A Quantum-Inspired Genetic K-Means Algorithm for Gene Clustering

Abstract

K-means is a widely used classical clustering algorithm in pattern recognition, image segmentation, bioinformatics and document clustering. But, it is easy to fall into local optimum and is sensitive to the initial choice of cluster centers. As a remedy, a popular trend is to integrate the swarm intelligence algorithm with K-means to obtain hybrid swarm intelligence K-means algorithms. Such as, K-means is combined with particle swarm optimization algorithm to obtain particle swarm optimization K-means, and is also combined with genetic mechanism to obtain Genetic K-means algorithms. The classical K-means clustering algorithm requires the number of cluster centers in advance. In this paper, an automatic quantum genetic K-means algorithm for unknown K (AQGUK) is proposed to accelerate the convergence speed and improve the global convergence of AGUK. In AQGUK, 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 genetic operations (selection, crossover and mutation) of Q-bits. The length of Q-bit individuals is variable during the evolution, which is Different from the typical genetic algorithms. Without knowing the exact number of clusters beforehand, AQGUK can obtain the optimal number of clusters and provide the optimal cluster centroids. Five gene datasets are used to validate AQGUK, AGUK and K-means. The experimental results show that AQGUK is effective and promising.