A Visual Analytics Approach to Monitor Time-Series Data with Incremental and Progressive Functional Data Analysis

Many real-world applications involve analyzing time-dependent phenomena, which are intrinsically functional---consisting of curves varying over a continuum, which is time in this case. 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 FDA methods often suffer from high computational costs. This is even more critical when we have new incoming data and want to update the FDA results in real-time. In this paper, we present a visual analytics approach to consecutively monitor and review the changing time-series data with a focus on identifying outliers by using FDA. To perform such an analysis while addressing the computational problem, we introduce new incremental and progressive algorithms that promptly generate the magnitude-shape (MS) plot, which reveals 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 three case studies using real-world and synthetic datasets.