Topology description for data distributions using a topology graph with divide-and-combine learning strategy.

The topologies of data distributions are very important for data description. Usually, it is not easy to find a description that can give us an intuitional understanding of the topologies for general distributions. In this paper, a novel concept, a topology graph, is proposed as a description for the principal topology of data distribution. The topology graph builds a one-to-one correspondence between the principal topology of the distribution and the topology itself: annularity features of the principal topology correspond to the loops of the graph, and the divarication features correspond to the branches of the graph. In general, the topology graph can be considered as the skeleton of the data distribution. A divide-and-combine learning strategy is developed to find the topology graphs for general data distributions. The learning strategy is focused on the constrained local description learning and automatic topology generation. Following the learning strategy, a cluster growing algorithm is developed. Experimental results on both artificial datasets and real-world applications show good performance of the proposed algorithm.