A Cure for Variance Inflation in High Dimensional Kernel Principal Component Analysis

Small sample high-dimensional principal component analysis (PCA) suffers from variance inflation and lack of generalizability. It has earlier been pointed out that a simple leave-one-out variance renormalization scheme can cure the problem. In this paper we generalize the cure in two directions: First, we propose a computationally less intensive approximate leave-one-out estimator, secondly, we show that variance inflation is also present in kernel principal component analysis (kPCA) and we provide a non-parametric renormalization scheme which can quite efficiently restore generalizability in kPCA. As for PCA our analysis also suggests a simplified approximate expression

A Randomized Heuristic for Kernel Parameter Selection with Large-scale Multi-class Data

Goal: Develop an efficient heuristic for kernel parameter selection with largescale multi-class data. Idea: Measure class dispersion by the radius of the minimum enclosing ball of the class means in the Reproducing Kernel Hilbert Space (RKHS) and choos