Functional Multiple-Set Canonical Correlation Analysis

Abstract

functional data, multiple-set canonical correlation analysis, functional canonical correlation analysis, functional magnetic resonance imaging data,

Canonical correlation analysis for irregularly and sparsely observed functional data

“…This can be also understood as the regularized covariance estimation: in the cross-correlation structure of X and Y , the covariance matrices X and Y have the moderate values of diagonal terms. This is closely related to the regularized CCA approaches studied in other literature (See, e.g., [15,4,3,11]). In our approach, the amount of regularization for covariances is regulated by the dimensions of matrices 1 and 2 (k 1 and k 2 , respectively, in our model).…”

“…Several approaches for FCCA have been developed so far. Recent work on FCCA includes [15,8,9,4,3,7,11]. However, the existing methods have been developed for dense and balanced functional data, and they cannot be directly applied or easily extended to the situations where the observed curves are measured at an irregular and sparse set of time points.…”

A unified approach to multiple‐set canonical correlation analysis and principal components analysis

“…Due to advances in technology, in various areas of psychology, data are being collected in the form of curves, surfaces, or images as a function of time, space, or other continua; for example, eye‐tracking data (e.g., Jackson & Sirois, 2009), music cognition data (e.g., Vines, Nuzzo, & Levitin, 2005), facial temperature data (e.g., Jang & Lee, 2009), and event‐contingent social interaction data (e.g., Moskowitz et al ., 2006). A functional version of the proposed approach would be a promising tool integrating functional MCCA (Hwang, Jung, Takane, & Woodward, 2012) and functional PCA (Rice & Silverman, 1991; Ramsay & Silverman, 2005, chapter 8) into a single framework. Finally, we may develop a constrained version of the proposed approach, which imposes a variety of linear constraints (e.g., zero, non‐additivity, or equality constraints) on both criteria of (1) in a manner similar to Takane and Shibayama (1991).…”

Multiway Canonical Correlation Analysis of Brain Signals

“…Extensions to connect multiple data matrices have been proposed under names such as multiple CCA (Gross and Tibshirani, 2015; Witten and Tibshirani, 2009), multiway CCA (Sturm, 2016; Zhang et al, 2011), multiset CCA (Takane et al, 2008; Correa et al, 2010b,a; Hwang et al, 2012; Lankinen et al, 2014; Zhang et al, 2017; Via, Javier, Ignacio Santamaria and Péez, 2005; Li et al, 2009), or generalized CCA (Kiers et al, 1994; Afshin-Pour et al, 2012; Melzer et al, 2001; Tenenhaus, 2011; Tenenhaus et al, 2015; Velden, 2011; Fu et al, 2017). This diversity in names covers a diversity of formulations (Kettenring, 1971) that all share the aim of finding components that are similar across data matrices.…”