Data Classification on Multiple Manifolds

Unlike most previous manifold-based data classification algorithms assume that all the data points are on a single manifold, we expect that data from different classes may reside on different manifolds of possible different dimensions. Therefore, better classification accuracy would be achieved by modeling the data by multiple manifolds each corresponding to a class. To this end, a general framework for data classification on multiple manifolds is presented. The manifolds are firstly learned for each class separately, and a stochastic optimization algorithm is then employed to get the near optimal dimensionality of each manifold from the classification viewpoint. Then, classification is performed under a newly defined minimum reconstruction error based classifier. Our method could be easily extended by involving various manifold learning methods and searching strategies. Experiments on both synthetic data and databases of facial expression images show the effectiveness of the proposed multiple manifold based approach.