A review on anisotropy analysis of spatial point patterns

Rajala, Tiina; Redenbach, Claudia; Särkkä, Aila; Sormani, Martina

doi:10.1016/j.spasta.2018.04.005

Cited by 28 publications

(16 citation statements)

References 49 publications

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“…Nevertheless, it is worth noting that for some of these operations, anisotropic options are theoretically available but have not yet been implemented. For instance, there is recent interest in anisotropic clustering and point pattern analysis (Mai, Janowicz, Hu, & Gao, ; Rajala, Redenbach, Särkkä, & Sormani, ).…”

Section: Rethinking Assumptions Of Isotropicitymentioning

confidence: 99%

“…To analyze spatial point patterns, researchers categorize the mechanisms of anisotropic patterns into geometric anisotropy, where points are converted from a stationary and isotropic pattern by a rotational transformation, and oriented clusters, where the intensity of points increases in a given direction (Illian et al, 2008;Lawson, Simeon, Kulldorff, Biggeri, & Magnani, 2007;Rajala et al, 2018). Anisotropic approaches, such as Fry plots (Fry, 1979), nearest neighbor orientation density (Illian et al, 2008), angle-dependent K function (Ohser & Stoyan, 1981), spectral (Bartlett, 1964) and wavelet (Rosenberg, 2004) analysis, were developed to achieve a broad range of analysis, including the detection of anisotropicity, testing for isotropicity, and estimation of the direction of point patterns.…”

Section: Direction In Spatial Structuresmentioning

confidence: 99%

“…Distance is a relation between two locations, while direction requires at least three (e.g., two targets plus the origin to form an angle), thereby requiring a larger sample size. Specifically, when the sample size is small, it is difficult to have enough replicates for statistical analysis on directional information, thus the assumption of isotropicity is often made for spatial analysis (Rajala et al., ). One can regard directional analysis as higher ordered.…”

Section: Rethinking Assumptions Of Isotropicitymentioning

confidence: 99%

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Making direction a first‐class citizen of Tobler's first law of geography

Zhu

Janowicz

Mai

2019

Transactions in GIS

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Waldo Tobler frequently reminded us that the law named after him was nothing more than calling for exceptions. This article discusses one of these exceptions. Spatial relations between points are frequently modeled as vectors in which both distance and direction are of equal prominence. However, in Tobler's first law of geography, such a relation is described only from the perspective of distance by relating the decreasing similarity of observations in some attribute space to their increasing distance in geographic space. Although anisotropic versions of many geographic analysis techniques, such as directional semivariograms, anisotropy clustering, and anisotropic point pattern analysis, have been developed over the years, direction remains on the level of an afterthought. We argue that, compared to distance, directional information is still under‐explored and anisotropic techniques are substantially less frequently applied in everyday GIS analysis. Commonly, when classical spatial autocorrelation indicators, such as Moran's I, are used to understand a spatial pattern, the weight matrix is only built from distance, without direction being considered. Similarly, GIS operations, such as buffering, do not take direction into account either, with distance in all directions being treated equally. In reality, meanwhile, particularly in urban structures and when processes are driven by the underlying physical geography, direction plays an essential role. In this article we ask whether the development of early GIS, data (sample) sparsity, and Tobler's law lead to a theory‐induced blindness for the role of direction. If so, is it possible to envision direction becoming a first‐class citizen of equal importance to distance instead of being an afterthought only considered when the deviation from a perfect circle becomes too obvious to be ignored?

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Section: Rethinking Assumptions Of Isotropicitymentioning

confidence: 99%

Section: Direction In Spatial Structuresmentioning

confidence: 99%

Section: Rethinking Assumptions Of Isotropicitymentioning

confidence: 99%

See 1 more Smart Citation

Making direction a first‐class citizen of Tobler's first law of geography

Zhu

Janowicz

Mai

2019

Transactions in GIS

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“…Literature has focused much more on building tools to account for non-stationarity (Baddeley, Møller, & Waagepetersen 2000;van Lieshout 2011), than to take care of anisotropy, which has largely received quite less attention (Comas, Conde, & Mateu 2018;Comas, Rodriguez-Cortes, & Mateu 2015;Rajala, Redenbach, Särkkä, & Sormani 2018).…”

Section: Introductionmentioning

confidence: 99%

Directional analysis for point patterns on linear networks

Moradi

Mateu

Comas

2021

Stat

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Statistical analysis of point processes often assumes that the underlying process is isotropic in the sense that its distribution is invariant under rotation. For point processes on R 2 , some tests based on the Kand nearest neighbour orientation functions have been proposedto check such an assumption. However, anisotropy and directional analysis need proper caution when dealing with point processes on linear networks, as the implicit geometry of the network forces particular directions that the points of the pattern have to necessarily meet. In this paper, we adapt such tests to the case of linear networks, and discuss how to use them to detect particular directional preferences, even at some angles that are different from the main angles imposed by the network. Through a simulation study, we check the performance of our proposals under different settings, over a linear network and a dendrite tree, showing that they are able to precisely detect the directional preferences of the points in the pattern, regardless the type of spatial interaction and the geometry of the network.We use our tests to highlight the directional preferences in the spatial distribution of traffic accidents in Barcelona (Spain) during 2019, and in Medellin (Colombia), during 2016.

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“…A DPT pattern can be seen as a collection of points, where the points all have a fractal shape. We note for instance that small point patterns are more naturally isotropic and stationary (Rajala et al, 2018). Hence, stationarity and isotropy of the DPT should be checked carefully.…”

Section: Introductionmentioning

confidence: 99%