Structured SUMCOR Multiview Canonical Correlation Analysis for Large-Scale Data
This work addresses a critical limitation in scalable multiview data analysis for signal processing and data analytics by enabling structural regularization, which is incremental but important for real-world applications.
The authors tackled the problem of large-scale multiview canonical correlation analysis (SUMCOR GCCA) by developing a new computational framework that incorporates structural regularization, which previous scalable algorithms could not handle. They demonstrated the algorithm's effectiveness through simulations and real-data experiments, showing lightweight updates, low memory complexity, and parallel implementation capabilities.
The sum-of-correlations (SUMCOR) formulation of generalized canonical correlation analysis (GCCA) seeks highly correlated low-dimensional representations of different views via maximizing pairwise latent similarity of the views. SUMCOR is considered arguably the most natural extension of classical two-view CCA to the multiview case, and thus has numerous applications in signal processing and data analytics. Recent work has proposed effective algorithms for handling the SUMCOR problem at very large scale. However, the existing scalable algorithms cannot incorporate structural regularization and prior information -- which are critical for good performance in real-world applications. In this work, we propose a new computational framework for large-scale SUMCOR GCCA that can easily incorporate a suite of structural regularizers which are frequently used in data analytics. The updates of the proposed algorithm are lightweight and the memory complexity is also low. In addition, the proposed algorithm can be readily implemented in a parallel fashion. We show that the proposed algorithm converges to a Karush-Kuhn-Tucker (KKT) point of the regularized SUMCOR problem. Judiciously designed simulations and real-data experiments are employed to demonstrate the effectiveness of the proposed algorithm.