GeoOutlier function

Spatio (temporal) outliers detection

Given a set of spatio (temporal) locations and data, the procedure select the spatial or spatiotemporal ouliers using a specific algorithm. UTF-8

GeoOutlier(data, coordx, coordy=NULL,coordz=NULL, coordt=NULL, coordx_dyn=NULL, 
             distance="Eucl", grid=FALSE,  neighb=10,alpha=0.001,
             method="Z-Median", radius=6371, bivariate=FALSE,X=NULL)

Arguments

• data: An optional $d$-dimensional vector (a single spatial realisation) or a ($d x d$)-matrix (a single spatial realisation on regular grid) or a ($t x d$)-matrix (a single spatial-temporal realisation) or an ($d x d x t$)-array (a single spatial-temporal realisation on regular grid).

• coordx: A numeric ($d x 2$)-matrix or ($d x 3$)-matrix Coordinates on a sphere for a fixed radius radius

  are passed in lon/lat format expressed in decimal degrees.

• coordy: A numeric vector giving 1-dimension of spatial coordinates; Optional argument, the default is NULL.

• coordz: A numeric vector giving 1-dimension of spatial coordinates; Optional argument, the default is NULL.

• coordt: A numeric vector giving 1-dimension of temporal coordinates. Optional argument, the default is NULL

  then a spatial RF is expected.

• coordx_dyn: A list of $m$ numeric ($d x 2$)-matrices containing dynamical (in time) spatial coordinates. Optional argument, the default is NULL

• distance: String; the name of the spatial distance. The default is Eucl, the euclidean distance. See the Section Details of GeoFit.

• grid: Logical; if FALSE (the default) the data are interpreted as spatial or spatial-temporal realisations on a set of non-equispaced spatial sites (irregular grid).

• neighb: Numeric; an optional positive integer indicating the order of neighborhoodused for Z-Median algorithm.

• alpha: Numeric; a numeric value between 0 and 1 used for Z-Median algorithm.

• method: String; The name of the algorithm for detecting spatial ouliers. Default is Z-median proposed in Chen et al. (2008)

• radius: Numeric; a value indicating the radius of the sphere when using the great circle distance. Default value is the radius of the earth in Km (i.e. 6371)

• bivariate: If TRUE then data is considered as spatial bivariate data.

• X: Numeric; an optional Matrix of spatio (temporal) covariates.

Returns

Return a matrix or a list containing the dected spatial or spatio-temporal outliers

References

Chen D, Lu C, Kou Y, Chen F (2008) On detecting spatial outliers. Geoinformatica 12:455–475

Bevilacqua M., Caamaño C., Arellano-Valle R. B., Camilo Gomez C. (2022) A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers. Test 10.1007/s11749-021-00797-5

Author(s)

Moreno Bevilacqua, moreno.bevilacqua89@gmail.com ,https://sites.google.com/view/moreno-bevilacqua/home, Víctor Morales Oñate, victor.morales@uv.cl , https://sites.google.com/site/moralesonatevictor/, Christian", Caamaño-Carrillo, chcaaman@ubiobio.cl ,https://www.researchgate.net/profile/Christian-Caamano

Examples

library(GeoModels)
set.seed(1428)
NN = 1500
coords = cbind(runif(NN),runif(NN))
###
scale=0.5/3
corrmodel = "Matern"; 

param = list(mean=0,sill=1,nugget=0,scale=scale,smooth=0.5,skew=0)
data = GeoSim(coordx = coords,corrmodel = corrmodel,
                  model = "TwoPieceGaussian",param = param)$data

K=15         #parameter for outliers detection alghoritm
alpha=0.005  #parameter for outliers detection alghoritm
outlier=GeoOutlier(data=data, coordx = coords,neighb=K,alpha=alpha)
quilt.plot(coords,data)
for (i in 1:nrow(outlier))  plotrix::draw.circle(outlier[i,1], outlier[i,2],radius=0.02,lwd=2) 
nrow(outlier) # number of outliers

param = list(mean=0,sill=1,nugget=0.4,scale=scale,smooth=0.5)
data = GeoSim(coordx = coords,corrmodel = corrmodel,
                  model = "Gaussian",param = param)$data

K=15         #parameter for outliers detection alghoritm
alpha=0.005  #parameter for outliers detection alghoritm
outlier=GeoOutlier(data=data, coordx = coords,neighb=K,alpha=alpha)
quilt.plot(coords,data)
for (i in 1:nrow(outlier))  plotrix::draw.circle(outlier[i,1], outlier[i,2],radius=0.02,lwd=2)
nrow(outlier) # number of outliers