论文标题
稀疏的广义规范相关分析：基于分布式交替迭代的方法
Sparse Generalized Canonical Correlation Analysis: Distributed Alternating Iteration based Approach
论文作者
论文摘要
稀疏规范相关分析（CCA）是一种有用的统计工具，可检测具有稀疏结构的潜在信息。但是，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。为了克服这一限制，在本文中，我们提出了一个稀疏的广义规范相关分析（GCCA），该分析可以检测到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视为规范变体上的拉普拉斯先验。具体来说，我们将GCCA转换为线性方程式系统，并对稀疏追踪施加$ \ ell_1 $最小化罚款。这导致了在Stiefel歧管上的非凸问题，这很难解决。由Boyd的共识问题激发，开发了基于分布式交替迭代方法的算法，并在轻度条件下精心研究了理论一致性分析。几个合成和现实世界数据集的实验证明了所提出的算法的有效性。
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.
