Dimensionality reduction using covariance operator inverse regression

We consider the task of dimensionality reduction for regression (DRR) whose goal is to find a low dimensional representation of input covariates, while preserving the statistical correlation with output targets. DDR is particularly suited for visualization of high dimensional data as well as the efficient regressor design with a reduced input dimension. In this paper we propose a novel nonlinear method for DRR that exploits the kernel Gram matrices of input and output. While most existing DDR techniques rely on the inverse regression, our approach removes the need for explicit slicing of the output space using covariance operators in RKHS. This unique property make DRR applicable to problem domains with high dimensional output data with potentially significant amounts of noise. Although recent kernel dimensionality reduction algorithms make use of RKHS covariance operators to quantify conditional dependency between the input and the targets via the dimension-reduced input, they are ei...

• Type: Conference
• Year: 2008
• Where: CVPR
• Authors: Minyoung Kim, Vladimir Pavlovic
• Keywords: Computer Vision, CVPR 2008, Dimension-reduced Input, Input Covariates, Input Dimension, Kernel Dimensionality Reduction, Linear Input Subspaces