| Title: | Functional Geostatistics: Univariate and Multivariate Functional Spatial Prediction |
|---|---|
| Description: | Performance of functional kriging, cokriging, optimal sampling and simulation for spatial prediction of functional data. The framework of spatial prediction, optimal sampling and simulation are extended from scalar to functional data. 'SpatFD' is based on the Karhunen-Loève expansion that allows to represent the observed functions in terms of its empirical functional principal components. Based on this approach, the functional auto-covariances and cross-covariances required for spatial functional predictions and optimal sampling, are completely determined by the sum of the spatial auto-covariances and cross-covariances of the respective score components. The package provides new classes of data and functions for modeling spatial dependence structure among curves. The spatial prediction of curves at unsampled locations can be carried out using two types of predictors, and both of them report, the respective variances of the prediction error. In addition, there is a function for the determination of spatial locations sampling configuration that ensures minimum variance of spatial functional prediction. There are also two functions for plotting predicted curves at each location and mapping the surface at each time point, respectively. References Bohorquez, M., Giraldo, R., and Mateu, J. (2016) <doi:10.1007/s10260-015-0340-9>, Bohorquez, M., Giraldo, R., and Mateu, J. (2016) <doi:10.1007/s00477-016-1266-y>, Bohorquez M., Giraldo R. and Mateu J. (2021) <doi:10.1002/9781119387916>. |
| Authors: | Martha Patricia Bohorquez Castañeda [aut, cre], Diego Alejandro Sandoval Skinner [aut], Angie Villamil [aut], Samuel Hernando Sanchez Gutierrez [aut], Nathaly Vergel Serrano [ctb], Miguel Angel Munoz Layton [ctb], Valeria Bejarano Salcedo [ctb], Venus Celeste Puertas [ctb], Ruben Dario Guevara Gonzalez [aut], Joan Nicolas Castro Cortes [ctb], Ramon Giraldo Henao [aut], Jorge Mateu [aut] |
| Maintainer: | Martha Patricia Bohorquez Castañeda <[email protected]> |
| License: | GPL-3 |
| Version: | 0.0.1 |
| Built: | 2024-11-20 04:36:08 UTC |
| Source: | https://github.com/cran/SpatFD |
Particular material 10 (PM10) of Bogota measure in 10 stations in the city.
data(AirQualityBogota)data(AirQualityBogota)
two data.frame of measurements 'PM10' and coordinates 'coord'. Also a map file of class SpatialPolygonDataFrame load from a shape file by rgdal::readOGR
Secretaria de Ambiente de Bogotá
Monitor network of air quality of Bogota http://rmcab.ambientebogota.gov.co
This function classifies new functional data based on PCA results from training data.
classification(data.train.pca, new.basis, k, distance, mcov = NULL)classification(data.train.pca, new.basis, k, distance, mcov = NULL)
data.train.pca |
A list of PCA results from training data. |
new.basis |
Basis object from the test data |
k |
Number of nearest neighbors to consider for classification. |
distance |
Type of distance to use (e.g., "euclidean", "mahalanobis"). |
mcov |
Optional covariance matrices for Mahalanobis distance. |
The predicted class for the new data.
data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis) # Create train and test data s4.sep=gfd_clasif_data(s4.gfdata, 0.8,seed = 2910) s4.train=s4.sep$train s4.test=s4.sep$test # Classification cla<-classification(data.train.pca = s4.train, new.basis=s4.test[[1]]$data_fd[[1]], k=4, distance='euclidean', mcov = mcov )data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis) # Create train and test data s4.sep=gfd_clasif_data(s4.gfdata, 0.8,seed = 2910) s4.train=s4.sep$train s4.test=s4.sep$test # Classification cla<-classification(data.train.pca = s4.train, new.basis=s4.test[[1]]$data_fd[[1]], k=4, distance='euclidean', mcov = mcov )
This function performs leave-one-out cross-validation for functional cokriging. It systematically leaves out one location at a time from the dataset, fits the model to the remaining data, and then makes a prediction for the left-out observation. It is used to assess the predictive performance of the functional cokriging model.
COK_crossval_loo(object, plot_show, var, show_all)COK_crossval_loo(object, plot_show, var, show_all)
object |
A 'COKS_pred' object obtained with function |
plot_show |
A logical value. If |
var |
A numerical value indicating the number of the variable to be used in the cross-validation. Default is |
show_all |
A logical value. If |
An object containing the results of the leave-one-out cross-validation. Includes:
performance_metrics |
Summary statistics describing the overall predictive performance, such as mean squared error. |
plots |
The generation of plots showing the cross-validation results, controlled by the |
Venus Puertas [email protected]
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Optimal sampling for spatial prediction of functional data. Statistical Methods & Applications, 25(1), 39-54.
