A Principal Curve-based method for Geospatial Data Smoothing

Abstract

GIScience 2016 Short Paper Proceedings A Principal Curve-based method for Geospatial Data Smoothing Xiliang Liu, Feng Lu, Kang Liu, Peiyuan Qiu, Li Yu, Mingxiao Li State Key Lab of Resources and Environmental Information system, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences {liuxl;luf;liukang;yul;limx}@lreis.ac.cn Abstract We propose a principal curve-based method for geospatial data smoothing. Firstly we test its performance with traditional approaches using floating car data (FCD). Secondly we evaluate its robustness with spatial-temporal dependence using Spearman rank correlation analysis. Final results show that the proposed method not only takes precedence over traditional methods (Mean and Median) in accuracy (about 10%-15% higher in RMSE), but also performs more robust, showing a distinct changing trend of the original data. These findings demonstrate the feasibility of the principal curve-based method in geospatial data smoothing. Keywords: Principal curves, Data smoothing, Robustness 1. Introduction Nowadays various GPS-equipped sensors, such as operating vehicles (taxicabs, probe cars, buses, private cars, etc.), mobile phones, wearable devices and so on, have become the mainstream in the research of GIScience and many other location based services (LBS) because of the cost-effectiveness and flexibility compared with other data sources. However, these geospatial data collected from GPS devices cannot be utilized directly owing to: (1) the sampling interval in most cities is low-frequency due to transmission bandwidth, energy consumption and storage pressures, and (2) the spatial-temporal distribution of these GPS- equipped devices among a city or a given region is heterogeneous. To further mine these data, the data sparseness, data missing and noise problem make geospatial data smoothing an unavoidable step. Previous studies mainly focus on parametric approaches including Kalman filter, particle filter, piecewise linear (PWL) curves, and so on. These methods can effectively deal with data noise problem, but behave unsatisfactory with data sparseness and data missing problems. Traditional Mean and Median are also conducted by using current and near-past records from a historical perspective. However, the prerequisite of Gaussian distribution in most cases cannot be satisfied so that the traditional Mean and Median methods can only be employed in linear systems. In this paper, we propose a principal curve-based method in geographical data interpolation. We evaluate its performance using floating car data (FCD), and analyze its robustness with Spearman's rank correlation analysis. A series of experiments demonstrate its feasibility for geospatial data smoothing. 2. Methodology Principal curves give a summarization of the data in terms of a 1-d space nonlinearly embedded in the data space (Hastie and Stuetzle 1989). The original definition of a principal curve f ( t ) ( f 1 ( t ),..., f d ( t )) relies on the self-consistency property of principal components,