Graph Embedding Model And Its Application On Dimensionality Reduction

As one of the most important fields in machine research, dimensionality reduction has been paid more and more attention and has achieved a prodigious progress in the theory research and algorithm. Linear Graph embedding (LGE) model is an efficient tool for dimensionality reduction. This paper mainly studies the model and its application on dimension reduction.Firstly, according to the problem of supervised dimensionality reduction with Non-Gaussian data distributions and at the same time consider neighborhood preserving relations among samples, a novel subspace learning method, neighborhood preserving and marginal discriminant embedding (NP-MDE), is proposed based on LGE and marginal Fisher analysis in this paper. NP-MDE could minimize the within-class scatter and meanwhile maximize the margin among different classes. Moreover, the neighborhood structure with each class is preserved.Secondly, in order to solve the problem of semi-supervised learning that uses limited labeled samples with assistance of a great many of unlabeled samples, this paper provide a new label propagation method based on L1-Graph which was constructed by using sparse representation to describe relationships between samples. Experimental results demonstrate the new label propagation method improves the accuracy when compared with that of Linear Neighborhood Propagation (LNP).Finally, because a major disadvantage of Non-negative Matrix Factorization (NMF) in dimensionality reduction is that it only considers data reconstruction error while fails to consider similarities between data samples. An objective function based on graph embedding, which add a regularizer to preserve sparse representation between data samples, is proposed in this paper. Experimental results on several datasets demonstrate the effectiveness of this method.