Robust path based semi-supervised dimensionality reduction

In many pattern recognition and data mining tasks, we often confront the problem of learning from a large amount of unlabeled data only with few pairwise constraints. This learning style is a kind of semi-supervised learning, and these pairwise constraints are called Side-Information. Generally speaking, these pairwise constraints are divided into two categories, one is called must-link if the pair of instances belongs to the same class, and the other is called cannot-link if the pair of instances belongs to different classes. Curse of dimensionality comes out simultaneously when the original data space is high, thus, many dimensionality reduction algorithms have proposed, and some of them utilize the side-information of the samples. However, the best learning result cannot be achieved only by using the side-information. So, we propose a novel algorithm called Robust Path Based Semi-Supervised Dimensionality Reduction (RPSSDR) in this paper. The proposed RPSSDR can not only utilize the pairwise constraints but also capture the manifold structure of the data by using robust path based similarity measure. A kernel extension of RPSSDR for the nonlinear dimensionality reduction is also presented. Besides, it can get a transformation matrix and handle unseen sample easily. Experimental results on high dimensional facial databases prove the effectiveness of our proposed method.