Abstract—It is getting harder to deal with the large data sets by the classical hierarchical clustering algorithm, so we propose an efficient quantum hierarchical clustering algorithm, in which the quantum bit (qubit) is used to represent the data point in the space. For quantum entanglement, the distance between two data points is calculated through adding an auxiliary particle to construct the entangled state. Then a projective measurement is performed on the auxiliary particle alone. The distance between two points is acquired by the projective measurement. We use the distance of the cluster centroids as a measure of similarity between clusters. Also, based on the principle of the minimum cluster centroids distance, the nearest two clusters are merged. We aim at improving time and space complexity and effect of the clustering of the hierarchical clustering algorithm.
Index Terms—Large data, hierarchical clustering, qubit, entangled states.
Fengbo Kong and Hailing Xiong are with College of Computer and Information Science, Southwest University, Chongqing 400715, China (e-mail: email@example.com, firstname.lastname@example.org).
Hong Lai is with College of Computer and Information Science and Centre for Research and Innovation in Software Engineering (RISE), Southwest University, Chongqing 400715, China (e-mail: email@example.com).
Cite: Fengbo Kong, Hong Lai, and Hailing Xiong, "Quantum Hierarchical Clustering Algorithm Based on the Nearest Cluster Centroids Distance," International Journal of Machine Learning and Computing vol. 7, no. 5, pp. 100-104, 2017.