Recover Fine-Grained Spatial Data from Coarse Aggregation

TL;DR

This paper introduces a novel Constrained Spatial Smoothing method to accurately recover fine-grained spatial data from coarse aggregate observations, leveraging local continuity and geographical attributes.

Contribution

The paper presents a new CSS approach combining finite-element methods and ADMM for spatial data recovery, outperforming existing methods.

Findings

CSS significantly outperforms state-of-the-art methods

Effective utilization of geographical attributes improves accuracy

Validated on large datasets from Milan

Abstract

In this paper, we study a new type of spatial sparse recovery problem, that is to infer the fine-grained spatial distribution of certain density data in a region only based on the aggregate observations recorded for each of its subregions. One typical example of this spatial sparse recovery problem is to infer spatial distribution of cellphone activities based on aggregate mobile traffic volumes observed at sparsely scattered base stations. We propose a novel Constrained Spatial Smoothing (CSS) approach, which exploits the local continuity that exists in many types of spatial data to perform sparse recovery via finite-element methods, while enforcing the aggregated observation constraints through an innovative use of the ADMM algorithm. We also improve the approach to further utilize additional geographical attributes. Extensive evaluations based on a large dataset of phone call records and a demographical dataset from the city of Milan show that our approach significantly outperforms various state-of-the-art approaches, including Spatial Spline Regression (SSR).