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D-CCA: A Decomposition-based Canonical Correlation Analysis for High-dimensional Datasets

This python package implements the D-CCA method proposed in [1] for K=2 datasets. See example.py for details, with Python 3.5 or above. For K>2 datasets, please use the D-GCCA method.

D-CCA conducts the following decomposition:

<img src="https://render.githubusercontent.com/render/math?math=\boldsymbol{Y}_k=\boldsymbol{X}_k %2B \boldsymbol{E}_k=\boldsymbol{C}_k %2B \boldsymbol{D}_k %2B \boldsymbol{E}_k"> for <img src="https://render.githubusercontent.com/render/math?math=k=1,2">

where <img src="https://render.githubusercontent.com/render/math?math=\boldsymbol{C}_1"> and <img src="https://render.githubusercontent.com/render/math?math=\boldsymbol{C}_2"> share the same latent factors, but <img src="https://render.githubusercontent.com/render/math?math=\boldsymbol{D}_1"> and <img src="https://render.githubusercontent.com/render/math?math=\boldsymbol{D}_2"> have uncorrelated latent factors.

Note that <img src="https://render.githubusercontent.com/render/math?math=\boldsymbol{Y}_k"> should be row-mean centered.

Please cite the article [1] for this package, which is available here.

[1] Hai Shu, Xiao Wang & Hongtu Zhu (2020) D-CCA: A Decomposition-based Canonical Correlation Analysis for High-dimensional Datasets. Journal of the American Statistical Association, 115(529): 292-306. DOI: 10.1080/01621459.2018.1543599