Sparse Canonical Correlation Analysis via Truncated ℓ₁-norm with Application to Brain Imaging Genetics

Discovering bi-multivariate associations between genetic markers and neuroimaging quantitative traits is a major task in brain imaging genetics. Sparse Canonical Correlation Analysis (SCCA) is a popular technique in this area for its powerful capability in identifying bi-multivariate relationships coupled with feature selection. The existing SCCA methods impose either the ℓ₁-norm or its variants. The ℓ₀-norm is more desirable, which however remains unexplored since the ℓ₀-norm minimization is NP-hard. In this paper, we impose the truncated ℓ₁-norm to improve the performance of the ℓ₁-norm based SCCA methods. Besides, we propose two efficient optimization algorithms and prove their convergence. The experimental results, compared with two benchmark methods, show that our method identifies better and meaningful canonical loading patterns in both simulated and real imaging genetic analyse.