Communication-Efficient Federated Linear and Deep Generalized Canonical Correlation Analysis

Classic and deep learning-based generalized canonical correlation analysis (GCCA) algorithms seek low-dimensional common representations of data entities from multiple "views" (e.g., audio and image) using linear transformations and neural networks, respectively. When the views are acquired and stored at different computing agents (e.g., organizations and edge devices) and data sharing is undesired due to privacy or communication cost considerations, federated learning-based GCCA is well-motivated. In federated learning, the views are kept locally at the agents and only derived, limited information exchange with a central server is allowed. However, applying existing GCCA algorithms onto such setting may incur prohibitively high communication overhead. This work puts forth a communication-efficient federated learning framework for both linear and deep GCCA under the maximum variance (MAX-VAR) formulation. The overhead issue is addressed by aggressively compressing (via quantization) the exchanging information between the computing agents and a central controller. Our synthetic and real-data experiments shows that the proposed algorithm enjoys a substantial reduction of communication overheads with virtually no loss in accuracy and convergence speed compared to the unquantized version. Rigorous convergence analyses are also presented, which is a nontrivial effort since generic federated optimization results do not cover the special problem structure of GCCA. Our result shows that the proposed algorithms for both linear and deep GCCA converge to critical points at a sublinear rate, even under heavy quantization and stochastic approximations. In addition, in the linear MAX-VAR case, the quantized algorithm approaches a global optimum in a geometric rate under reasonable conditions.