Sparse Canonical Correlation Analysis via Concave Minimization

by   Omid S. Solari, et al.

A new approach to the sparse Canonical Correlation Analysis (sCCA)is proposed with the aim of discovering interpretable associations in very high-dimensional multi-view, i.e.observations of multiple sets of variables on the same subjects, problems. Inspired by the sparse PCA approach of Journee et al. (2010), we also show that the sparse CCA formulation, while non-convex, is equivalent to a maximization program of a convex objective over a compact set for which we propose a first-order gradient method. This result helps us reduce the search space drastically to the boundaries of the set. Consequently, we propose a two-step algorithm, where we first infer the sparsity pattern of the canonical directions using our fast algorithm, then we shrink each view, i.e. observations of a set of covariates, to contain observations on the sets of covariates selected in the previous step, and compute their canonical directions via any CCA algorithm. We also introduceDirected Sparse CCA, which is able to find associations which are aligned with a specified experiment design, andMulti-View sCCA which is used to discover associations between multiple sets of covariates. Our simulations establish the superior convergence properties and computational efficiency of our algorithm as well as accuracy in terms of the canonical correlation and its ability to recover the supports of the canonical directions. We study the associations between metabolomics, trasncriptomics and microbiomics in a multi-omic study usingMuLe, which is an R-package that implements our approach, in order to form hypotheses on mechanisms of adaptations of Drosophila Melanogaster to high doses of environmental toxicants, specifically Atrazine, which is a commonly used chemical fertilizer.



There are no comments yet.


page 1

page 2

page 3

page 4


BLOCCS: Block Sparse Canonical Correlation Analysis With Application To Interpretable Omics Integration

We introduce Block Sparse Canonical Correlation Analysis which estimates...

Conditional canonical correlation estimation based on covariates with random forests

Investigating the relationships between two sets of variables helps to u...

Collaborative Regression

We consider the scenario where one observes an outcome variable and sets...

A simple and provable algorithm for sparse diagonal CCA

Given two sets of variables, derived from a common set of samples, spars...

Finding the needle in high-dimensional haystack: A tutorial on canonical correlation analysis

Since the beginning of the 21st century, the size, breadth, and granular...

Canonical Correlation Analysis for Misaligned Satellite Image Change Detection

Canonical correlation analysis (CCA) is a statistical learning method th...

Scalable and Flexible Multiview MAX-VAR Canonical Correlation Analysis

Generalized canonical correlation analysis (GCCA) aims at finding latent...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.