Combinatorial clustering based on an externally-defined one-hot constraint

Masahito Kumagai, Kazuhiko Komatsu, Fumiyo Takano, Takuya Araki, Masayuki Sato, Hiroaki Kobayashi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Recently, a clustering method using a combinatorial optimization problem, called combinatorial clustering, has been drawing attention due to the rapid spreads of quantum annealing and simulated annealing. Combinatorial clustering is performed by minimizing an objective function under a condition to satisfy a constraint. The objective function and the constraint function are generally formulated to a unified objective function of a QUBO (Quadratic Unconstrained Binary Optimization) problem by the method of the Lagrange multiplier. Although the Lagrange multiplier needs to be large enough to avoid violating the one-hot constraint, the Lagrange multiplier usually cannot be set appropriately due to the limitation of the bit precision. The latest quantum annealer can handle values represented by only six or fewer bits. Even conventional computing systems cannot handle the larger value of the Lagrange multiplier as the number of data points increases. To solve this problem, this paper proposes combinatorial clustering that overcomes the limitations of the method of the Lagrange multiplier. The proposed method uses a QUBO solver that can externally define the one-hot constraint independent from the objective function, and the externally-defined constraint is satisfied by the bit-flip operations. Since the constraint function is not included in the objective function, it is no longer needed to determine the Lagrange multiplier. The experimental results show that the proposed method can improve the quality of clustering results.

Original languageEnglish
Title of host publicationProceedings - 2020 8th International Symposium on Computing and Networking, CANDAR 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages59-68
Number of pages10
ISBN (Electronic)9781728182216
DOIs
Publication statusPublished - 2020 Nov
Event8th International Symposium on Computing and Networking, CANDAR 2020 - Virtual, Naha, Japan
Duration: 2020 Nov 242020 Nov 27

Publication series

NameProceedings - 2020 8th International Symposium on Computing and Networking, CANDAR 2020

Conference

Conference8th International Symposium on Computing and Networking, CANDAR 2020
Country/TerritoryJapan
CityVirtual, Naha
Period20/11/2420/11/27

Keywords

  • Combinatorial Clustering
  • Constraint Function
  • Quantum Annealing
  • Simulated Annealing

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Computer Science Applications
  • Software

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