Dimension Reduction and Classification with Categorical Predictors

• Activity Number: 43
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Graphics*
• Author(s): Liqiang Ni*+
• Affiliation(s): University of Minnesota
• Keywords: Dimension Reduction ; Classification ; central subspaces ; Regression Graphics ; sliced inverse regression (SIR) ; General Partial SIR

Abstract

In a general regression analysis, $Y\in R^{1}$ is the response and $ X \in R^{p}$ is the predictor. The conditional distribution of $Y|X$ very often is identical to the conditional distribution of Y given q linear combinations of X, $\eta_{1}^{T}X,\eta_{2}^{T}X,...,\eta_{q}^{T}X, \ q < p$. Therefore, we are able to decrease the dimension of the predictor from p to q. We review a framework for this type of dimension reduction via the concept of central subspaces.

Qualitative predictors often appear in regression analysis. These predictors may be intrinsic factors, and may also be categorical versions of continuous predictors. The current framework for dimension reduction does not allow for qualitative predictors. We propose an extension of the dimension reduction framework to accommodate qualitative predictors. In particular, we focus on multiple factors like species/location.

This framework are not only effective tools to address dimension reduction issues, but also are very useful in classification problems, which opens the door to an important application field. We investigate the discovery of latent factors and classification within this dimension reduction framework.