The Quantile Method for Symbolic Principal Component Analysis

Abstract

In this article, we present a new quantification method to realize the principal component analysis (PCA) for symbolic data tables. We first describe the nesting property for the monotone point sequences and the correlation matrix by the rank correlation coefficient. Then, we present the object splitting method by which interval valued data table can be transformed to a usual numerical data table. We are able to apply the traditional PCA to this transformed data table. The quantile method is a generalization of the object splitting method, and can manipulate histograms, nominal multi-value types, and other types simultaneously. We present several experimental results in order to illustrate the usefulness of the quantile method. 2011 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 4: 184–198, 2011