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
# Load the data and the required packages library(SpatFD) library(gstat) data(COKMexico) # Create the SpatFD data objects SFD_PM10_NO2 <- SpatFD(Mex_PM10, coords = coord_PM10, basis = "Fourier", nbasis = 21, lambda = 0.000001, nharm = 2, name = names(Mex_PM10)) SFD_PM10_NO2 <- SpatFD(NO2, coords = coord_NO2, basis = "Fourier", nbasis = 27, lambda = 0.000001, nharm = 2, add = SFD_PM10_NO2,name = names(NO2)) # Fit the model model1 <- gstat::vgm(647677.1,"Gau",23317.05) model1 <- gstat::vgm(127633,"Wav",9408.63, add.to = model1) # Perform the cokriging newcoords <- data.frame(x = 509926,y = 2179149) coks <- COKS_scores_lambdas(SFD_PM10_NO2,newcoords,model1) # Perform the cross-validation along NO2 COK_crossval_loo(object = coks, var = 2,show_all=TRUE)# Load the data and the required packages library(SpatFD) library(gstat) data(COKMexico) # Create the SpatFD data objects SFD_PM10_NO2 <- SpatFD(Mex_PM10, coords = coord_PM10, basis = "Fourier", nbasis = 21, lambda = 0.000001, nharm = 2, name = names(Mex_PM10)) SFD_PM10_NO2 <- SpatFD(NO2, coords = coord_NO2, basis = "Fourier", nbasis = 27, lambda = 0.000001, nharm = 2, add = SFD_PM10_NO2,name = names(NO2)) # Fit the model model1 <- gstat::vgm(647677.1,"Gau",23317.05) model1 <- gstat::vgm(127633,"Wav",9408.63, add.to = model1) # Perform the cokriging newcoords <- data.frame(x = 509926,y = 2179149) coks <- COKS_scores_lambdas(SFD_PM10_NO2,newcoords,model1) # Perform the cross-validation along NO2 COK_crossval_loo(object = coks, var = 2,show_all=TRUE)
Particular material 10 (PM10) and NO2 measured in 13 and 18 locations in Mexico. The data correspond to consecutive hours from January 01, 2015 at 1:00 a.m. to May 30, 2015 at 12:00 a.m., at 23 environmental stations. The stations in the air quality network RAMA (Red Automática de Monitoreo Atmosférico), monitor hourly particulate matter up to 10 micrometers in size (PM10) and Nitrogen dioxide (NO2) among others. The particulate matter (PM) is an important component of air pollution. NO2 is a gaseous air pollutant produced by the road traffic and other fossil fuel combustion processes and it contributes to the formation and modification of other air pollutants such as particulate matter.
data(COKMexico)data(COKMexico)
four data.frame of measurements 'Mex_PM10','NO2' and their coordinates 'coord_PM10' and 'coord_NO2'. Also a map (map_mex) file of class SpatialPolygonDataFrame
Mexico
Linear Spatial functional prediction. Two predictors are possible: scores or lambda.
COKS_scores_lambdas(SFD, newcoords, model, method = "scores", fill.all=TRUE)COKS_scores_lambdas(SFD, newcoords, model, method = "scores", fill.all=TRUE)
SFD |
object of class 'SpatFD'. |
newcoords |
The N × 2 matrix or data.frame with the spatial coordinates corresponding to the N prediction locations. |
model |
The linear model of coregionalization of all functional variable scores. A variogram model. A variogramModel object. See gstat package. |
method |
Prediction method: "scores" |
fill.all |
gstat function parameter. If there are more than 1 score vector and not all models or a valid and complete linear model of coregionalization is given, fill all of the direct and cross variogram model with the only model given. |
Each functional variable is represented in terms of its functional principal components
where
The goal is the prediction of a spatial functional variable of at the unsampled site based on P spatial functional variables. The method performs cokriging directly on the scores chosen for all functional variables involved.
Scores predictions are used to build the cokriging functional predictor.
Returns a 'COKS_pred' object with functional cokriging
Valeria Bejarano <[email protected]>
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
Bohorquez M.; Giraldo R. and Mateu J. Spatial prediction and optimal sampling of functional data in Geostatistical Functional Data Analysis: Theory and Methods (2021). John Wiley Sons, Chichester, UK. ISBN: 978-1-119-38784-8. https://www.wiley.com/en-us/Geostatistical+Functional+Data+Analysis-p-9781119387848.
