Robustness in Dimensionality Reduction

• Activity Number: 44
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jiaxi Liang*+ and Christopher Small and Shoja'eddin Chenouri
• Companies: and University of Waterloo and University of Waterloo
• Keywords: Robustness ; dimensionality reduction ; intrinsic dimensionality ; local topology preservation ; global topology preservation

Abstract

Many popular dimensionality reduction methods are considered to be highly sensitive to outliers, and some robust procedures are proposed without a general and well-established criterion. We extend several classical concepts (both local and global) to measure and compare the robustness of the dimensionality reduction methods (both linear and non-linear). Measures concerning the local and global topology preservation are defined as badness criterion, and based on these measures, the performances of different types of methods are assessed under contaminated dataset or misspecified model. Also, we consider the estimation of intrinsic dimensionality and the effect of outliers on this estimation.