Manifold clustering via energy minimization

Manifold clustering aims to partition a set of input data into several clusters each of which contains data points from a separate, simple low-dimensional manifold. This paper presents a novel solution to this problem. The proposed algorithm begins by randomly selecting some neighboring orders of the input data and defining an energy function that is described by geometric features of underlying manifolds. By minimizing such energy using the tabu search method, an approximately optimal sequence could be found with ease, and further different manifolds are separated by detecting some crucial points, boundaries between manifolds, along the optimal sequence. We have applied the proposed method to both synthetic data and real image data and experimental results show that the method is feasible and promising in manifold clustering.