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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...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2023
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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. |
format | Online Article Text |
id | pubmed-10217722 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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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