Taxicab correspondence analysis of sparse two-way contingency tables

Abstract

Visualization and interpretation of contingency tables by correspondence analysis (CA), as developed by Benzécri, have a rich structure based on Euclidean geometry. However, it is a well established fact that, often CA is very sensitive to sparse contingency tables, where we characterize sparsity as the existence of relatively highvalued counts, rare observations and zero-block structure. Our main aim in this paper is to highlight the above mentioned three interrelated points in two ways: First, we propose a 7-number summary of sparsity based on the minimal size of an equivalent contingency table, where the invariance property of CA and TCA (a L1 variant of CA named taxicab) is used to construct the equivalence class of contingency tables; second, we compare the maps obtained by CA and TCA to explore under what conditions the CA and TCA maps produce similar, somewhat similar or dissimilar maps. Examples are provided.