Recently there has been a lot of interest in geometrically motivated approaches dealing with data in high dimensional spaces. We consider the case where data is sampled from a low dimensional manifold which is embedded in high dimensional Euclidean space. In this paper, we propose a novel unsupervised linear subspace learning algorithm called Local and Global Manifold Preserving Embedding (LGMPE). Different from existing manifold learning based linear subspace learning algorithms which aims at preserving either single kind of local manifold structure or single kind of global manifold structure on the data manifold, LGMPE can preserve different local and global manifold structures simultaneously in the graph embedding framework. Several experiments on real face datasets demonstrate the effectiveness of the proposed algorithm.
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