Quantum clustering using kernel entropy component analysis

Abstract

In this paper, a novel method quantum clustering using kernel entropy component analysis (KECA-QC) is proposed. This method has two phases: preprocessing and clustering stages. The main idea of preprocessing is to map the original data to a high-dimensional feature space, and to select the useful components using Renyi entropy as our similarity metric. After data preprocessing, different clusters will be distributed more or less in different places, and for high-dimensional datasets, it can achieve the purpose of dimensionality reduction at the same time. In the second phase, quantum clustering method is used, which can find clusters of any shape without knowing the number of clusters. Based on the traditional quantum clustering, we develop a new method estimating the wave function from distributions of K-nearest neighbors statistics, which can further reduce the running time and improve the calculation efficiency. In order to evaluate the effectiveness of this method, we compare the proposed method with k-means clustering (KM), the classical spectral clustering algorithm called Ng-Jordan-Weiss (NJW), the traditional QC, and kernel entropy component analysis spectral clustering algorithm (KECA-KM). The experimental results demonstrate that the proposed algorithm outperforms the compared algorithms on synthesized datasets and UCI datasets.