  Data-driven problem solving in many real-world applications involves analysis
of time-dependent multivariate data, for which dimensionality reduction (DR)
methods are often used to uncover the intrinsic structure and features of the
data. However, DR is usually applied to a subset of data that is either
single-time-point multivariate or univariate time-series, resulting in the need
to manually examine and correlate the DR results out of different data subsets.
When the number of dimensions is large either in terms of the number of time
points or attributes, this manual task becomes too tedious and infeasible. In
this paper, we present MulTiDR, a new DR framework that enables processing of
time-dependent multivariate data as a whole to provide a comprehensive overview
of the data. With the framework, we employ DR in two steps. When treating the
instances, time points, and attributes of the data as a 3D array, the first DR
step reduces the three axes of the array to two, and the second DR step
visualizes the data in a lower-dimensional space. In addition, by coupling with
a contrastive learning method and interactive visualizations, our framework
enhances analysts' ability to interpret DR results. We demonstrate the
effectiveness of our framework with four case studies using real-world
datasets.
