Streaming PCA and Subspace Tracking: The Missing Data Case
Streaming PCA and Subspace Tracking: The Missing Data Case
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DOI：
10.1109/jproc.2018.2847041
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发表时间：
2018-08-01
影响因子：
20.6
通讯作者：
Lu, Yue M.
中科院分区：
文献类型：
--
作者：
Balzano, Laura;Chi, Yuejie;Lu, Yue M.
对于许多现代科学和工程中的现代应用，数据是以携带时间变化信息的流方式收集的，从业人员需要及时用有限的记忆和计算资源来处理它们以进行决策。这通常与缺少的数据问题相结合，因此仅观察到一小部分数据属性。这些并发症对流媒体主成分分析（PCA）和子空间跟踪的问题施加了显着且非常规的限制，这对于信号处理和机器学习中许多推理任务是必不可少的基础。本调查文章回顾了各种经典和最新的算法，以通过低计算和记忆复杂性解决此问题，尤其是那些适用于大数据制度的算法，而数据丢失了。我们说明可以通过代数和几何视角理解流式PCA和子空间跟踪算法，并且需要仔细调整它们以处理缺失的数据。审查了渐近和非肿瘤收敛保证。最后，我们在有良好条件和条件的系统的无限数据的存在下基准了几种竞争算法的性能。
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 nonasymptotic convergence guarantees are reviewed. Finally, we benchmark the performance of several competitive algorithms in the presence ofmissing data for both well-conditioned and ill-conditioned systems.