HoLens: A Visual Analytics Design for Higher-order Movement Modeling and Visualization

TL;DR

HoLens addresses urban movement analysis by extracting higher-order movement patterns through context-aware, multi-scale aggregation and a DAG-based representation. It couples an auto-adaptive aggregation algorithm with entropy-based region formation to build a DAG whose nodes are region centroids and edges capture inter-region flows, incorporating temporal variability via period-aware edge weights. The interactive visual analytics interface includes the H-Flow and a higher-order state sequence chart to reveal and compare second- and third-order patterns across space and time. Case studies in New York City and expert interviews demonstrate HoLens' feasibility, usability, and potential impact on urban planning, traffic management, and epidemiological investigations.

Abstract

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.

Figures (11)

• Figure 1: Illustration of higher-order patterns: (A) Raw movement data describe the change of positions over time, modeled as trajectories. We can extract (B) first-order and (C) higher-order dependencies from these movement data. Moreover, a set of first-/higher-order dependencies can form (D) higher-order patterns.
• Figure 2: The overview of HoLens. HoLens consists of two stages: movement modeling (A, B, C, and D) and interactive visual exploration (E, F, G, and H).
• Figure 3: HoLens supports visually exploring the urban higher-order patterns, which consists of four views: (A) the overview provides a configuration panel and a global representation to the end-users, (B) the map view displays the result of movement aggregation and supports visualizing the higher-order patterns in a spatial dimension, (C) the statistic view shows the detailed statistical information of the selected region, and (D) the state transition view provides the function for the further exploration the higher-order patterns.
• Figure 4: Illustration of H-Flow. (A) The design scheme of H-Flow, which aims to represent the higher-order dependencies in (B) the higher-order pattern from the (C) spatial dimension.
• Figure 5: Illustration of the higher-order state sequence chart. The higher-order state sequence chart includes two types: (A) the global and (B) the local higher-order state sequence chart.