Density Gain-Rate Peaks for Spectral Clustering

Abstract

Clustering has been troubled by varying shapes of sample distributions, such as line and spiral shapes. Spectral clustering and density peak clustering are two feasible techniques to address this problem, and have attracted much attention from academic community. However, spectral clustering still cannot well handle some shapes of sample distributions in the space of extracted features, and density peak clustering encounters performance problems because it cannot mine the local structures of data and well deal with non-uniform distributions. In order to solve above problems, we propose the density gain-rate peak clustering (DGPC), a new type of density peak clustering method, and then embed it in spectral clustering for performance promotion. Firstly, in order to well handle non-uniform sample distributions, we propose density gain-rate for density peak clustering. Density gain-rate is based on the assumption that the density of a clustering center will be higher with the reduce of the radius. Even under non-uniform distributions, the cluster center in low density region will still have a significant density gain-rate thus can be detected. We combine density gain-rate in density peak clustering to construct DGPC method. Then in the framework of spectral clustering, we use our new density peak clustering to cluster the samples by their extracted features from a similarity graph of these samples, such as the neighbor-based similarity graph or the self-expressiveness similarity graph. Compared with the previous spectral clustering and density peak clustering, our method leads to better clustering performances on varying shapes of sample distributions. The experiment measures the performances of our clustering method and existing clustering methods by NMI and ACC on seven real-world datasets to illustrate the effectiveness of our method.