Quantum Hierarchical Agglomerative Clustering Based on One Dimension Discrete Quantum Walk with Single-Point Phase Defects

Abstract

As an important branch of machine learning, clustering analysis is widely used in some fields, e.g., image pattern recognition, social network analysis, information security, and so on. In this paper, we consider the designing of clustering algorithm in quantum scenario, and propose a quantum hierarchical agglomerative clustering algorithm, which is based on one dimension discrete quantum walk with single-point phase defects. In the proposed algorithm, two nonclassical characters of this kind of quantum walk, localization and ballistic effects, are exploited. At first, each data point is viewed as a particle and performed this kind of quantum walk with a parameter, which is determined by its neighbors. After that, the particles are measured in a calculation basis. In terms of the measurement result, every attribute value of the corresponding data point is modified appropriately. In this way, each data point interacts with its neighbors and moves toward a certain center point. At last, this process is repeated several times until similar data points cluster together and form distinct classes. Simulation experiments on the synthetic and real world data demonstrate the effectiveness of the presented algorithm. Compared with some classical algorithms, the proposed algorithm achieves better clustering results. Moreover, combining quantum cluster assignment method, the presented algorithm can speed up the calculating velocity.