data(COKMexico) SFD_PM10_NO2 <- SpatFD(Mex_PM10, coords = coord_PM10, basis = "Fourier", nbasis = 21, lambda = 0.000001, nharm = 2) SFD_PM10_NO2 <- SpatFD(NO2, coords = coord_NO2, basis = "Fourier", nbasis = 27, lambda = 0.000001, nharm = 2, add = SFD_PM10_NO2) model1 <- gstat::vgm(647677.1,"Gau",23317.05) model1 <- gstat::vgm(127633,"Wav",9408.63, add.to = model1) newcoords <- data.frame(x = 509926,y = 2179149) COKS_scores_lambdas(SFD_PM10_NO2,newcoords,model1)data(COKMexico) SFD_PM10_NO2 <- SpatFD(Mex_PM10, coords = coord_PM10, basis = "Fourier", nbasis = 21, lambda = 0.000001, nharm = 2) SFD_PM10_NO2 <- SpatFD(NO2, coords = coord_NO2, basis = "Fourier", nbasis = 27, lambda = 0.000001, nharm = 2, add = SFD_PM10_NO2) model1 <- gstat::vgm(647677.1,"Gau",23317.05) model1 <- gstat::vgm(127633,"Wav",9408.63, add.to = model1) newcoords <- data.frame(x = 509926,y = 2179149) COKS_scores_lambdas(SFD_PM10_NO2,newcoords,model1)
Coordinates of 10 stations in the city.
data(AirQualityBogota)data(AirQualityBogota)
data.frame of coordinates
Secretaria de Ambiente de Bogotá
Monitor network of air quality of Bogota http://rmcab.ambientebogota.gov.co
18 locations in Mexico where measured NO2.
data(COKMexico)data(COKMexico)
data.frame of coordinates 'coord_NO2'
Mexico
13 locations in Mexico where measured Mex_PM10.
data(COKMexico)data(COKMexico)
data.frame of coordinates 'coord_PM10'
Mexico
This function creates covariance matrices for spatial data based on the provided model parameters.
create_mcov(coordenadas, t.models)create_mcov(coordenadas, t.models)
coordenadas |
A matrix of coordinates. |
t.models |
A data frame with model parameters. |
A list of covariance matrices.
data(vowels) t.models = data.frame(sill = c(1887.47,1447.27,3533.96,1850.27,432.63), phi = c(106.68,109.1,19.4,150.32,31.52), tausq =c(0,0,0,0,0), model = as.character(c("gaussian","gneiting", "matern","cubic", "wave")), kappa = c(0,0,7.3,0,0) ) create_mcov(vowels_coords,t.models)data(vowels) t.models = data.frame(sill = c(1887.47,1447.27,3533.96,1850.27,432.63), phi = c(106.68,109.1,19.4,150.32,31.52), tausq =c(0,0,0,0,0), model = as.character(c("gaussian","gneiting", "matern","cubic", "wave")), kappa = c(0,0,7.3,0,0) ) create_mcov(vowels_coords,t.models)
Creates univariate and multivariate CrossSpatFD object considering the base od a SpatFD or FD object to perform crossed validation for functional spatial prediction.
CrossSpatFD(data,coords,basis,lambda=0,nharm=NULL,name=NULL,add=NULL,...)CrossSpatFD(data,coords,basis,lambda=0,nharm=NULL,name=NULL,add=NULL,...)
data |
Data must be provided in a data-frame or a matrix where each column corresponds to a location, and the rows are a sequence of data points, that is, the rows are ordered according to time, frequency, depth, …. Data can also be an fd-object from the fda package. |
coords |
A data-frame or a matrix with spatial coordinates (x,y). The number of columns in data must coincide with the number of rows in coords for each variable. |
basis |
The basis from the SpatFD or FD object. |
lambda |
The value of the smoothing parameter. |
nharm |
The number of harmonics or eigenfunctions to be reported in the Functional Principal Components results if vp is not given. |
name |
A new name for data can be assigned. |
add |
Other variables can be added for spatial multivariate functional prediction, that is, for functional cokriging. It is not necessary that all variables are observed at the same spatial locations. |
... |
arguments from fda create.bspline.basis or create.fourier.basis. |
The CrossSpatFD-objects storage the functional data, its parameters, the functional principal component analysis results, and the spatial coordinates for each variable. Each variable has its own functional data, data-frame or matrix and its spatial coordinates file.
For each variable: The functional data and functional principal components linked with spatial coordinates.
1. This function is for internal use and should not be implemented directly
Diego Sandoval [email protected] & Angie Villamil [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Optimal sampling for spatial prediction of functional data. Statistical Methods & Applications, 25(1), 39-54.
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
This function performs leave-one-out cross-validation for functional kriging and cokriging. It systematically leaves out one observation at a time from the dataset, fits the model to the remaining data, and then makes a prediction for the left-out observation. It is used to assess the predictive performance of the functional kriging model.
crossval_loo(object, plot_show)crossval_loo(object, plot_show)
object |
A 'KS_pred' object obtained with function |
plot_show |
A logical value. If |
An object containing the results of the leave-one-out cross-validation. Includes:
performance_metrics |
Summary statistics describing the overall predictive performance, such as mean squared error. |
plots |
The generation of plots showing the cross-validation results, controlled by the |
Joan Castro [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Optimal sampling for spatial prediction of functional data. Statistical Methods & Applications, 25(1), 39-54.
