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.

翻译：高阶模式揭示了序列多步状态转换，其通常优于仅描述一阶地理空间运动模式的起讫点分析。传统高阶运动建模方法首先构建有向无环图（DAG），然后从中提取高阶模式。然而，基于DAG的方法严重依赖运动关键点的识别——这对稀疏运动场景具有挑战性——且未能考虑对城市环境运动至关重要的时间变异因素。为突破这些局限，我们提出HoLens——一种面向城市环境的高阶运动模式建模与可视化的创新方法。HoLens主要做出两项贡献：第一，我们设计了自适应运动聚合算法，通过整合空间邻近性、上下文信息与时间变异性，实现运动数据的层次化自组织；第二，我们构建了交互式可视化分析界面，集成包括用于地图空间高阶模式可视化的H-Flow流图与用于呈现高阶状态转换的高阶状态序列图在内的成熟可视化技术。两项真实案例研究表明，该方法能自适应地聚合数据，并展示通过HoLens探索高阶模式的完整过程。我们还通过三位领域专家的深度访谈，验证了该方法的可行性、易用性与有效性。