稀疏广义典型相关分析：基于分布式交替迭代的方法
Sparse Generalized Canonical Correlation Analysis: Distributed Alternating Iteration based Approach
摘要：
稀疏典型相关分析（CCA）是一种有用的统计工具，用于检测具有稀疏结构的潜在信息。然而，稀疏CCA仅适用于两个数据集，即，只有两个视图或两个不同的对象。为了克服这一局限性，本文提出了一种稀疏广义典型相关分析（GCCA），它可以检测具有稀疏结构的多视图数据的潜在关系。此外，引入的稀疏性可以被认为是典型变量的拉普拉斯先验。具体来说，我们将GCCA转换成一个线性方程组，并施加$\ell_1$最小化惩罚稀疏追求。这导致Stiefel流形上的非凸问题，这是很难解决的。受Boyd一致性问题的启发，提出了一种基于分布式交替迭代的算法，并在较弱的条件下详细研究了算法的理论一致性分析。在多个人工数据集和真实数据集上的实验证明了该算法的有效性。
英文摘要：
Sparse canonical correlation analysis (CCA) is a useful statistical tool to detect latent information with sparse structures. However, sparse CCA works only for two datasets, i.e., there are only two views or two distinct objects. To overcome this limitation, in this paper, we propose a sparse generalized canonical correlation analysis (GCCA), which could detect the latent relations of multiview data with sparse structures. Moreover, the introduced sparsity could be considered as Laplace prior on the canonical variates. Specifically, we convert the GCCA into a linear system of equations and impose $\ell_1$ minimization penalty for sparsity pursuit. This results in a nonconvex problem on Stiefel manifold, which is difficult to solve. Motivated by Boyd's consensus problem, an algorithm based on distributed alternating iteration approach is developed and theoretical consistency analysis is investigated elaborately under mild conditions. Experiments on several synthetic and real world datasets demonstrate the effectiveness of the proposed algorithm.
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