Discriminant Analysis on Embedded Manifold

Abstract—Traditional manifold learning algorithms, such as ISOMAP, LLE, and Laplacian Eigenmap, mainly focus on un-covering the latent low-dimensional geometry structure of the training samples in an unsupervised manner where useful class information is ignored. Therefore, the derived low-dimensional representations are not necessarily optimal in discriminative ca-pability. In this paper, we study the discriminant analysis problem by considering the nonlinear manifold structure of data space. To this end, firstly, a new clustering algorithm, called Intra-Cluster Balanced-Means (ICBKM), is proposed to partition the samples into multiple clusters while ensure that there are balanced samples for the classes within each cluster; approximately, each cluster can be considered as a local patch on the embedded manifold. Then, the local discriminative projections for different clusters are simultaneously calculated by optimizing the global Fishe