On Kernel-Based Intensity Estimation of Spatial Point Patterns on Linear Networks

Moradi, Mehdi; Rodríguez‐Cortés, Francisco J.; Mateu, Jorge

doi:10.1080/10618600.2017.1360782

Cited by 34 publications

(37 citation statements)

References 22 publications

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“…There is currently no general agreement on how to perform kernel smoothing on a network (Borruso, ; Downs & Horner, ; Xie & Yan, ; Okabe et al ., ; Sugihara et al ., ; Okabe & Sugihara, , chapter 9; McSwiggan et al ., ; Moradi et al ., ).…”

Section: Background and Definitionsmentioning

confidence: 97%

“…Moradi et al () introduced a network counterpart of using the shortest‐path distance,

{\overset{λ}{false}}^{normalM} false(u false) = true \sum_{i = 1}^{n} \frac{κ false(d_{L} false(u, x_{i} false) false)}{A_{L} false(x_{i} false)}, u \in L,

where κ is a one‐dimensional kernel and

A_{L} false(u false) = \int_{L} κ false(d_{L} false(u, v false) false) {normald}_{1} v .

The estimator conserves mass and is a continuous function on the network if κ is continuous. Computation of is costly in large networks.…”

Section: Background and Definitionsmentioning

confidence: 99%

“…The data were presented and analysed by Ang et al () and in Baddeley et al . (, chapter 17), Baddeley et al (), Moradi et al () and Rakshit et al ().…”

Section: Chicago Examplementioning

confidence: 99%

“…For spatial point pattern data in two dimensions, kernel estimates are conceptually simple (Diggle, 1985;Bithell, 1990) and very fast to compute using the fast Fourier transform (FFT) (Silverman, 1982). However, for points on a network, kernel estimation is mathematically intricate and computationally expensive (Okabe et al, 2009;Sugihara et al, 2010;Okabe & Sugihara, 2012, chapter 9;McSwiggan et al, 2016;Moradi et al, 2017). The fastest algorithm available hitherto (McSwiggan et al, 2016) has computation times that increase quadratically with bandwidth; current implementations can easily deal with datasets of the size of Figure 1 but have difficulty with Figure 2, with computation times ranging from seconds to hours depending on the spatial resolution and error tolerance.…”

Section: Introductionmentioning

confidence: 99%

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Fast Kernel Smoothing of Point Patterns on a Large Network using Two‐dimensional Convolution

Rakshit

Davies

Moradi

et al. 2019

Int Statistical Rev

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Summary We propose a computationally efficient and statistically principled method for kernel smoothing of point pattern data on a linear network. The point locations, and the network itself, are convolved with a two‐dimensional kernel and then combined into an intensity function on the network. This can be computed rapidly using the fast Fourier transform, even on large networks and for large bandwidths, and is robust against errors in network geometry. The estimator is consistent, and its statistical efficiency is only slightly suboptimal. We discuss bias, variance, asymptotics, bandwidth selection, variance estimation, relative risk estimation and adaptive smoothing. The methods are used to analyse spatially varying frequency of traffic accidents in Western Australia and the relative risk of different types of traffic accidents in Medellín, Colombia.

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Section: Background and Definitionsmentioning

confidence: 97%

“…Moradi et al () introduced a network counterpart of using the shortest‐path distance,

{\overset{λ}{false}}^{normalM} false(u false) = true \sum_{i = 1}^{n} \frac{κ false(d_{L} false(u, x_{i} false) false)}{A_{L} false(x_{i} false)}, u \in L,

where κ is a one‐dimensional kernel and

A_{L} false(u false) = \int_{L} κ false(d_{L} false(u, v false) false) {normald}_{1} v .

