Combinatorial Clustering Based on an Externally-Defined One-Hot Constraint

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

doi:10.1109/candar51075.2020.00015

Cited by 10 publications

(6 citation statements)

References 16 publications

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“…For example, when the number of clusters K is 4, and the number of data points N is 3, d ≤ 62. On the actual quantum annealer, 1 8 d < 8 from Eq. (12).…”

Section: Problems Of the Annealing-based Clustering Algorithmmentioning

confidence: 99%

“…Variable q 1 1 = 1 means data point i = 1 belongs to cluster a = 1. If a variable q 1 1 = 1 is flipped, all variables q 1 1 , q 1 2 , and q 1 3 become zero, which violates a constraint. Data point i = 1 does not belong to any cluster.…”

Section: Combinatorial Clustering Using Simulated Annealing With An External Constraintmentioning

confidence: 99%

“…The number of sweeps is set to 100. Inverse temperature 1 T is set to 0.1 when starting the solver, and increases until 50 at the end.…”

Section: Experimental Environmentsmentioning

confidence: 99%

“…For example, the latest quantum annealer can handle values represented by only six or fewer bits [4,5]. Even in the case of conventional computing systems with A short version of this work [1] has appeared in the proceedings of the CANDAR '20. high bit precision, their bit precisions are not sufficient when the problem size is large. Moreover, the time for the QUBO matrix generation is one of the dominant computations in combinatorial clustering.…”

Section: Introductionmentioning

confidence: 99%

“…The quality of a clustering result is evaluated by Cost as the value of an exact objective function shown in Eq (1)…”

mentioning

confidence: 99%

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An External Definition of the One-Hot Constraint and Fast QUBO Generation for High-Performance Combinatorial Clustering

Kumagai

Komatsu

Takano³

et al. 2021

IJNC

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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 one-hot constraint. The objective function and the constraint function are generally formulated to a unified objective function of a QUBO (Quadratic Unconstrained Binary Optimization) problem using the method of the Lagrange multiplier. The coefficients of the QUBO function can be represented by a square matrix, which is called the QUBO matrix.Although the Lagrange multiplier needs to be large enough to avoid violating the constraint, it is usually hard to be set appropriately due to the limitation of the bit precision. For example, the latest quantum annealer can handle values represented by only six or fewer bits. Even conventional computing systems cannot control the larger value of the Lagrange multiplier as the number of data points increases. Besides, the execution time for combinatorial clustering increases exponentially as the problem size increases. This is because the time for the QUBO matrix generation is long and a dominant factor of the total execution time when the problem size is large.To solve these problems, this paper proposes combinatorial clustering that overcomes the limitation of the method of the Lagrange multiplier. The proposed method uses a QUBO solver

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“…For example, when the number of clusters K is 4, and the number of data points N is 3, d ≤ 62. On the actual quantum annealer, 1 8 d < 8 from Eq. (12).…”

Section: Problems Of the Annealing-based Clustering Algorithmmentioning

confidence: 99%

Section: Combinatorial Clustering Using Simulated Annealing With An External Constraintmentioning

confidence: 99%

“…The number of sweeps is set to 100. Inverse temperature 1 T is set to 0.1 when starting the solver, and increases until 50 at the end.…”

Section: Experimental Environmentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The quality of a clustering result is evaluated by Cost as the value of an exact objective function shown in Eq (1)…”

mentioning

confidence: 99%

See 3 more Smart Citations

An External Definition of the One-Hot Constraint and Fast QUBO Generation for High-Performance Combinatorial Clustering

Kumagai

Komatsu

Takano³

et al. 2021

IJNC

Self Cite

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Analysis of Precision Vectors for Ising-Based Linear Regression

Aoyama¹,

Komatsu²,

Kumagai³

et al. 2023

Lecture Notes in Computer Science

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How to Solve Combinatorial Optimization Problems Using Real Quantum Machines: A Recent Survey

Heng

Kim

et al. 2022

IEEE Access

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A combinatorial optimization problem (COP) is the problem of finding the optimal solution in a finite set. When the size of the feasible solution set is large, the complexity of the problem increases, and it is not easy to solve in a reasonable time with the current classical computer technology. Quantum annealing (QA) is a method that replaces classical simulated annealing (SA) methods that do not solve these cases. Therefore, several attempts have been made to solve this problem using a special-purpose quantum annealer to which the QA method is applied. In this survey, we analyze recent studies that solve real-scale COPs using quantum annealers. Through this, we discuss how to reduce the size of the COP to be input to overcome the hardware limitations of the existing quantum annealer. Additionally, we demonstrated the applicability of quantum annealer to COP on a practical scale by comparing and analyzing the results of the classical simulated annealing (SA) and QA method from each study. INDEX TERMSCombinatorial optimization problem (COP), Simulated annealing (SA), Quantum annealing (QA), Real quantum machine

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Combinatorial Clustering Based on an Externally-Defined One-Hot Constraint

Cited by 10 publications

References 16 publications

An External Definition of the One-Hot Constraint and Fast QUBO Generation for High-Performance Combinatorial Clustering

An External Definition of the One-Hot Constraint and Fast QUBO Generation for High-Performance Combinatorial Clustering

Analysis of Precision Vectors for Ising-Based Linear Regression

How to Solve Combinatorial Optimization Problems Using Real Quantum Machines: A Recent Survey

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