Iterative optimization clustering algorithm based on manifold distance

Aiming at the problem that classical Euclidean distance metric may be invalid when it is used to measure the complicated data structures, a manifold distance based on similarity metric and being able to measure the geodesic distance along the manifold is introduced, and a criterion function used to express the clustering target is designed, where the samples in the same cluster are somehow more similar than samples in different one. Accordingly, the clustering problem is converted to function optimization problem, and an iterative optimization clustering algorithm is proposed. The steps of the algorithm are discussed in detail. Simulation results on four artificial datasets with different manifold structures show that the new algorithm is more straightforward due to the less pre-defined parameters and it is a deterministic algorithm due to the lack of random operations. A comparison with k-means clustering algorithms indicates the ability to determine the cluster number automatically and identify complex non-convex clusters.