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D-GCCA: Decomposition-based Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data

This python package implements the D-GCCA method proposed in [1]. See example.py for details, with Python 3.

D-GCCA decomposes the observed multi-view data <img src="https://render.githubusercontent.com/render/math?math=\boldsymbol{Y}_k\in \mathbb{R}^{p_k\times n}, k=1,\dots, K\ge 2"> into

where <img src="https://render.githubusercontent.com/render/math?math=\{\boldsymbol{C}_k\}_{k=1}^K"> are low-rank common-source matrices that represent the signal data coming from the common latent factors shared across all data views, and <img src="https://render.githubusercontent.com/render/math?math=\{\boldsymbol{D}_k\}_{k=1}^K"> are low-rank distinctive-source matrices each from the distinctive latent factors of the corresponding view, and <img src="https://render.githubusercontent.com/render/math?math=\{\boldsymbol{E}_k\}_{k=1}^K"> are noise matrices. In other words, the common-source and distinctive-source matrices contain the variation information in each view, respectively, explained by the common and distinctive latent factors of the K views.

Please cite the article [1] for this package.

For K=2 data views, please use the D-CCA package, instead.

[1] Shu, H., Qu, Z., & Zhu, H. "D-GCCA: Decomposition-based Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data". Journal of Machine Learning Research, 23(169):1−64