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
# Example code demonstrating how to use the crossval_loo function library(SpatFD) library(gstat) # Load data and coordinates data(AirQualityBogota) #s_0 nonsampled location. It could be data.frame or matrix and one or more locations of interest newcoorden=data.frame(X=seq(93000,105000,len=100),Y=seq(97000,112000,len=100)) #newcoorden=data.frame(X=110000,Y=126000) #newcoorden=matrix(c(110000.23,109000,109500,130000.81,129000,131000),nrow=3,ncol=2,byrow=TRUE) # Building the SpatFD object SFD_PM10 <- SpatFD(PM10, coords = coord[, -1], basis = "Bsplines", nbasis = 17,norder=5, lambda = 0.00002, nharm=3) # Semivariogram models for each spatial random field of scores modelos <- list(vgm(psill = 2199288.58, "Wav", range = 1484.57, nugget = 0), vgm(psill = 62640.74, "Mat", range = 1979.43, nugget = 0,kappa=0.68), vgm(psill =37098.25, "Exp", range = 6433.16, nugget = 0)) # Functional kriging. Functional spatial prediction at each location of interest #method = "lambda" #Computation of lambda_i KS_SFD_PM10_l <- KS_scores_lambdas(SFD_PM10, newcoorden ,method = "lambda", model = modelos) # method = "scores" #Simple kriging of scores KS_SFD_PM10_sc <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "scores", model = modelos) # method = "both" KS_SFD_PM10_both <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "both", model = modelos) # Cross Validation crossval_loo(KS_SFD_PM10_l) crossval_loo(KS_SFD_PM10_sc) crossval_loo(KS_SFD_PM10_both)# Example code demonstrating how to use the crossval_loo function library(SpatFD) library(gstat) # Load data and coordinates data(AirQualityBogota) #s_0 nonsampled location. It could be data.frame or matrix and one or more locations of interest newcoorden=data.frame(X=seq(93000,105000,len=100),Y=seq(97000,112000,len=100)) #newcoorden=data.frame(X=110000,Y=126000) #newcoorden=matrix(c(110000.23,109000,109500,130000.81,129000,131000),nrow=3,ncol=2,byrow=TRUE) # Building the SpatFD object SFD_PM10 <- SpatFD(PM10, coords = coord[, -1], basis = "Bsplines", nbasis = 17,norder=5, lambda = 0.00002, nharm=3) # Semivariogram models for each spatial random field of scores modelos <- list(vgm(psill = 2199288.58, "Wav", range = 1484.57, nugget = 0), vgm(psill = 62640.74, "Mat", range = 1979.43, nugget = 0,kappa=0.68), vgm(psill =37098.25, "Exp", range = 6433.16, nugget = 0)) # Functional kriging. Functional spatial prediction at each location of interest #method = "lambda" #Computation of lambda_i KS_SFD_PM10_l <- KS_scores_lambdas(SFD_PM10, newcoorden ,method = "lambda", model = modelos) # method = "scores" #Simple kriging of scores KS_SFD_PM10_sc <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "scores", model = modelos) # method = "both" KS_SFD_PM10_both <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "both", model = modelos) # Cross Validation crossval_loo(KS_SFD_PM10_l) crossval_loo(KS_SFD_PM10_sc) crossval_loo(KS_SFD_PM10_both)
Given a variogram model and a set of points in which we want to predict certain variable optimally, this function finds where must be placed the stations in which the information will be collected for functional or scalar data.
FD_optimal_design(k, s0, model, fixed_stations = NULL, scalar = FALSE, nharm = NULL, method = "lambda", grid = NULL, map = NULL, plt = FALSE)FD_optimal_design(k, s0, model, fixed_stations = NULL, scalar = FALSE, nharm = NULL, method = "lambda", grid = NULL, map = NULL, plt = FALSE)
k |
The number of new stations that are going to be located. |
s0 |
|
model |
A |
fixed_stations |
If there are already some stations on the field that are not going to be removed, here should be passed their coordinates. The object must be of class |
scalar |
Boolean that indicates if the optimization is for functional data (FALSE) or scalar data (TRUE). If TRUE, nharm is set to 1. |
nharm |
Number of harmonics of the functional principal components that will be used in the prediction. If it is not specified it will be set to the number of models passed, then this parameter shouldn't be specified for scalar data. |
method |
Functional kriging method that will be used. Currently available "lambda" and "scores". See details bellow. |
grid |
Coordinates in which the new stations can be located. |
map |
Spatial object from sp package such as |
plt |
|
Bohorquez, M., Giraldo, R., Mateu, J. (2016) present several methods for finding the best combination predictor-design according to the kriging prediction error variance for functional data. They show different functional kriging methods and two of them are implemented on this function.
