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An Approach to Canonical Correlation Analysis Based on Rényi’s Pseudodistances

Canonical Correlation Analysis (CCA) infers a pairwise linear relationship between two groups of random variables, [Formula: see text] and [Formula: see text] In this paper, we present a new procedure based on Rényi’s pseudodistances (RP) aiming to detect linear and non-linear relationships between...

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Autores principales: Jaenada, María, Miranda, Pedro, Pardo, Leandro, Zografos, Konstantinos
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10217722/
https://www.ncbi.nlm.nih.gov/pubmed/37238468
http://dx.doi.org/10.3390/e25050713
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author Jaenada, María
Miranda, Pedro
Pardo, Leandro
Zografos, Konstantinos
author_facet Jaenada, María
Miranda, Pedro
Pardo, Leandro
Zografos, Konstantinos
author_sort Jaenada, María
collection PubMed
description Canonical Correlation Analysis (CCA) infers a pairwise linear relationship between two groups of random variables, [Formula: see text] and [Formula: see text] In this paper, we present a new procedure based on Rényi’s pseudodistances (RP) aiming to detect linear and non-linear relationships between the two groups. RP canonical analysis (RPCCA) finds canonical coefficient vectors, [Formula: see text] and [Formula: see text] , by maximizing an RP-based measure. This new family includes the Information Canonical Correlation Analysis (ICCA) as a particular case and extends the method for distances inherently robust against outliers. We provide estimating techniques for RPCCA and show the consistency of the proposed estimated canonical vectors. Further, a permutation test for determining the number of significant pairs of canonical variables is described. The robustness properties of the RPCCA are examined theoretically and empirically through a simulation study, concluding that the RPCCA presents a competitive alternative to ICCA with an added advantage in terms of robustness against outliers and data contamination.
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spelling pubmed-102177222023-05-27 An Approach to Canonical Correlation Analysis Based on Rényi’s Pseudodistances Jaenada, María Miranda, Pedro Pardo, Leandro Zografos, Konstantinos Entropy (Basel) Article Canonical Correlation Analysis (CCA) infers a pairwise linear relationship between two groups of random variables, [Formula: see text] and [Formula: see text] In this paper, we present a new procedure based on Rényi’s pseudodistances (RP) aiming to detect linear and non-linear relationships between the two groups. RP canonical analysis (RPCCA) finds canonical coefficient vectors, [Formula: see text] and [Formula: see text] , by maximizing an RP-based measure. This new family includes the Information Canonical Correlation Analysis (ICCA) as a particular case and extends the method for distances inherently robust against outliers. We provide estimating techniques for RPCCA and show the consistency of the proposed estimated canonical vectors. Further, a permutation test for determining the number of significant pairs of canonical variables is described. The robustness properties of the RPCCA are examined theoretically and empirically through a simulation study, concluding that the RPCCA presents a competitive alternative to ICCA with an added advantage in terms of robustness against outliers and data contamination. MDPI 2023-04-25 /pmc/articles/PMC10217722/ /pubmed/37238468 http://dx.doi.org/10.3390/e25050713 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Jaenada, María
Miranda, Pedro
Pardo, Leandro
Zografos, Konstantinos
An Approach to Canonical Correlation Analysis Based on Rényi’s Pseudodistances
title An Approach to Canonical Correlation Analysis Based on Rényi’s Pseudodistances
title_full An Approach to Canonical Correlation Analysis Based on Rényi’s Pseudodistances
title_fullStr An Approach to Canonical Correlation Analysis Based on Rényi’s Pseudodistances
title_full_unstemmed An Approach to Canonical Correlation Analysis Based on Rényi’s Pseudodistances
title_short An Approach to Canonical Correlation Analysis Based on Rényi’s Pseudodistances
title_sort approach to canonical correlation analysis based on rényi’s pseudodistances
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10217722/
https://www.ncbi.nlm.nih.gov/pubmed/37238468
http://dx.doi.org/10.3390/e25050713
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