A Novel Density-Based Clustering Framework by Using Level Set Method

Abstract

In this paper, a new density-based clustering framework is proposed by adopting the assumption that the cluster centers in data space can be regarded as target objects in image space. First, the level set evolution is adopted to find an approximation of cluster centers by using a new initial boundary formation scheme. Accordingly, three types of initial boundaries are defined so that each of them can evolve to approach the cluster centers in different ways. To avoid the long iteration time of level set evolution in data space, an efficient termination criterion is presented to stop the evolution process in the circumstance that no more cluster centers can be found. Then, a new effective density representation called level set density (LSD) is constructed from the evolution results. Finally, the valley seeking clustering is used to group data points into corresponding clusters based on the LSD. The experiments on some synthetic and real data sets have demonstrated the efficiency and effectiveness of the proposed clustering framework. The comparisons with DBSCAN method, OPTICS method, and valley seeking clustering method further show that the proposed framework can successfully avoid the overfitting phenomenon and solve the confusion problem of cluster boundary points and outliers.