[Paper Review] Graph-Based Deep Modeling and Real Time Forecasting of Sparse Spatio-Temporal Data

Bao Wang, Xiyang Luo+4 more|arXiv (Cornell University)|Apr 2, 2018

Traffic Prediction and Management TechniquesEngineering15 references56 citations

TL;DR

This paper proposes a two-part framework for sparse spatio-temporal data: (1) inferring a sparse spatio-temporal weighted graph (STWG) via a multivariate Hawkes process, and (2) forecasting with a graph-structured recurrent neural network (GSRNN) built on that graph, demonstrated on crime and traffic data.

ABSTRACT

We present a generic framework for spatio-temporal (ST) data modeling, analysis, and forecasting, with a special focus on data that is sparse in both space and time. Our multi-scaled framework is a seamless coupling of two major components: a self-exciting point process that models the macroscale statistical behaviors of the ST data and a graph structured recurrent neural network (GSRNN) to discover the microscale patterns of the ST data on the inferred graph. This novel deep neural network (DNN) incorporates the real time interactions of the graph nodes to enable more accurate real time forecasting. The effectiveness of our method is demonstrated on both crime and traffic forecasting.

Motivation & Objective

• Motivate accurate forecasting of ST data that are sparse in both space and time.
• Introduce an STWG that encodes macroscale spatio-temporal dependencies.
• Develop a graph-structured DNN (GSRNN) to capture microscale patterns on the inferred graph.
• Demonstrate real-time forecasting performance on crime and traffic datasets.

Proposed method

• Represent SP sparse data as an STWG where nodes correspond to geographic regions (e.g., zip codes) and edges encode self- and mutual-excitation learned via a multivariate Hawkes process.
• Infer STWG by maximizing a penalized log-likelihood with an L1 regularizer to induce sparsity, solved via an EM algorithm with a split-Bregman step.
• Augment sparse time series by mapping to diurnal cumulative functions and applying local super-resolution to create augmented inputs for DNNs.
• Deploy a graph-structured RNN (GSRNN) where edge LSTMs propagate information along graph edges and node LSTMs aggregate to predict future counts, forming a feed-forward-like architecture.
• Use a bi-directional SRNN extension with weighted averaging pooling based on Hawkes weights for improved forecasting.]
• Apply data augmentation and a cascaded LSTM per node to improve micro-scale prediction accuracy.

Experimental results

Research questions

• RQ1 How can sparse spatio-temporal data be effectively modeled on an irregular spatial domain?
• RQ2 Can a Hawkes-process-based graph inference capture macroscale spatio-temporal dependencies suitable for forecasting?
• RQ3 Does a graph-structured RNN leveraging inferred STWG improve real-time forecasting of sparse ST data (crime, traffic) over traditional baselines?

Key findings

• The STWG captures macro-scale spatio-temporal dependencies and enables sparse graph representations of crime data across cities.
• The GSRNN with edge LSTMs and weighted pooling outperforms single-node and joint-training baselines in crime forecasting on LA and CHI datasets.
• Data augmentation via diurnal cumulative transformation significantly improves DNN performance on sparse time series.
• Bidirectional extension and weighted pooling in the GSRNN improve forecasting accuracy relative to unidirectional SRNN variants.
• Traffic forecasting experiments show competitive RMSE performance of the GSRNN compared to ST-ResNet and baseline models on BikeNYC and TaxiBJ datasets.