If method is "lambda", optimal spatial sampling using FPCA and simple kriging will be used (see section 3.2 of Bohorquez, M., Giraldo, R., Mateu, J. (2016)). If method is "scores", simple kriging will be applied on each harmonic and the total variance will be minimized. This total variance is computed as follows:
where is the variance of the simple kriging prediction of j-th score.
The function returns an OptimalSpatialDesign object that is a list with the following elements:
new_stations |
|
fixed_stations |
|
plot |
|
When method is 'lambda', the minimized value is not the variance, but the negative of expression (12) in Bohorquez, M., Giraldo, R., & Mateu, J. (2016), that is
'lambda' method tends to be faster than 'scores' method.
Nathaly Vergel Serrano [email protected] & Samuel Sánchez Gutiérrez [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Optimal sampling for spatial prediction of functional data. Statistical Methods & Applications, 25(1), 39-54.
library(gstat) s0 <- cbind(2*runif(100),runif(100)) # random coordinates on (0,2)x(0,1) fixed_stations <- cbind(2*runif(4),runif(4)) x_grid <- seq(0,2,length = 30) y_grid <- seq(0,1,length = 30) grid <- cbind(rep(x_grid,each = 30),rep(y_grid,30)) model <- vgm(psill = 5.665312, model = "Exc", range = 8000, kappa = 1.62, add.to = vgm(psill = 0.893, model = "Nug", range = 0, kappa = 0)) FD_optimal_design(k = 10, s0 = s0, model = model, grid = grid, nharm = 2, plt = TRUE, fixed_stations = fixed_stations) -> OSD OSD$new_stations OSD$fixed_stations OSD$plot class(OSD)library(gstat) s0 <- cbind(2*runif(100),runif(100)) # random coordinates on (0,2)x(0,1) fixed_stations <- cbind(2*runif(4),runif(4)) x_grid <- seq(0,2,length = 30) y_grid <- seq(0,1,length = 30) grid <- cbind(rep(x_grid,each = 30),rep(y_grid,30)) model <- vgm(psill = 5.665312, model = "Exc", range = 8000, kappa = 1.62, add.to = vgm(psill = 0.893, model = "Nug", range = 0, kappa = 0)) FD_optimal_design(k = 10, s0 = s0, model = model, grid = grid, nharm = 2, plt = TRUE, fixed_stations = fixed_stations) -> OSD OSD$new_stations OSD$fixed_stations OSD$plot class(OSD)
This function returns the first nth elements of a functional basis as an fd object.
generate_basis(basis = "Fourier",n_functions = 10,L = NULL,fda_basis = NULL)generate_basis(basis = "Fourier",n_functions = 10,L = NULL,fda_basis = NULL)
basis |
Name of the functional basis. Currently only |
n_functions |
Positive integer giving the number of functions that are going to be generated. |
L |
For |
fda_basis |
|
Fourier basis functions are given by:
for , and
for .
Furthermore, Legendre basis functions are given by:
for .
fda::fd object with n_functions curves.
Generating Legendre basis functions requires to evaluate derivates, so its recomended to use values below 10.
Samuel Sánchez Gutiérrez [email protected].
Conway, J. B. (2019). A course in functional analysis (Vol. 96). Springer.
library(fda) # 10 Fourier functions res <- generate_basis(L=1) plot(res) # 20 Fourier functions res <- generate_basis(n_functions = 20,L = 3) plot(res) # 10 Legendre functions res <- generate_basis(basis = "Legendre") plot(res) # 7 Legendre functions res <- generate_basis(basis = "Legendre", n_functions = 7) plot(res)library(fda) # 10 Fourier functions res <- generate_basis(L=1) plot(res) # 20 Fourier functions res <- generate_basis(n_functions = 20,L = 3) plot(res) # 10 Legendre functions res <- generate_basis(basis = "Legendre") plot(res) # 7 Legendre functions res <- generate_basis(basis = "Legendre", n_functions = 7) plot(res)
This function divides the data in train and test datasets
gfd_clasif_data(gfd_data, prop.train, seed = NULL)gfd_clasif_data(gfd_data, prop.train, seed = NULL)
gfd_data |
Object of class 'gfdata'. Not NULL. |
prop.train |
Number between 0 and 1, indicating the proportion to be left on train dataset |
seed |
seed for the sampling algorithms |
gfdata divided object
Diego Sandoval [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
library(SpatFD) data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis) s4.sep=gfd_clasif_data(s4.gfdata, 0.8,seed = 2910) s4.train=s4.sep$train s4.test=s4.sep$testlibrary(SpatFD) data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis) s4.sep=gfd_clasif_data(s4.gfdata, 0.8,seed = 2910) s4.train=s4.sep$train s4.test=s4.sep$test
This function generates variograms for functional data based on PCA results.
