  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 updating 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.
