Tensor Multiple Canonical Correlation Analysis (TMCCA): A Framework for Multi-View High-Dimensional Data Integration

Manuscript in Preparation

Current Status: Manuscript in preparation. This page summarizes the dissertation chapter and my contribution; no manuscript PDF is hosted.

Abstract

Canonical Correlation Analysis (CCA) and its multi-view extension (MCCA) are fundamental tools for analyzing associations between data sets. However, traditional vector-based MCCA methods suffer from the “curse of dimensionality” and structural information loss when applied to high-order tensor data, such as time-frequency-space EEG or fMRI data.

Tensor Multiple Canonical Correlation Analysis (TMCCA) is collaborative doctoral research, included as Chapter 4 of my dissertation. It looks for shared structure across several tensor-valued views without first flattening them into vectors.

My contribution

  • Contributed software, numerical simulations, and data analyses to tensor multiple canonical correlation analysis, evaluating recovery and optimization behavior.
  • Examined a single-participant EEG example with three sessions, 319 trials, 14 channels, and four aligned views including task labels; five components were fixed in advance.

David Degras is the author and maintainer of the tensorMCCA package. My contributions do not establish sole ownership of the algorithm or the package.

Problem Statement

In neuroimaging, data often comes in the form of high-dimensional tensors (e.g., $Channels \times Time \times Frequency$). Traditional approaches require reshaping these tensors into vectors (vectorization), which leads to:

  1. Explosion of Parameters: Increasing the risk of overfitting in small-sample scenarios.
  2. Loss of Spatial/Temporal Structure: Ignoring the natural correlations between adjacent dimensions.

Method and scope

  • Tensor weights: Canonical components are defined through tensor-structured weights rather than vectorized loadings.
  • Optimization: The dissertation chapter studies constrained optimization, initialization, convergence, estimation error, and local-optimum behavior in simulations. The tensorMCCA package implements covariance- and correlation-based objectives with block-coordinate ascent.
  • EEG example: A single-participant, multi-view interpretation example. It is not a large-scale unsupervised predictive benchmark, and it is not an EEG–fMRI fusion study.

For inquiries regarding this research or potential collaboration, please contact the author directly.