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.

翻译：本文研究多视图数据的降维问题，这类数据在科学研究中日益常见。通过将多视图数据建模为具有块结构的多变量数据（每个块对应不同的数据视图），我们估计多视图数据的顶部特征向量，该向量具有双重稀疏性：元素级稀疏性和块级稀疏性。我们提出了一种基于Fantope的优化准则，通过多重惩罚项实现期望的稀疏模式，并采用去噪步骤处理不同数据视图间可能存在的异方差噪声。优化过程采用交替方向乘子法（ADMM）算法。我们推导了估计顶部特征向量的l2收敛性，并建立了其稀疏性与支撑集恢复性质。数值研究用于验证所提方法的有效性。