A neighborhood-based robust clustering algorithm using Apollonius function kernel

Abstract

Density Peak Clustering (DPC) is a useful algorithm for grouping data points based on their closeness and density. It is widely used in various areas of computer science. It can detect the peak density in each period of the clustering steps and assign the rest of the data to the next steps. Peak density clustering analysis is able to discover clusters of arbitrary shapes, but usually, when the data set is large, it is computationally expensive and difficult to apply to high-dimensional data. When the distance between clusters is significantly different, it is unable to distinguish adjacent clusters with different densities. To deal with such issues, a new clustering algorithm based on neighborhoods and the Apollonius kernel is proposed. The proposed algorithm can be implemented with four steps. 1) Estimation of natural neighbor, 2) Identification of core points, 3) Merging the cores of a cluster and separating the cores of different clusters, 4) Using the Apollonius kernel between the core points and the farthest points to assign the remaining points to the clusters and find the noise points. The local density estimation process based on the natural neighborhood of high-density points and their integration, as well as border point classification, allows the proposed method to reveal the local cluster structure. As a result, the adjoining clusters with distinctive densities are recognized, and the computation is substantially reduced. The proposed method is validated on some synthetic data sets and the UCI data set experimentally and has a high 10% accuracy.