How to reduce dimensionality of data: Robustness point of view

Abstract

Data analysis in management applications often requires to handle data with a large number of variables. Therefore, dimensionality reduction represents a common and important step in the analysis of multivariate data by methods of both statistics and data mining. This paper gives an overview of robust dimensionality procedures, which are resistant against the presence of outlying measurements. A simulation study represents the main contribution of the paper. It compares various standard and robust dimensionality procedures in combination with standard and robust methods of classification analysis. While standard methods turn out not to perform too badly on data which are only slightly contaminated by outliers, we give practical recommendations concerning the choice of a suitable robust dimensionality reduction method for highly contaminated data. Namely the highly robust principal component analysis based on the projection pursuit approach turns out to yield the most satisfactory results over four different simulation studies. At the same time, we give recommendations on the choice of a suitable robust classification method.