Sparse Canonical Correlation Analysis for Multiple Measurements With Latent Trajectories

Canonical correlation analysis (CCA) is a widely used multivariate method in omics research for integrating high-dimensional datasets. CCA identifies hidden links by deriving linear projections of observed features that maximally correlate datasets. An important requirement of standard CCA is that observations are independent of each other. As a result, it cannot properly deal with repeated measurements. Current CCA extensions dealing with these challenges either perform CCA on summarized data or estimate correlations for each measurement. While these techniques factor in the correlation between measurements, they are suboptimal for high-dimensional analysis and exploiting this data's longitudinal qualities. We propose a novel extension of sparse CCA that incorporates time dynamics at the latent variable level through longitudinal models. This approach addresses the correlation of repeated measurements while drawing latent paths, focusing on dynamics in the correlation structures. To aid interpretability and computational efficiency, we implement an ${\ell }_0$ penalty to enforce fixed sparsity levels. We estimate these trajectories fitting longitudinal models to the low-dimensional latent variables, leveraging the clustered structure of high-dimensional datasets, thus exploring shared longitudinal latent mechanisms. Furthermore, modeling time in the latent space significantly reduces computational burden. We validate our model's performance using simulated data and show its real-world applicability with data from the Human Microbiome Project. This application highlights the model's ability to handle high-dimensional, sparsely, and irregularly observed data. Our CCA method for repeated measurements enables efficient estimation of canonical correlations across measurements for clustered data. Compared to existing methods, ours substantially reduces computational time in high-dimensional analyses as well as provides longitudinal trajectories that yield interpretable and insightful results.