The estimator conserves mass and is a continuous function on the network if κ is continuous. Computation of is costly in large networks.…”

Section: Background and Definitionsmentioning

confidence: 99%

“…The data were presented and analysed by Ang et al () and in Baddeley et al . (, chapter 17), Baddeley et al (), Moradi et al () and Rakshit et al ().…”

Section: Chicago Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fast Kernel Smoothing of Point Patterns on a Large Network using Two‐dimensional Convolution

Rakshit

Davies

Moradi

et al. 2019

Int Statistical Rev

Self Cite

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show abstract

“…Thus, the aim is to discover how such events behave and to understand whether they are uniformly distributed over the space. Adaptive and non-adaptive methods have been defined like kernel smoothing and Voronoi estimates for hot-spot analysis (Moradi et al, 2017). As time is typical an intrinsic dimension of the events being analysed, the interaction and correlation of time and space are also of interest.…”

Section: Pairing Quantitative and Qualitative Datamentioning

confidence: 99%

Geo-C: Enabling Open Cities and the Open City Toolkit

Granell

Bhattacharya

Casteleyn

et al. 2018

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:The GEO-C doctoral programme, entitled "Geoinformatics: Enabling Open Cities", is funded by the EU Marie Skłodowska-Curie actions (International Training Networks (ITN), European Joint Doctorates) until December 2018, and is managed by three European universities in Germany, Portugal and Spain. 15 doctoral grantholders (Early Stage Researchers) were selected to work on specific three-year projects, all contributing to improving the notion of open cities, and specifically to an Open City Toolkit of methodologies, code, and best practice examples. Contributions include volunteered geographic information (VGI), public information displays, mobility apps to encourage green living, providing open data to immigrant populations, reducing the second-order digital divide, sensing of quality of life, proximity based privacy protection, and spatio-temporal online social media analysis. All doctoral students conducted long-term visits and were embedded in city governments and businesses, to gain experience from multiple perspectives in addition to the researcher and users' perspective. The projects are situated within three areas: transparency, participation, and collaboration. They took mostly a bottom-up (citizen-centric) approach to (smart) open cities, rather than relying on large IT companies to create smart open cities in a top-down manner. This paper discusses the various contributions to enabling open cities, explains in some detail the Open City Toolkit, and its possible uses and impact on stakeholders. A follow-up doctoral program has been solicited and, if successful, will continue this line of research and will strengthen aspects of privacy, data provenance, and trust, in an effort to improve relations between data (e.g. news) publishers and consumers.

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Spatial Statistics along Networks

Okabe

2018

Wiley StatsRef: Statistics Reference Online

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Spatial statistics along networks is a branch of spatial statistics. Traditional spatial statistics deals with events occurring on a plane, referred to as planar spatial statistics . By contrast, spatial statistics along networks, referred to in parallel as network spatial statistics , deals with events occurring along networks. The events occurring “along” a network are of two types: those directly occurring on a network, for example, traffic accidents, and those occurring alongside a network, for example, stores facing a street. Networks may potentially include corridors, roads, railways, gas and oil pipelines, sewer systems, rivers, canals, electric wires, neurons, the Internet, social networks (e.g., SNS), and so on. Network spatial statistics is applied to various studies, for instance, pedestrian, car, and bicycle accidents, roadkill, street crimes, contamination of rivers, floods, facility locations, tree falls on a railway, etc. This article first describes the most basic hypothesis used in network spatial statistics, called the completely spatial randomness ( CSR ) hypothesis. Next, the article introduces nine methods used for network spatial statistics, that is, Voronoi diagrams, nearest‐neighbor distance method, K function method, spatial autocorrelation, point cluster analysis, kernel density estimation, spatial interpolation, and software for network spatial statistics.

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On Kernel-Based Intensity Estimation of Spatial Point Patterns on Linear Networks

Cited by 34 publications

References 22 publications

Fast Kernel Smoothing of Point Patterns on a Large Network using Two‐dimensional Convolution

Fast Kernel Smoothing of Point Patterns on a Large Network using Two‐dimensional Convolution

Geo-C: Enabling Open Cities and the Open City Toolkit

Spatial Statistics along Networks

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