Learn More
In dealing with large data sets, the reduced support vector machine (RSVM) was proposed for the practical objective to overcome some computational difficulties as well as to reduce the model complexity. In this paper, we study the RSVM from the viewpoint of sampling design, its robustness, and the spectral analysis of the reduced kernel. We consider the(More)
Kernel Fisher discriminant analysis (KFDA) has been proposed for nonlin-ear binary classification. It is a hybrid method of the classical Fisher linear discriminant analysis and a kernel machine. Experimental results have shown that the KFDA performs slightly better in terms of prediction error than the popular support vector machines and is a strong(More)
The problem of choosing a good parameter setting for a better generalization performance in a learning task is the so-called model selection. A nested uniform design (UD) methodology is proposed for efficient, robust and automatic model selection for support vector machines (SVMs). The proposed method is applied to select the candidate set of parameter(More)
This letter discusses the robustness issue of kernel principal component analysis. A class of new robust procedures is proposed based on eigenvalue decomposition of weighted covariance. The proposed procedures will place less weight on deviant patterns and thus be more resistant to data contamination and model deviation. Theoretical influence functions are(More)
The main purpose of this article is to study the wavelet shrinkage method from a Bayesian viewpoint. Nonparametric mixed-effects models are proposed and used for interpretation of the Bayesian structure. Bayes and empirical Bayes estimation are discussed. The latter is shown to have the Gauss-Markov type optimality (i.e., BLUP), to be equivalent to a method(More)
The multiclass classification problem is considered and resolved through coding and regression. There are various coding schemes for transforming class labels into response scores. An equivalence notion of coding schemes is developed, and the regression approach is adopted for extracting a low-dimensional discriminant feature subspace. This feature subspace(More)
BACKGROUND The maximal number of live births (k) per donor was usually determined by cultural and social perspective. It was rarely decided on the basis of scientific evidence or discussed from mathematical or probabilistic viewpoint. METHODS AND RESULTS To recommend a value for k, we propose three criteria to evaluate its impact on consanguinity and(More)
Sliced inverse regression (SIR) is a renowned dimension reduction method for finding an effective low-dimensional linear subspace. Like many other linear methods, SIR can be extended to nonlinear setting via the ldquokernel trick.rdquo The main purpose of this paper is two-fold. We build kernel SIR in a reproducing kernel Hilbert space rigorously for a more(More)
Kernel Fisher's linear discriminant analysis (KFLDA) has been proposed for non-It is a hybrid method of the classical Fisher's linear discriminant analysis and a kernel machine. Experimental results (e.g., Schölkopf and Smola, 2002) have shown that the KFLDA performs slightly better in terms of prediction error than the popular support vector machines and(More)