A regularization framework for robust dimensionality reduction with applications to image reconstruction and feature extraction

Dimensionality reduction has many applications in pattern recognition, machine learning and computer vision. In this paper, we develop a general regularization framework for dimensionality reduction by allowing the use of different functions in the cost function. This is especially important as we can achieve robustness in the presence of outliers. It is shown that optimizing the regularized cost function is equivalent to solving a nonlinear eigenvalue problem under certain conditions, which can be handled by the self-consistent field (SCF) iteration. Moreover, this regularization framework is applicable in unsupervised or supervised learning by defining the regularization term which provides some types of prior knowledge of projected samples or projected vectors. It is also noted that some linear projection methods can be obtained from this framework by choosing different functions and imposing different constraints. Finally, we show some applications of our framework by various data sets including handwritten characters, face images, UCI data, and gene expression data.