Federated multi-modal learning for cross-platform image computation: A functional analysis and nonlinear optimization approach to privacy preservation
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Keywords:
Federated Learning; Functional Analysis; Nonlinear Optimization; Hilbert Spaces; Privacy Preservation; Variational Problems; Multi-Modal Imaging; Image Computation.Abstract
In Federated multi-modal learning, raw data is not concentrated in a single location because it can perform distributed image computation on heterogeneous platforms. Nonetheless, it is still open to guarantee that the convergence, stability and privacy properties of such systems are mathematically rigorous. In this paper, a functional-analytic, nonlinear-optimization system of federated cross-platform image computation is developed in which local image modalities, and global learning goals are posed as nonlinear variational problems, with local image modalities modelled as an element of separable Hilbert spaces. We present a Nonlinear Federated Proximal Operator (NFPO) that provides a privacy limiting functionality by a dual functional mechanism. We prove existence and uniqueness results of the global minimizer in the presence of coercivity and strong monotonicity, convergence of the NFPO in a contractive mapping argument, and test the framework on synthetic multimodal image datasets given across a plurality of virtual platforms. Numerical experiments show that the proposed approach provides better privacy guarantees with the competitive reconstruction and classification performance. This paper introduces a mathematical based theoretical foundation of a privacy-
conserving federated image computation to cross-platform and multi-modal imaging systems.
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