ReeSPOT: Reeb Graph Models Semantic Patterns of Normalcy in Human Trajectories

TL;DR

ReeSPOT is introduced, a novel Reeb graph-based method to model patterns of life in human trajectories (akin to a fingerprint) and how it captures the critically significant spatial and temporal deviations using the nodes of the Reeb graph.

Abstract

This paper introduces ReeSPOT, a novel Reeb graph-based method to model patterns of life in human trajectories (akin to a fingerprint). Human behavior typically follows a pattern of normalcy in day-to-day activities. This is marked by recurring activities within specific time periods. In this paper, we model this behavior using Reeb graphs where any deviation from usual day-to-day activities is encoded as nodes in the Reeb graph. The complexity of the proposed algorithm is linear with respect to the number of time points in a given trajectory. We demonstrate the usage of ReeSPOT and how it captures the critically significant spatial and temporal deviations using the nodes of the Reeb graph. Our case study presented in this paper includes realistic human movement scenarios: visiting uncommon locations, taking odd routes at infrequent times, uncommon time visits, and uncommon stay durations. We analyze the Reeb graph to interpret the topological structure of the GPS trajectories. Potential applications of ReeSPOT include urban planning, security surveillance, and behavioral research.

Figures (5)

• Figure 1: Map overlay of normal and anomalous trajectories from scenario 2 of the case study, annotated with semantic labels for points of interest (POIs).
• Figure 2: Reeb Graph Construction Over Time. We show the construction of Reeb graphs $R(V,E)$ for a set of five trajectories. The appear, disappear, connect, and disconnect events are shown in the top subfigure. Changes in the grouping of trajectories due to these events are encoded as nodes in the bottom figure. Nodes of the Reeb graph $\mathcal{R}$ in the bottom figure are shown in green color and the edges are shown in black color.
• Figure 3: 3D trajectory plots with computed Reeb graph nodes for scenario 1 in Section \ref{['sec:experiments']}, where day 0 to day 4 are normal trajectories, and the anomalous trajectory is in red.
• Figure 4: 2D Trajectory plots displaying time and latitude dimensions alongside computed Reeb graph nodes. These plots illustrate both normal and anomalous scenarios as outlined in Section \ref{['ssec:scenario']}. The detailed discussions on node generation and behavioral analysis can be found in Section \ref{['ssec:plots_desc']}.
• Figure 5: (a) illustrates the Reeb graph node-level distances for both anomalous days. (b) shows the day-level anomaly scores.