A Novel Semi-Supervised Dimensionality Reduction Framework for Multi-manifold Learning

In pattern recognition, traditional single manifold assumption can hardly guarantee the best classification performance, since the data from multiple classes does not lie on a single manifold. When the dataset contains multiple classes and the structure of the classes are different, it is more reasonable to assume each class lies on a particular manifold. In this paper, we propose a novel framework of semi-supervised dimensionality reduction for multi-manifold learning. Within this framework, methods are derived to learn multiple manifold corresponding to multiple classes in a data set, including both the labeled and unlabeled examples. In order to connect each unlabeled point to the other points from the same manifold, a similarity graph construction, based on sparse manifold clustering, is introduced when constructing the neighbourhood graph. Experimental results verify the advantages and effectiveness of this new framework.