For many modern applications in science and engineering, data are collected in a streaming fashion carrying time-varying information, and practitioners need to process them with a limited amount of memory and computational resources in a timely manner for decision making. This often is coupled with the missing data problem, such that only a small fraction of data attributes are observed. These complications impose significant, and unconventional, constraints on the problem of streaming Principal Component Analysis (PCA) and subspace tracking, which is an essential building block for many inference tasks in signal processing and machine learning. This survey article reviews a variety of classical and recent algorithms for solving this problem with low computational and memory complexities, particularly those applicable in the big data regime with missing data. We illustrate that streaming PCA and subspace tracking algorithms can be understood through algebraic and geometric perspectives, and they need to be adjusted carefully to handle missing data. Both asymptotic and non-asymptotic convergence guarantees are reviewed. Finally, we benchmark the performance of several competitive algorithms in the presence of missing data for both well-conditioned and ill-conditioned systems.

针对流数据中所缺少的数据属性，本篇综述论文回顾了各种低计算和内存复杂度的算法，特别是适用于缺失数据的大数据环境中的算法。此外，通过代数和几何视角来观察流PCA和子空间跟踪算法的性能分析。最后，文中还对几种竞争算法在良好和不良条件系统下缺失数据的性能进行基准测试。

流式PCA和子空间跟踪:缺失数据情况下的处理