Multi-Factor Spatio-Temporal Prediction based on Graph Decomposition Learning

TL;DR

This work proposes a multi-factor ST prediction task that predicts partial ST data evolution under different factors, and combines them for a final prediction, and instantiates a novel model-agnostic framework, named spatio-temporal graph decomposition learning (STGDL), for multi-Factor ST prediction.

Abstract

Spatio-temporal (ST) prediction is an important and widely used technique in data mining and analytics, especially for ST data in urban systems such as transportation data. In practice, the ST data generation is usually influenced by various latent factors tied to natural phenomena or human socioeconomic activities, impacting specific spatial areas selectively. However, existing ST prediction methods usually do not refine the impacts of different factors, but directly model the entangled impacts of multiple factors. This amplifies the modeling complexity of ST data and compromises model interpretability. To this end, we propose a multi-factor ST prediction task that predicts partial ST data evolution under different factors, and combines them for a final prediction. We make two contributions to this task: an effective theoretical solution and a portable instantiation framework. Specifically, we first propose a theoretical solution called decomposed prediction strategy and prove its effectiveness from the perspective of information entropy theory. On top of that, we instantiate a novel model-agnostic framework, named spatio-temporal graph decomposition learning (STGDL), for multi-factor ST prediction. The framework consists of two main components: an automatic graph decomposition module that decomposes the original graph structure inherent in ST data into subgraphs corresponding to different factors, and a decomposed learning network that learns the partial ST data on each subgraph separately and integrates them for the final prediction. We conduct extensive experiments on four real-world ST datasets of two types of graphs, i.e., grid graph and network graph. Results show that our framework significantly reduces prediction errors of various ST models by 9.41% on average (35.36% at most). Furthermore, a case study reveals the interpretability potential of our framework.

Figures (8)

• Figure 1: (a) The architecture of our STGDL framework. The graph structure of the input ST graph is decomposed as several subgraphs via Automatic Graph Decomposition constrained by completeness and independence regularizers. Then, ST graph signals are fed into the Decomposed Learning Network (DLN) for ST prediction corresponding to each subgraph and the overall graph. The residual item of DLN is expected to be zero after subtracting recovered all subgraphs' signals from the input graph signals. (b) An illustration of the ST Block.
• Figure 2: Effectiveness of the automatic graph decomposition w.r.t. MAE.
• Figure 3: Effectiveness of regularization terms w.r.t. MAE.
• Figure 4: Illustration of variants about the dual residual mechanism. Without loss of generality, we take three ST blocks as an example. There can be more blocks in practice.
• Figure 5: Effectiveness of the decomposed learning network w.r.t. MAE.

Theorems & Definitions (9)

• Definition 1: Spatio-Temporal Graph
• Theorem 1
• Lemma 1: Divide
• Lemma 2: Conquer
• Lemma 3: Combine
• Definition 2: Problem Scale
• Definition 3: Problem Independence
• Theorem 2
• Lemma 4