gfd_variog_geoR(gfd_pca_Data, pairsmin = 2)gfd_variog_geoR(gfd_pca_Data, pairsmin = 2)
gfd_pca_Data |
A list of PCA results for functional data. |
pairsmin |
Minimum number of pairs for variogram calculation. |
A list containing geodata objects and variograms.
data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis) s4.sep=gfd_clasif_data(s4.gfdata, 0.8,seed = 2910) s4.train=s4.sep$train s4.var.geoR=gfd_variog_geoR(s4.train)data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis) s4.sep=gfd_clasif_data(s4.gfdata, 0.8,seed = 2910) s4.train=s4.sep$train s4.var.geoR=gfd_variog_geoR(s4.train)
Creates an object of the class gfdata from spatial coordinates, and functions or time-series observed at each spatial location. Time series is a generic term. In fact, observations might be across the frequency or across another spatial dimension such as depth, instead of time.
gfdata(data, p, basis = "Bsplines", coords = NULL, nbasis = NULL, names = NULL, lambda = 0)gfdata(data, p, basis = "Bsplines", coords = NULL, nbasis = NULL, names = NULL, lambda = 0)
data |
Data must be provided in a matrix where each column corresponds to a subject, and the rows are a sequence of data points, that is, the rows are ordered according to time, frequency, depth, …. Also must include a column with classes for classification in the last column |
p |
Number of repetitions for each class |
basis |
Basis functions. "Fourier" or "Bsplines". By default, "Bsplines". |
coords |
A matrix with spatial coordinates (x,y). |
nbasis |
The number of basis functions. |
names |
Names for the data classes. |
lambda |
The value of the smoothing parameter. |
The gfdata-objects storage the functional data, its parameters, the functional principal component analysis results, and the spatial coordinates for each variable. Each variable has its own functional data, data-frame or matrix and its spatial coordinates file.
For each subject and class: The functional data and functional principal components linked with spatial coordinates.
Venus Puertas [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Optimal sampling for spatial prediction of functional data. Statistical Methods & Applications, 25(1), 39-54.
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
library(SpatFD) data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis)library(SpatFD) data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis)
A visualization of the predicted kriging in a colormap for a specific window time.
ggmap_KS(KS, map_path, window_time = NULL, method = "lambda", map_n = 5000, zmin = NULL, zmax = NULL, graph = "plotly")ggmap_KS(KS, map_path, window_time = NULL, method = "lambda", map_n = 5000, zmin = NULL, zmax = NULL, graph = "plotly")
KS |
Object of class 'KS_pred'. Not NULL. |
map_path |
Character indicating the directory of the shape file or an object of class SpatialPolygonDataFrame load from a shape file by |
window_time |
numeric. Vector of window time to see the spatial prediction. If NULL choose the range values of KS$SFD. Default NULL. |
method |
character. "lambda" or "scores". Default "lambda". |
map_n |
numeric. Number of points to sample in the map. Default 5000. |
zmin |
numeric. Minimum value predicted for the color scale. If NULL is chosen from the data. Default NULL. |
zmax |
numeric. Maximum value predicted for the color scale. If NULL is chosen from the data. Default NULL. |
graph |
character. "plotly" or "gg" whether to use plotly or ggplot graphics. Default "plotly". |
Plotly or ggplot image
Diego Sandoval [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
library(gstat) data(AirQualityBogota) newcoorden=data.frame(X=seq(93000,105000,len=100),Y=seq(97000,112000,len=100)) SFD_PM10 <- SpatFD(PM10, coords = coord[, -1], basis = "Bsplines", nbasis = 17, norder=5, lambda = 0.00002, nharm=3) modelos <- list(vgm(psill = 2634000, "Exp", range = 2103.25, nugget = 0), vgm(psill = 101494.96, "Exp", range = 1484.57, nugget = 0), vgm(psill =53673, "Exp", range = 42406, nugget = 0)) KS_SFD_PM10_both <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "both", model = modelos) ggmap_KS(KS_SFD_PM10_both, map_path = map, window_time = c(5108,5109,5110), method = "scores", zmin = 50, zmax = 120)library(gstat) data(AirQualityBogota) newcoorden=data.frame(X=seq(93000,105000,len=100),Y=seq(97000,112000,len=100)) SFD_PM10 <- SpatFD(PM10, coords = coord[, -1], basis = "Bsplines", nbasis = 17, norder=5, lambda = 0.00002, nharm=3) modelos <- list(vgm(psill = 2634000, "Exp", range = 2103.25, nugget = 0), vgm(psill = 101494.96, "Exp", range = 1484.57, nugget = 0), vgm(psill =53673, "Exp", range = 42406, nugget = 0)) KS_SFD_PM10_both <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "both", model = modelos) ggmap_KS(KS_SFD_PM10_both, map_path = map, window_time = c(5108,5109,5110), method = "scores", zmin = 50, zmax = 120)
Plot with or without predicted variance in each spatial location of the functional kriging.
