Kernel alignment unsupervised discriminative dimensionality reduction

Abstract

The performance of most existing adaptive graph learning methods, which adjust data similarity matrix according to the data representation, depends on the hypotheses that the data representation is a good indicator of the underlying data structure. However, this hypothesis is not always applicable when dealing with high dimensional data. In this paper, we propose a novel kernel alignment unsupervised discriminative dimensionality reduction (KaUDDR) algorithm. By integrating adaptive graph learning and feature learning into a joint learning framework, graph construction and dimensionality reduction are conducted simultaneously to guarantee the optimality of graph for feature learning in the proposed algorithm. Data kernel and similarity indicator kernel are defined by learned graph and the projected data in a low-dimensional subspace, a compact and discriminative data representation in the projected subspace is obtained by means of kernel alignment to explore the consistency between the projected data kernel and similarity indicator kernel. Experimental results on dimensionality reduction as well as clustering show that our method consistently outperforms the related unsupervised dimensionality reduction algorithm.