Kernel Sliced Inverse Regression: Regularization and Consistency

Kernel sliced inverse regression (KSIR) is a natural framework for nonlinear dimension reduction using the mapping induced by kernels. However, there are numeric, algorithmic, and conceptual subtleties in making the method robust and consistent. We apply two types of regularization in this framework to address computational stability and generalization performance. We also provide an interpretation of the algorithm and prove consistency. The utility of this approach is illustrated on simulated and real data

PAPER A Kernel-Based Fisher Discriminant Analysis for Face Detection

SUMMARY This paper presents a modification of kernel-based Fisher discriminant analysis (FDA) to design one-class classifier for face detection. In face detection, it is reasonable to assume “face ” images to cluster in certain way, but “non face ” images usually do not cluster since different kinds of images are included. It is difficult to model “non face ” images as a single distribution in the discriminant space constructed by the usual two-class FDA. Also the dimension of the discriminant space constructed by the usual two-class FDA is bounded by 1. This means that we can not obtain higher dimensional discriminant space. To overcome these drawbacks of the usual two-class FDA, the discriminant criterion of FDA is modified such that the trace of covariance matrix of “face ” class is minimized and the sum of squared errors between the average vector of “face” class and feature vectors of “non face ” images are maximized. By this modification a higher dimensional discriminant space can be obtained. Experiments are conducted on “face ” and “non face ” classification using face images gathered from the available face databases and many face images on the Web. The results show that the proposed method can outperform the support vector machine (SVM). A close relationship between the proposed kernel-based FDA and kernel-based Principal Component Analysis (PCA) is also discussed. key words: face detection, kernel Fisher discriminant analysis, kernel principal component analysis 1