Robust Regularized Cluster Analysis for High-Dimensional Data

Abstrakt

This paper presents new approaches to the hierarchical agglomerative cluster analysis for high-dimensional data. First, we propose a regularized version of the hierarchical cluster analysis for categorical data with a large number of categories. It exploits a regularized version of various test statistics of homogeneity in contingency tables as the measure of distance between two clusters. Further, our aim is cluster analysis of continuous data with a large number of variables. Various regularization techniques tailor-made for high-dimensional data have been proposed, which have however turned out to suffer from a high sensitivity to the presence of outlying measurements in the data. As a robust solution, we recommend to combine two newly proposed methods, namely a regularized version of robust principal component analysis and a regularized Mahalanobis distance, which is based on an asymptotically optimal regularization of the covariance matrix. We bring arguments in favor of the newly proposed methods.