Semi-supervised dimensionality reduction via sparse locality preserving projection

The dimensionality reduction of the unbalanced semi-supervised problem is difficult because there are too few labeled samples. In this paper, we propose a new dimensionality reduction method for the unbalanced semi-supervised problem, called sparse locality preserving projection (SLPP for short). In the past work of solving the semi-supervised dimensionality reduction problems, they either abandon some unlabeled samples or do not utilize the implicit discriminant information of unlabeled samples. While, SLPP learns the optimal projection matrix with the full use of the discriminant information and the geometric structure of the unlabeled samples. Here, we preserve the geometric structure of the rest unlabeled samples and their k-nearest neighbors after increasing the number of labeled samples by label propagation. The optimization problem of SLPP can be easily solved by a generalized eigenvalue problem. Results on various data sets from UCI machine learning repository and two hyperspectral data sets demonstrate that SLPP is superior to other conventional reduction methods.