Least-Squares Canonical Dependency Analysis (LSCDA)

Description

Least-Squares Canonical Dependency Analysis (LSCDA) is a dimensionality reduction method for a set of two different data sources. LSCDA learns linear projections by maximizing a squared-loss variant of mutual information between two projected variables. It can be interpreted as an extention of the traditional Canonical Correlation Analysis (CCA), which maximizes the linear correlation between two projected variables. LSCDA accurately estimates squared-loss mutual information by direct density-ratio estimation, and all tuning parameters such as the Gaussian width and the regularization parameter can be automatically chosen based on a cross-validation method.

Download

MATLAB implementation of LSCDA: LSCDA.zip

"LSCDA.m" is the main function.
"demo_LSCDA.m" is a demo script.
"ICCA.m", "HSIC_CDA.m" and "KCCA_CDA.m" are the implementations of related methods (See our paper for detail).

Examples

Input dataset (x1 x2) and (y1 y2), in which only x1 and y1 has (quadratic) dependency.

LSCDA learns projection matrices U and V, which are 1x2 matrices in this example, such that dependency of projected variables are maximized.

References

Karasuyama, M. & Sugiyama, M.
Canonical dependency analysis based on squared-loss mutual information.
xxx journal , vol.xxx, no.xxx, pp.xxx-xxx, 20xx.

Masayuki Karasuyama (karasuyama [at] kuicr.kyoto-u.ac.jp)

Bioinformatics Center, Institute for Chemical Research, Kyoto University Gokasyo, Uji, Kyoto 611-0011, Japan
TEL: +81-774-38-3024