ggplot_KS(KS, show.varpred = FALSE, main = "Functional Data", main2 = "Functional Data", ylab = "Value", xlab = "Time", ndigits = 2, palette.plot = c("#440154FF", "#3336FF", "#33FCFF", "#33FF4C", "#FDE725FF"))ggplot_KS(KS, show.varpred = FALSE, main = "Functional Data", main2 = "Functional Data", ylab = "Value", xlab = "Time", ndigits = 2, palette.plot = c("#440154FF", "#3336FF", "#33FCFF", "#33FF4C", "#FDE725FF"))
KS |
Object of class 'KS_pred'. Not NULL. |
show.varpred |
Boolean. If the predicted variance is shown. Default FALSE. |
main |
character. Title of the plot.Default "Functional Data". |
main2 |
character. If there are two methods where used, the title of the second plot. Default "Functional Data". |
ylab |
character. Name of the y-axis. |
xlab |
character. Name of the x-axis. |
ndigits |
numeric. Number of decimals for the predicted variance if shown. Default 2. |
palette.plot |
list. String values of hexadecimal colors. Default c("#440154FF", "#3336FF", "#33FCFF", "#33FF4C", "#FDE725FF") |
ggplot. If there are two plots a list of ggplots.
Diego Sandoval [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
library(gstat) data(AirQualityBogota) newcoorden=data.frame(X=seq(93000,105000,len=10),Y=seq(97000,112000,len=10)) SFD_PM10 <- SpatFD(PM10, coords = coord[, -1], basis = "Bsplines", nbasis = 17, norder=5, lambda = 0.00002, nharm=3) modelos <- list(vgm(psill = 2634000, "Exp", range = 2103.25, nugget = 0), vgm(psill = 101494.96, "Exp", range = 1484.57, nugget = 0), vgm(psill =53673, "Exp", range = 42406, nugget = 0)) KS_SFD_PM10_both <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "both", model = modelos) ggplot_KS(KS_SFD_PM10_both,show.varpred = FALSE, main = "Plot 1 - Using Scores", main2 = "Plot 2 - Using Lambda", ylab = "PM10")library(gstat) data(AirQualityBogota) newcoorden=data.frame(X=seq(93000,105000,len=10),Y=seq(97000,112000,len=10)) SFD_PM10 <- SpatFD(PM10, coords = coord[, -1], basis = "Bsplines", nbasis = 17, norder=5, lambda = 0.00002, nharm=3) modelos <- list(vgm(psill = 2634000, "Exp", range = 2103.25, nugget = 0), vgm(psill = 101494.96, "Exp", range = 1484.57, nugget = 0), vgm(psill =53673, "Exp", range = 42406, nugget = 0)) KS_SFD_PM10_both <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "both", model = modelos) ggplot_KS(KS_SFD_PM10_both,show.varpred = FALSE, main = "Plot 1 - Using Scores", main2 = "Plot 2 - Using Lambda", ylab = "PM10")
Linear Spatial functional prediction. Two predictors are possible: scores or lambda.
KS_scores_lambdas(SFD, newcoords, model, method = "lambda", name = NULL, fill.all = NULL)KS_scores_lambdas(SFD, newcoords, model, method = "lambda", name = NULL, fill.all = NULL)
SFD |
object of class 'SpatFD'. |
newcoords |
The N × 2 matrix or data.frame with the spatial coordinates corresponding to the N prediction locations. |
model |
The scores variogram model. A variogramModel object. See gstat package. |
method |
Prediction method: "lambda" or "scores". By default "lambda". See details. |
name |
The variable to predict in SpatFD object. By default, the predictions is performed for the first variable in the SpatFD object. |
fill.all |
gstat function parameter. If there are more than 1 score vector and not all models or a valid and complete linear model of coregionalization is given, fill all of the direct and cross variogram model with the only model given. |
"lambda" option corresponds to the predictor , given by
and weigths are found such that minimize
.
"scores" method performs kriging or cokriging directly on the scores and predictions are used to build the functional prediction
It is used simple cokriging to predict the vector at the unsampled location . The predictor is , so the prediction of the curve is .
Returns a 'KS_pred' object with functional kriging: weights (lambda) using the first method and kriging score predictions using the second method in Bohorquez, M., Giraldo, R., & Mateu, J. (2016).
