关键词: 维数约简, 辅助信息, 成对约束, 先验隶属度, 邻接矩阵

Abstract: Semi-supervised dimensionality reduction refers to find the optimal low-dimensional structures from the original high-dimensional data in terms of the joint knowledge from side information and a large number of unlabeled instances. It has been regarded as an effective way to grasp the high-dimensional data such as gene sequence, text data and face images. In this paper, it develops a general framework for semi-supervised dimensionality reduction with pairwise constraints（SSPC）. SSPC learns a discriminant adjacent matrix by using pairwise constraints and nearest neighbors of data. Then, it can learn a projection embedding the data from the original space to the low-dimensional space such that intra-cluster instances become even more nearby while extra-cluster instances become as far away from each other as possible. The proposed method can not only find a linear subspace which is optimal for discrimination, but also discover the nonlinear structure of the manifold. Experimental results on various real data sets demonstrate that SSPC is superior to established dimensionality reduction approaches.

Key words: dimensionality reduction, side information, pairwise constraints, prior membership degree, adjacent matrix