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Multi-granularity Spatiotemporal Flow Patterns

Chrysanthi Kosyfaki, Nikos Mamoulis, Reynold Cheng, Ben Kao

TL;DR

This work formalizes Origin-Destination-Time ($ODT$) patterns and introduces a bottom-up, weak-monotonicity-based enumeration framework to discover significant spatiotemporal flows at varying granularities. It presents a robust baseline algorithm with multiple optimizations, along with practical pattern variants (size-bounded, constrained, rank-based) and an approximate, generate-and-test method to scale to large datasets. The approach is validated on three real networks (NYC taxi, MTR, and Flights), demonstrating substantial speedups, controllable pattern explosion, and useful use cases for emergency planning and urban analytics. Overall, the paper contributes a scalable toolkit for discovering generalized ODT flow patterns under minimal trajectory data, enabling targeted insights and decision support for transportation systems and urban planning.

Abstract

Analyzing flow of objects or data at different granularities of space and time can unveil interesting insights or trends. For example, transportation companies, by aggregating passenger travel data (e.g., counting passengers traveling from one region to another), can analyze movement behavior. In this paper, we study the problem of finding important trends in passenger movements between regions at different granularities. We define Origin (O), Destination (D), and Time (T ) patterns (ODT patterns) and propose a bottom-up algorithm that enumerates them. We suggest and employ optimizations that greatly reduce the search space and the computational cost of pattern enumeration. We also propose pattern variants (constrained patterns and top-k patterns) that could be useful to different applications scenarios. Finally, we propose an approximate solution that fast identifies ODT patterns of specific sizes, following a generate-and-test approach. We evaluate the efficiency and effectiveness of our methods on three real datasets and showcase interesting ODT flow patterns in them.

Multi-granularity Spatiotemporal Flow Patterns

TL;DR

This work formalizes Origin-Destination-Time () patterns and introduces a bottom-up, weak-monotonicity-based enumeration framework to discover significant spatiotemporal flows at varying granularities. It presents a robust baseline algorithm with multiple optimizations, along with practical pattern variants (size-bounded, constrained, rank-based) and an approximate, generate-and-test method to scale to large datasets. The approach is validated on three real networks (NYC taxi, MTR, and Flights), demonstrating substantial speedups, controllable pattern explosion, and useful use cases for emergency planning and urban analytics. Overall, the paper contributes a scalable toolkit for discovering generalized ODT flow patterns under minimal trajectory data, enabling targeted insights and decision support for transportation systems and urban planning.

Abstract

Analyzing flow of objects or data at different granularities of space and time can unveil interesting insights or trends. For example, transportation companies, by aggregating passenger travel data (e.g., counting passengers traveling from one region to another), can analyze movement behavior. In this paper, we study the problem of finding important trends in passenger movements between regions at different granularities. We define Origin (O), Destination (D), and Time (T ) patterns (ODT patterns) and propose a bottom-up algorithm that enumerates them. We suggest and employ optimizations that greatly reduce the search space and the computational cost of pattern enumeration. We also propose pattern variants (constrained patterns and top-k patterns) that could be useful to different applications scenarios. Finally, we propose an approximate solution that fast identifies ODT patterns of specific sizes, following a generate-and-test approach. We evaluate the efficiency and effectiveness of our methods on three real datasets and showcase interesting ODT flow patterns in them.

Paper Structure

This paper contains 26 sections, 2 theorems, 1 equation, 14 figures, 9 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Definitions
  4. Pattern extraction
  5. Baseline Algorithm
  6. Optimizations
  7. Pattern Variants
  8. Size-bounded Patterns
  9. Constrained Patterns
  10. Rank-based patterns
  11. Baseline approach for rank-based pattern enumeration
  12. Optimized rank-based pattern enumeration
  13. Approximate Computation and Sampling of ODT patterns
  14. Description and analysis
  15. A weighted approximate ODT pattern detection variant
  16. ...and 11 more sections

Key Result

Lemma 1

The maximum possible $P'$.cnt that can be added to $P$.cnt, to derive the support of $CandP$ is as follows:

Figures (14)

  • Figure 1: Example of an ODT pattern
  • Figure 2: A detailed example
  • Figure 3: Pattern enumeration example
  • Figure 4: Prefix sum example
  • Figure 5: Illustration of the approximate algorithm. Suppose that we are looking for patterns with 2 regions in the origin ($S_O=2$), 3 regions in the destination ($S_D=3$), and 4 timeslot ($S_T=4$). We apply BFS from each node in the region neighborhood graph to generate candidate O and D components of the desired sizes and randomly pick them and combine them with random T periods of 4 timeslots to generate candidate ODT triples, which are eventually verified.
  • ...and 9 more figures

Theorems & Definitions (12)

  • Definition 1: Region/Timeslot
  • Definition 2: Generalization of a region/timeslot
  • Definition 3: Minimal generalization of a region/timeslot
  • Definition 4: Atomic ODT triple
  • Definition 5: ODT triple
  • Definition 6: ODT triple generalization
  • Definition 7: Minimal generalization of ODT triple
  • Definition 8: Atomic ODT pattern
  • Definition 9: ODT pattern
  • Definition 10: ODT pattern (rank-based)
  • ...and 2 more