Identifying cluster centroids from decision graph automatically using a statistical outlier detection method

Abstract

Cluster centroid identification is a crucial step for many clustering methods. Recently, Rodriguez and Laio have proposed an effective density-based clustering method called Density Peak Clustering (DPC), in which the density value of each data point and the minimum distance from the points with higher density values are used to identify cluster centroids from the decision graph. However, there is still a lack of automatic methods for the identification of cluster centroids from the decision graph. In this work, a novel statistical outlier detection method is designed to identify cluster centroids automatically from the decision graph, so that the number of clusters is also automatically determined. In the proposed method, one-dimensional probability density functions at specific density values in the decision graph are estimated using two-dimensional Gaussian kernel functions. Then the cluster centroids are identified automatically as outliers in the decision graph using expectation values and standard deviations computed at specific density values. Experiments on several synthetic and real-world datasets show the superiority of the proposed method in centroid identification from the datasets with various distributions and dimensionalities. Furthermore, it is also shown that the proposed method can be effectively applied to image segmentation.