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A Unified Model for Spatio-Temporal Prediction Queries with Arbitrary Modifiable Areal Units

Liyue Chen, Jiangyi Fang, Tengfei Liu, Shaosheng Cao, Leye Wang

TL;DR

An ST network with hierarchical spatial modeling and scale normalization modules to efficiently and equally learn multi-scale representations and a dynamic programming scheme to solve the formulated optimal combination problem, minimizing predicted error through theoretical analysis.

Abstract

Spatio-Temporal (ST) prediction is crucial for making informed decisions in urban location-based applications like ride-sharing. However, existing ST models often require region partition as a prerequisite, resulting in two main pitfalls. Firstly, location-based services necessitate ad-hoc regions for various purposes, requiring multiple ST models with varying scales and zones, which can be costly to support. Secondly, different ST models may produce conflicting outputs, resulting in confusing predictions. In this paper, we propose One4All-ST, a framework that can conduct ST prediction for arbitrary modifiable areal units using only one model. To reduce the cost of getting multi-scale predictions, we design an ST network with hierarchical spatial modeling and scale normalization modules to efficiently and equally learn multi-scale representations. To address prediction inconsistencies across scales, we propose a dynamic programming scheme to solve the formulated optimal combination problem, minimizing predicted error through theoretical analysis. Besides, we suggest using an extended quad-tree to index the optimal combinations for quick response to arbitrary modifiable areal units in practical online scenarios. Extensive experiments on two real-world datasets verify the efficiency and effectiveness of One4All-ST in ST prediction for arbitrary modifiable areal units. The source codes and data of this work are available at https://github.com/uctb/One4All-ST.

A Unified Model for Spatio-Temporal Prediction Queries with Arbitrary Modifiable Areal Units

TL;DR

An ST network with hierarchical spatial modeling and scale normalization modules to efficiently and equally learn multi-scale representations and a dynamic programming scheme to solve the formulated optimal combination problem, minimizing predicted error through theoretical analysis.

Abstract

Spatio-Temporal (ST) prediction is crucial for making informed decisions in urban location-based applications like ride-sharing. However, existing ST models often require region partition as a prerequisite, resulting in two main pitfalls. Firstly, location-based services necessitate ad-hoc regions for various purposes, requiring multiple ST models with varying scales and zones, which can be costly to support. Secondly, different ST models may produce conflicting outputs, resulting in confusing predictions. In this paper, we propose One4All-ST, a framework that can conduct ST prediction for arbitrary modifiable areal units using only one model. To reduce the cost of getting multi-scale predictions, we design an ST network with hierarchical spatial modeling and scale normalization modules to efficiently and equally learn multi-scale representations. To address prediction inconsistencies across scales, we propose a dynamic programming scheme to solve the formulated optimal combination problem, minimizing predicted error through theoretical analysis. Besides, we suggest using an extended quad-tree to index the optimal combinations for quick response to arbitrary modifiable areal units in practical online scenarios. Extensive experiments on two real-world datasets verify the efficiency and effectiveness of One4All-ST in ST prediction for arbitrary modifiable areal units. The source codes and data of this work are available at https://github.com/uctb/One4All-ST.
Paper Structure (36 sections, 3 theorems, 13 equations, 17 figures, 4 tables, 1 algorithm)

This paper contains 36 sections, 3 theorems, 13 equations, 17 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. System Workflow
  4. Methodology
  5. Framework Overview
  6. Multi-scale Joint Learning
  7. Temporal Modeling
  8. Hierarchical Spatial Modeling
  9. Cross-scale Modeling
  10. Multi-task Learning
  11. Optimal Combination Search and Index
  12. Optimal Combination Search with Dynamic Programming for Union Operations
  13. Improvement by Subtraction Operations
  14. Extended Quad-tree Index
  15. Modifiable Areal Units Prediction
  16. ...and 21 more sections

Key Result

Theorem 4.1

Given a union system, for any rasterized region $R$, which can be decomposed into a set of fine-grained grids $\tilde{R}=\{r_1,r_2,...,r_m\}$ (by Algorithm alg: decomposition). We have $\Lambda^*(R) = \Lambda^*(r_1)+\Lambda^*(r_2)+...+\Lambda^*(r_m)$.

Figures (17)

  • Figure 1: Research motivation. Left: Location-based services require ad-hoc regions for various purposes, necessitating numerous ST models to support the service. Right: The prediction inconsistency raised by different ST models.
  • Figure 2: Three combinations with different predictability for representing the same modifiable areal unit.
  • Figure 3: (a): Example of hierarchical grids. (b): A rasterized region and its assignment matrix. (c): Example of the mapping function. (d): Example of a grid combination.
  • Figure 4: The workflow of One4All-ST system.
  • Figure 5: Overall framework of One4All-ST.
  • ...and 12 more figures

Theorems & Definitions (3)

  • Theorem 4.1
  • Lemma 4.2
  • Theorem 4.3