Many real-world applications involve analyzing time-dependent phenomena, which are intrinsically functional, consisting of curves varying over a continuum (e.g., time). When analyzing continuous data, functional data analysis (FDA) provides substantial benefits, such as the ability to study the derivatives and to restrict the ordering of data. However, continuous data inherently has infinite dimensions, and for a long time series, FDA methods often suffer from high computational costs. The analysis problem becomes even more challenging when we must update the FDA results for continuously arriving data. In this paper, we present a visual analytics approach for monitoring and reviewing time series data streamed from a hardware system with a focus on identifying outliers by using FDA. To perform FDA while addressing the computational problem, we introduce new incremental and progressive algorithms that promptly generate the magnitude-shape (MS) plot, which conveys both the functional magnitude and shape outlyingness of time series data. In addition, by using an MS plot in conjunction with an FDA version of principal component analysis, we enhance the analyst's ability to investigate the visually-identified outliers. We illustrate the effectiveness of our approach with two use scenarios using real-world datasets. The resulting tool is evaluated by industry experts using real-world streaming datasets.
翻译:许多现实世界应用都涉及分析取决于时间的现象,这些现象在本质上是功能性的,由一系列(例如时间)的不同曲线组成。在分析连续数据时,功能数据分析(FDA)提供大量好处,例如研究衍生物和限制数据顺序的能力。然而,连续数据本身具有无限的层面,而且长期以来,林业发展局的方法往往具有很高的计算成本。分析问题在我们必须更新林业发展局的结果以不断获取数据时变得更加困难。在本文件中,我们提出了一个视觉分析方法,用于监测和审查从硬件系统流出的时间序列数据,重点是利用林业发展局查明外部关系。为了在计算问题时执行林业发展局的工作,我们采用了新的渐进式和渐进式算法,迅速生成星形状图,既传达了功能规模,又形成了时间序列数据的外围地带。此外,我们利用一个MS图与林业发展局的主要组成部分分析版本一起,加强了分析员调查直观识别的外部关系的能力。我们用现实世界数据集评估了我们的方法的有效性。我们用现实世界的数据集评估了我们的方法。