Nonlinear functional canonical correlation analysis via distance covariance

Hanbing Zhu; Rui Li; Riquan Zhang; Heng Lian

doi:10.1016/j.jmva.2020.104662

Nonlinear functional canonical correlation analysis via distance covariance

Hanbing Zhu, Rui Li^*, Riquan Zhang, Heng Lian

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

3 Citations (Scopus)

Abstract

Functional canonical correlation analysis (FCCA) is a tool for exploring the associations between a pair of functional data. However, when the association is nonlinear or even nonmonotone, FCCA can fail to discover any meaningful relationship between the pair. In this paper, nonlinear FCCA estimators are constructed based on some popular measures of dependence — distance covariance and distance correlation. Consistency of the estimators is shown. Numerical studies are presented that demonstrate nonlinear FCCA can uncover new association patterns between functional covariates.

Original language	English
Article number	104662
Number of pages	15
Journal	Journal of Multivariate Analysis
Volume	180
Online published	29 Jul 2020
DOIs	https://doi.org/10.1016/j.jmva.2020.104662
Publication status	Published - Nov 2020

Research Keywords

Canonical correlation analysis
Distance correlation
Distance covariance
Statistical consistency

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@article{369a81926fe24e2d97b6cdadadd37697,

title = "Nonlinear functional canonical correlation analysis via distance covariance",

abstract = "Functional canonical correlation analysis (FCCA) is a tool for exploring the associations between a pair of functional data. However, when the association is nonlinear or even nonmonotone, FCCA can fail to discover any meaningful relationship between the pair. In this paper, nonlinear FCCA estimators are constructed based on some popular measures of dependence — distance covariance and distance correlation. Consistency of the estimators is shown. Numerical studies are presented that demonstrate nonlinear FCCA can uncover new association patterns between functional covariates.",

keywords = "Canonical correlation analysis, Distance correlation, Distance covariance, Statistical consistency, Canonical correlation analysis, Distance correlation, Distance covariance, Statistical consistency, Canonical correlation analysis, Distance correlation, Distance covariance, Statistical consistency",

author = "Hanbing Zhu and Rui Li and Riquan Zhang and Heng Lian",

year = "2020",

month = nov,

doi = "10.1016/j.jmva.2020.104662",

language = "English",

volume = "180",

journal = "Journal of Multivariate Analysis",

issn = "0047-259X",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Nonlinear functional canonical correlation analysis via distance covariance

AU - Zhu, Hanbing

AU - Li, Rui

AU - Zhang, Riquan

AU - Lian, Heng

PY - 2020/11

Y1 - 2020/11

N2 - Functional canonical correlation analysis (FCCA) is a tool for exploring the associations between a pair of functional data. However, when the association is nonlinear or even nonmonotone, FCCA can fail to discover any meaningful relationship between the pair. In this paper, nonlinear FCCA estimators are constructed based on some popular measures of dependence — distance covariance and distance correlation. Consistency of the estimators is shown. Numerical studies are presented that demonstrate nonlinear FCCA can uncover new association patterns between functional covariates.

AB - Functional canonical correlation analysis (FCCA) is a tool for exploring the associations between a pair of functional data. However, when the association is nonlinear or even nonmonotone, FCCA can fail to discover any meaningful relationship between the pair. In this paper, nonlinear FCCA estimators are constructed based on some popular measures of dependence — distance covariance and distance correlation. Consistency of the estimators is shown. Numerical studies are presented that demonstrate nonlinear FCCA can uncover new association patterns between functional covariates.

KW - Canonical correlation analysis

KW - Distance correlation

KW - Distance covariance

KW - Statistical consistency

KW - Canonical correlation analysis

KW - Distance correlation

KW - Distance covariance

KW - Statistical consistency

KW - Canonical correlation analysis

KW - Distance correlation

KW - Distance covariance

KW - Statistical consistency

UR - http://www.scopus.com/inward/record.url?scp=85089011762&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85089011762&origin=recordpage

U2 - 10.1016/j.jmva.2020.104662

DO - 10.1016/j.jmva.2020.104662

M3 - RGC 21 - Publication in refereed journal

SN - 0047-259X

VL - 180

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

M1 - 104662

ER -

Nonlinear functional canonical correlation analysis via distance covariance

Abstract

Research Keywords

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GRF: Low-rank tensor as a Dimension Reduction Tool in Complex Data Analysis

GRF: Divide and Conquer in High-dimensional Statistical Models

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Nonlinear functional canonical correlation analysis via distance covariance

Abstract

Research Keywords

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GRF: Low-rank tensor as a Dimension Reduction Tool in Complex Data Analysis

GRF: Divide and Conquer in High-dimensional Statistical Models

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