  Higher-order patterns reveal sequential multistep state transitions, which
are usually superior to origin-destination analysis, which depicts only
first-order geospatial movement patterns. Conventional methods for higher-order
movement modeling first construct a directed acyclic graph (DAG) of movements,
then extract higher-order patterns from the DAG. However, DAG-based methods
heavily rely on the identification of movement keypoints that are challenging
for sparse movements and fail to consider the temporal variants that are
critical for movements in urban environments. To overcome the limitations, we
propose HoLens, a novel approach for modeling and visualizing higher-order
movement patterns in the context of an urban environment. HoLens mainly makes
twofold contributions: first, we design an auto-adaptive movement aggregation
algorithm that self-organizes movements hierarchically by considering spatial
proximity, contextual information, and temporal variability; second, we develop
an interactive visual analytics interface consisting of well-established
visualization techniques, including the H-Flow for visualizing the higher-order
patterns on the map and the higher-order state sequence chart for representing
the higher-order state transitions. Two real-world case studies manifest that
the method can adaptively aggregate the data and exhibit the process of how to
explore the higher-order patterns by HoLens. We also demonstrate our approach's
feasibility, usability, and effectiveness through an expert interview with
three domain experts.
