  We consider dimension reduction of multiview data, which are emerging in
scientific studies. Formulating multiview data as multi-variate data with block
structures corresponding to the different views, or views of data, we estimate
top eigenvectors from multiview data that have two-fold sparsity, elementwise
sparsity and blockwise sparsity. We propose a Fantope-based optimization
criterion with multiple penalties to enforce the desired sparsity patterns and
a denoising step is employed to handle potential presence of heteroskedastic
noise across different data views. An alternating direction method of
multipliers (ADMM) algorithm is used for optimization. We derive the l2
convergence of the estimated top eigenvectors and establish their sparsity and
support recovery properties. Numerical studies are used to illustrate the
proposed method.
