We propose an efficient linear-time graph-based divisive cluster analysis approach called Sampling Clustering. It constructs a lite informative dendrogram by recursively dividing a graph into subgraphs. In each recursive call, a graph is sampled first with a set of vertices being removed to disconnect latent clusters, then condensed by adding edges to the remaining vertices to avoid graph fragmentation caused by vertex removals. We also present some sampling and condensing methods and discuss the effectiveness in this paper. Our implementations run in linear time and achieve outstanding performance on various types of datasets. Experimental results show that they outperform state-of-the-art clustering algorithms with significantly less computing resource requirements.
We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging. We have developed a novel algorithm for cluster analysis that is based on graph theoretic techniques. A similarity graph is defined and clusters in that graph correspond to highly connected subgraphs. A polynomial algorithm to compute them efficiently is presented. Our algorithm produces a solution with some provably good properties and performs well on simulated and real data.