ℓ_0-based Sparse Canonical Correlation Analysis [article]

Ofir Lindenbaum, Moshe Salhov, Amir Averbuch, Yuval Kluger
2021 arXiv   pre-print
Canonical Correlation Analysis (CCA) models are powerful for studying the associations between two sets of variables. The canonically correlated representations, termed canonical variates are widely used in unsupervised learning to analyze unlabeled multi-modal registered datasets. Despite their success, CCA models may break (or overfit) if the number of variables in either of the modalities exceeds the number of samples. Moreover, often a significant fraction of the variables measures
more » ... specific information, and thus removing them is beneficial for identifying the canonically correlated variates. Here, we propose ℓ_0-CCA, a method for learning correlated representations based on sparse subsets of variables from two observed modalities. Sparsity is obtained by multiplying the input variables by stochastic gates, whose parameters are learned together with the CCA weights via an ℓ_0-regularized correlation loss. We further propose ℓ_0-Deep CCA for solving the problem of non-linear sparse CCA by modeling the correlated representations using deep nets. We demonstrate the efficacy of the method using several synthetic and real examples. Most notably, by gating nuisance input variables, our approach improves the extracted representations compared to other linear, non-linear and sparse CCA-based models.
arXiv:2010.05620v2 fatcat:nzc2ielsenbnbkwul77p4ciodq