  Finding the similarities and differences between groups of datasets is a
fundamental analysis task. For high-dimensional data, dimensionality reduction
(DR) methods are often used to find the characteristics of each group. However,
existing DR methods provide limited capability and flexibility for such
comparative analysis as each method is designed only for a narrow analysis
target, such as identifying factors that most differentiate groups. This paper
presents an interactive DR framework where we integrate our new DR method,
called ULCA (unified linear comparative analysis), with an interactive visual
interface. ULCA unifies two DR schemes, discriminant analysis and contrastive
learning, to support various comparative analysis tasks. To provide flexibility
for comparative analysis, we develop an optimization algorithm that enables
analysts to interactively refine ULCA results. Additionally, the interactive
visualization interface facilitates interpretation and refinement of the ULCA
results. We evaluate ULCA and the optimization algorithm to show their
efficiency as well as present multiple case studies using real-world datasets
to demonstrate the usefulness of this framework.
