A Regularized Approach for Geodesic-Based Semi supervised Multimanifold Learning

Geodesic distance, as an essential measurement for data dissimilarity, has been successfully used in manifold learn-ing. However, most geodesicdistance-based manifold learning algorithms have two limitations when applied to classification: 1) class information is rarely used in computing the geodesic distances between data points on manifolds and 2) little attention has been paid to building an explicit dimension reduction mapping for extracting the discriminative information hidden in the geodesic distances. In this paper, we regard geodesic distance as a kind of kernel, which maps data from linearly inseparable space to linear separable distance space. In doing this, a new semisupervised manifold learning algorithm, namely regularized geodesic feature learning algorithm, is proposed. The method consists of three techniques: a semisupervised graph construction method, replacement of original data points with feature vectors which are built by geodesic distances, and a new semi supervised dimension reduction method for feature vectors. Experiments on the MNIST, USPS handwritten digit data sets, MIT CBCL faceversus nonface data set, and an intelligent traffic data set show  the effectiveness of the proposed algorithm.