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This paper presents an extension of Correspondence Analysis (CA) to tensorsthrough High Order Singular Value Decomposition (HOSVD) from a geometricviewpoint. Correspondence analysis is a well-known tool, developed fromprincipal component analysis, for studying contingency tables. Differentalgebraic extensions of CA to multi-way tables have been proposed over theyears, nevertheless neglecting its geometric meaning. Relying on the Tuckermodel and the HOSVD, we propose a direct way to associate with each tensor modea point cloud. We prove that the point clouds are related to each other.Specifically using the CA metrics we show that the barycentric relation isstill true in the tensor framework. Finally two data sets are used to underlinethe advantages and the drawbacks of our strategy with respect to the classicalmatrix approaches.

Extension of Correspondence Analysis to multiway data-sets through High Order SVD: a geometric framework