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

Olivier Coulaud 1 Alain Franc 2, 3 Martina Iannacito 1 
1 HiePACS - High-End Parallel Algorithms for Challenging Numerical Simulations
LaBRI - Laboratoire Bordelais de Recherche en Informatique, Inria Bordeaux - Sud-Ouest
3 PLEIADE - from patterns to models in computational biodiversity and biotechnology
LaBRI - Laboratoire Bordelais de Recherche en Informatique, Inria Bordeaux - Sud-Ouest, BioGeCo - Biodiversité, Gènes & Communautés
Abstract : This paper presents an extension of Correspondence Analysis (CA) to tensors through High Order Singular Value Decomposition (HOSVD) from a geometric viewpoint. Correspondence analysis is a well-known tool, developed from principal component analysis, for studying contingency tables. Different algebraic extensions of CA to multi-way tables have been proposed over the years, nevertheless neglecting its geometric meaning. Relying on the Tucker model and the HOSVD, we propose a direct way to associate with each tensor mode a point cloud. We prove that the point clouds are related to each other. Specifically using the CA metrics we show that the barycentric relation is still true in the tensor framework. Finally two data sets are used to underline the advantages and the drawbacks of our strategy with respect to the classical matrix approaches.
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Reports (Research report)
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https://hal.inria.fr/hal-03418404
Contributor : Martina Iannacito Connect in order to contact the contributor
Submitted on : Sunday, November 7, 2021 - 1:53:51 PM
Last modification on : Wednesday, October 26, 2022 - 8:15:40 AM
Long-term archiving on: : Tuesday, February 8, 2022 - 6:09:34 PM

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Olivier Coulaud, Alain Franc, Martina Iannacito. Extension of Correspondence Analysis to multiway data-sets through High Order SVD: a geometric framework. [Research Report] RR-9429, Inria Bordeaux - Sud-Ouest; Inrae. 2021. ⟨hal-03418404⟩

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