A quantum-inspired genetic algorithm for <i>k</i>-means clustering

Abstract

The number of clusters has to be known in advance for the conventional k-means clustering algorithm and moreover the clustering result is sensitive to the selection of the initial cluster centroids. This sensitivity may make the algorithm converge to the local optima. This paper proposes a quantum-inspired genetic algorithm for k-means clustering (KMQGA). In KMQGA, a Q-bit based representation is employed for exploration and exploitation in discrete 0-1 hyperspace using rotation operation of quantum gate as well as the typical genetic algorithm operations (selection, crossover and mutation) of Q-bits. Different from the typical quantum-inspired genetic algorithms (QGA), the length of a Q-bit in KMQGA is variable during evolution. Without knowing the exact number of clusters beforehand. KMQGA can obtain the optimal number of clusters as well as providing the optimal cluster centroids. Both the simulated datasets and the real datasets are used to validate KMQGA. respectively. The experimental results show that KMQGA is promising and effective. (C) 2009 Elsevier Ltd. All rights reserved.