Exploring Linear Homeomorphic Clusters on Nonlinear Manifold

Abstract

This paper proposed a new clustering alogorithm based on ant colony optimization and Grassmann manifold for exploring linear homeomorphic clusters on non-linear dataset manifold. The minimum processed units of algorithm were first lifted to suppress the influence of noise, and then the similarity of unit was measured according to Grassmann manifold and a geodesic-like distance was designed for ensuring the connectivity of cluster. To improve the quality of cluster generated by ant colony clustering, the direction of minimum surface complexity was defined and introduced into the pheromone update strategy as heuristic information. Experiments and analysis on several datasets have shown the successful performance on linear homeomorphic clustering compared to traditional clustering algorithms.