We propose a new efficient algorithm for solving the cluster labeling problem in support vector clustering (SVC). The proposed algorithm analyzes the topology of the function describing the SVC cluster contours and explores interconnection paths between critical points separating distinct cluster contours. This process allows distinguishing disjoint clusters and associating each point to its respective one. The proposed algorithm implements a new fast method for detecting and classifying critical points while analyzing the interconnection patterns between them. Experiments indicate that the proposed algorithm significantly improves the accuracy of the SVC labeling process in the presence of clusters of complex shape, while reducing the processing time required by existing SVC labeling algorithms by orders of magnitude.

Clustering categorical data faces two challenges, one is lacking of inherent similarity measure, and the other is that the clusters are prone to being embedded in different subspace. In this paper, we propose the first divisive hierarchical clustering algorithm for categorical data. The algorithm, which is based on multiple correspondence analysis (MCA), is systematic, efficient and effective. In our algorithm, MCA plays an important role in analyzing the data globally. The proposed algorithm has five merits. First, our algorithm yields a dendrogram representing nested groupings of patterns and similarity levels at different granularities. Second, it is parameter-free, fully automatic and, most importantly, requires no assumption regarding the number of clusters. Third, it is independent of the order in which the data are processed. Forth, it is scalable to large data sets; and finally, using the novel data representation and Chi-square distance measures makes our algorithm capable of seamlessly discovering the clusters embedded in the subspaces. Experiments on both synthetic and real data demonstrate the superior performance of our algorithm.