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Canonical correlation analysis in high dimensions with structured regularization
Elena Tuzhilina1, Leonardo Tozzi2, Trevor Hastie1
1Department of Statistics, Stanford University, Stanford, CA, USA.
Statistical Modelling
|June 19, 2023
Summary
Group regularized canonical correlation analysis (GRCCA) enhances multivariate data analysis by incorporating data structure. This method improves upon regularized canonical correlation analysis (RCCA) for high-dimensional datasets with grouped variables.
Area of Science:
- Statistics
- Machine Learning
- Computational Neuroscience
Background:
- Canonical correlation analysis (CCA) measures associations between two data matrices.
- Regularized CCA (RCCA) uses L2 penalty for high-dimensional data but ignores data structure.
- Ignoring data structure in RCCA can be suboptimal for certain applications.
Purpose of the Study:
- Introduce novel regularized CCA methods that account for data structure.
- Propose Group Regularized Canonical Correlation Analysis (GRCCA) for data with grouped variables.
- Develop efficient computational strategies for high-dimensional regularized CCA.
Main Methods:
- Developed group regularized canonical correlation analysis (GRCCA).
- Implemented computational strategies for efficient high-dimensional regularized CCA.
- Applied methods to neuroscience data and simulation examples.
Main Results:
- GRCCA effectively incorporates variable grouping into CCA.
- Proposed computational methods reduce excessive computations in high-dimensional settings.
- Demonstrated applicability in neuroscience and simulation.
Conclusions:
- GRCCA offers an improved approach to regularized CCA when data exhibits group structure.
- Efficient computation strategies make advanced CCA methods accessible for high-dimensional data.
- The methods show promise for applications in neuroscience and beyond.
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