Distortion in Correspondence Analysis and in Taxicab Correspondence Analysis: A Comparison

2024/03/01 by Vartan Choulakian, Choulakian, Vartan
Economics, Econometrics and Finance · Environmental Science · #62H30 #AMS 2010 subject classifications: 62H25 #FOS: Computer and information sciences #Korean Urban and Social Studies #Methodology (stat.ME) #Spatial and Panel Data Analysis

paper · pdf · doi:10.48550/arxiv.2403.00617

openalex publication_date 2024/03/01 · openalex created_date 2024/03/05 · openalex updated_date 2026/07/28

Abstract

Distortion is a fundamental well-studied topic in dimension reduction papers, and intimately related with the underlying intrinsic dimension of a mapping of a high dimensional data set onto a lower dimension. In this paper, we study embedding distortions produced by Correspondence Analysis and its robust l1 variant Taxicab Correspondence analysis, which are visualization methods for contingency tables. For high dimensional data, distortions in Correspondence Analysis are contractions; while distortions in Taxicab Correspondence Analysis could be contractions or stretchings. This shows that Euclidean geometry is quite rigid, because of the orthogonality property; while Taxicab geometry is quite flexible, because the orthogonality property is replaced by the conjugacy property.

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