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Abstract:
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We consider dimension reduction of multi-view data, which are emerging in scientific studies. Formulating multi-view data as multivariate data with block structures corresponding to the different views, or sources of data, we estimate top eigenvectors from multi-view data that have two-fold sparsity, element-wise sparsity and view-wise sparsity, and we propose a Fantope-based optimization criterion with multiple penalties to enforce the desired sparsity patterns. An alternating direction method of multipliers (ADMM) algorithm is used for optimization. We establish the sparsistency as well as the $\ell_2$ convergence of the estimated top eigenvectors. Finally, numerical studies are used to illustrate the proposed method.
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