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, and . 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...

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Detalles Bibliográficos
Autores: Jaenada Malagón, María, Miranda Menéndez, Pedro, Pardo Llorente, Leandro, Zografos, Konstantinos
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/87289
Acceso en línea:https://hdl.handle.net/20.500.14352/87289
Access Level:acceso abierto
Palabra clave:519.237
Information canonical correlation analysis
Kullback-Leibler divergence
Mutual information
Renyi's pseudodistances
Robustness
Consistency
Estadística matemática (Matemáticas)
1209.09 Análisis Multivariante
Descripción
Sumario:Canonical Correlation Analysis (CCA) infers a pairwise linear relationship between two groups of random variables, and . 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, and , 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.