A novel dimensionality reduction technique based on kernel optimization through graph embedding

Abstract

In this paper, we propose a new method for kernel optimization in kernel-based dimensionality reduction techniques such as kernel principal component analysis and kernel discriminant analysis. The main idea is to use the graph embedding framework for these techniques and, therefore, by formulating a new minimization problem to simultaneously optimize the kernel parameters and the projection vectors of the chosen dimensionality reduction method. Experimental results are conducted in various datasets, varying from real-world publicly available databases for classification benchmarking to facial expressions and face recognition databases. Our proposed method outperforms other competing ones in classification performance. Moreover, our method provides a systematic way to deal with kernel parameters whose calculation was treated rather superficially so far and/or experimentally, in most of the cases.