A manifold learning framework for both clustering and classification

In recent years, a great deal of manifold clustering algorithms was presented to identify the subsets of the manifolds data. Meanwhile, numerous classification algorithms were also developed to classified data shaped in the form of manifold. However, nearly none of them pay attention to the statistical relationship between the manifold structures and class labels, thus failing to discover the knowledge concealed in data. In this paper, a manifold learning framework for both clustering and classification is presented, which involves two steps. In the first step, the clustering through ranking on manifolds is executed to explore structures in data; in the second step, the class posterior probability is calculated by using the Bayesian rule. The core of this framework lies in employing the Bayesian theory to establish the relationship between manifolds and classes thus creates a bridge between clustering learning and classification learning. Our new manifold learning framework is interesting from a number of perspectives: (1) our algorithm can perform manifold clustering learning which can auto-determine the clustering parameters without manual determining; (2) our algorithm can perform manifold classification learning which models the posterior probabilities p(ωl|xi)p(ωl|xi) by using the Bayesian rule; (3) our algorithm can provide the statistical relationship between the manifold structure and the given classes. Encouraging experimental results are obtained on 2 artificial and 16 real-life benchmark datasets.