论文标题
在线PCA的随机高斯牛顿算法
Stochastic Gauss-Newton Algorithms for Online PCA
论文作者
论文摘要
在本文中，我们提出了一种随机的高斯 - 纽顿（SGN）算法来研究在线主成分分析（OPCA）问题，该问题是通过使用对称的低级别产品（SLRP）模型来进行主导特征空间计算来提出的。与现有的OPCA求解器相比，相对于不同的输入数据和算法参数，SGN具有改善的鲁棒性。此外，在基于近似目标函数的数据流评估数据流时，我们为SGN（ADASGN）开发了新的自适应步骤策略，该策略不需要先验了解输入数据，并数值说明了其与SGN采用Manaully-tuned nuned Speming步骤的相当性能。在不假设特征gap为正的情况下，我们还使用扩散近似理论建立了SGN的全局和最佳收敛速率。
In this paper, we propose a stochastic Gauss-Newton (SGN) algorithm to study the online principal component analysis (OPCA) problem, which is formulated by using the symmetric low-rank product (SLRP) model for dominant eigenspace calculation. Compared with existing OPCA solvers, SGN is of improved robustness with respect to the varying input data and algorithm parameters. In addition, turning to an evaluation of data stream based on approximated objective functions, we develop a new adaptive stepsize strategy for SGN (AdaSGN) which requires no priori knowledge of the input data, and numerically illustrate its comparable performance with SGN adopting the manaully-tuned diminishing stepsize. Without assuming the eigengap to be positive, we also establish the global and optimal convergence rate of SGN with the specified stepsize using the diffusion approximation theory.
