A supervised method for building a regularized map for general multi-view multi-manifold learning

In this paper, we consider the issue of automatic and unsupervised class-manifold selection in a multi-view multi-manifold space. General multi-manifold learning methods achieve multiple independent manifolds, so it is challenging for them to adjust the intra-class local manifold information and global inter-class discriminative structure. In this paper, we propose a multi-manifold embedding method, which can explicitly obtain multi-view multi-manifold structure while considering both intra-class compactness and inter-class separability without using the class label information. Furthermore, to the generalization of embedding to novel points, known as the out-of-sample extension problem in multi-view multi-manifold learning, we propose a supervised method for building a regularized map that provides an out-of-sample extension for general multi-view multi-manifold learning studied in the context of classification. Experimental results on face and object images demonstrate the potential of the proposed method for the classification of multi-view multi-manifold data sets and the proposed out-of-sample extension algorithm for the classification of manifold-modeled data sets.