutions. The numerical experiments demonstrate that our proposed method has high accuracy and is much faster than the currently known algorithms, even for large-scale problems.

Keywords: clustering; convex biclustering; optimization; gradient descent method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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