A Unified Approach to Functional Principal Component Analysis and Functional Multiple-Set Canonical Correlation

Area of Science:

• Statistics
• Functional Data Analysis
• Neuroimaging Analysis

Background:

• Functional principal component analysis (FPCA) and functional multiple-set canonical correlation analysis (FMCCA) are established techniques for reducing dimensionality in functional data.
• FPCA focuses on maximizing variance within a single dataset, while FMCCA prioritizes associations across multiple datasets.

Purpose of the Study:

• To propose a unified approach that integrates FPCA and FMCCA, offering a flexible compromise between variance explanation and cross-dataset association.
• To develop an efficient algorithm for optimizing the proposed unified method.

Main Methods:

• A novel unified optimization criterion is proposed for functional data reduction.
• An alternating regularized least squares algorithm is developed, utilizing basis function approximations for efficient computation.
• The approach is validated through simulation studies with synthetic data.

Main Results:

• The unified approach successfully extracts low-dimensional components from functional data.
• Application to functional magnetic resonance imaging (fMRI) data reveals highly correlated components across subjects.
• The method effectively identifies common neural activity networks during working memory tasks.

Conclusions:

• The proposed unified method offers a powerful and flexible tool for functional data analysis, extending capabilities beyond traditional FPCA and FMCCA.
• This approach facilitates the identification of shared functional patterns in complex datasets, such as neuroimaging data.
• The technique holds promise for uncovering synchronized neural activity and understanding brain function across individuals.