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A Coupled Manifold Optimization Framework to Jointly Model the Functional Connectomics and Behavioral Data Spaces

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Document pages: 12 pages

Abstract: The problem of linking functional connectomics to behavior is extremelychallenging due to the complex interactions between the two distinct, butrelated, data domains. We propose a coupled manifold optimization frameworkwhich projects fMRI data onto a low dimensional matrix manifold common to thecohort. The patient specific loadings simultaneously map onto a behavioralmeasure of interest via a second, non-linear, manifold. By leveraging thekernel trick, we can optimize over a potentially infinite dimensional spacewithout explicitly computing the embeddings. As opposed to conventionalmanifold learning, which assumes a fixed input representation, our frameworkdirectly optimizes for embedding directions that predict behavior. Ouroptimization algorithm combines proximal gradient descent with the trust regionmethod, which has good convergence guarantees. We validate our framework onresting state fMRI from fifty-eight patients with Autism Spectrum Disorderusing three distinct measures of clinical severity. Our method outperformstraditional representation learning techniques in a cross validated setting,thus demonstrating the predictive power of our coupled objective.

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