Diego Sandoval [email protected] & Angie Villamil [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Optimal sampling for spatial prediction of functional data. Statistical Methods & Applications, 25(1), 39-54.
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
Bohorquez M.; Giraldo R. and Mateu J. Spatial prediction and optimal sampling of functional data in Geostatistical Functional Data Analysis: Theory and Methods (2021). John Wiley Sons, Chichester, UK. ISBN: 978-1-119-38784-8. https://www.wiley.com/en-us/Geostatistical+Functional+Data+Analysis-p-9781119387848.
library(gstat) data(AirQualityBogota) newcoorden=data.frame(X=110000,Y=125000) # Recibir los datos, suavizarlos y ACP SFD_PM10 <- SpatFD(PM10, coords = coord[,2:3], basis = "Bsplines", nbasis = 17,norder=5, lambda = 0.00002, nharm=3) #Variogram model for each component modelos <- list(vgm(psill = 2634000, "Exp", range = 2103.25, nugget = 0), vgm(psill = 101494.96, "Exp", range = 1484.57, nugget = 0), vgm(psill =53673, "Exp", range = 42406, nugget = 0)) #Genera los scores y los lambdas para predecir en nuevas coordenadas #method = "lambda" KS_SFD_PM10_l <- KS_scores_lambdas(SFD_PM10, newcoorden ,method = "lambda", model = modelos) class(KS_SFD_PM10_l) #method = "scores" KS_SFD_PM10_sc <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "scores", model = modelos) #method = "both" KS_SFD_PM10_both <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "both", model = modelos)library(gstat) data(AirQualityBogota) newcoorden=data.frame(X=110000,Y=125000) # Recibir los datos, suavizarlos y ACP SFD_PM10 <- SpatFD(PM10, coords = coord[,2:3], basis = "Bsplines", nbasis = 17,norder=5, lambda = 0.00002, nharm=3) #Variogram model for each component modelos <- list(vgm(psill = 2634000, "Exp", range = 2103.25, nugget = 0), vgm(psill = 101494.96, "Exp", range = 1484.57, nugget = 0), vgm(psill =53673, "Exp", range = 42406, nugget = 0)) #Genera los scores y los lambdas para predecir en nuevas coordenadas #method = "lambda" KS_SFD_PM10_l <- KS_scores_lambdas(SFD_PM10, newcoorden ,method = "lambda", model = modelos) class(KS_SFD_PM10_l) #method = "scores" KS_SFD_PM10_sc <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "scores", model = modelos) #method = "both" KS_SFD_PM10_both <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "both", model = modelos)
Map of Bogota.
data(AirQualityBogota)data(AirQualityBogota)
Map file of class SpatialPolygonDataFrame
Unidad Administrativa Especial de Catastro Distrital
https://datosabiertos.bogota.gov.co/dataset/sector-catastral
Map of Mexico.
data(COKMexico)data(COKMexico)
Map file of class SpatialPolygonDataFrame
Automatic Monitoring System SEDEMA
http://www.aire.df.gob.mx/default.php
This function generates multivariate vowel data based on the provided mean functions and basis functions.
mclass_data(mean.mean, n.basis, type.basis = "bspline")mclass_data(mean.mean, n.basis, type.basis = "bspline")
mean.mean |
A list of means for each class. |
n.basis |
A list of basis functions for each class. |
type.basis |
Type of basis functions to use (e.g., "bspline", "fourier"). |
A data frame containing the generated vowel data.
data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis) s4.sep=gfd_clasif_data(s4.gfdata, 0.8,seed = 2910) s4.train=s4.sep$train s4.test=s4.sep$test mean_mean <- mean_mean(s4.train) class_mean <- mclass_data(mean_mean,n.basis)data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis) s4.sep=gfd_clasif_data(s4.gfdata, 0.8,seed = 2910) s4.train=s4.sep$train s4.test=s4.sep$test mean_mean <- mean_mean(s4.train) class_mean <- mclass_data(mean_mean,n.basis)
This function calculates the mean functions for each class based on PCA results from training data.
mean_mean(data.train.pca)mean_mean(data.train.pca)
data.train.pca |
A list of PCA results from training data. |
A list of mean functions for each class.
data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis) s4.sep=gfd_clasif_data(s4.gfdata, 0.8,seed = 2910) s4.train=s4.sep$train mean_mean <- mean_mean(s4.train)data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis) s4.sep=gfd_clasif_data(s4.gfdata, 0.8,seed = 2910) s4.train=s4.sep$train mean_mean <- mean_mean(s4.train)
Particular material 10 (PM10) measured in 13 locations in Mexico.
data(COKMexico)data(COKMexico)
data.frame of measurements 'Mex_PM10'
Mexico
NO2 measured in 18 locations in Mexico.
data(COKMexico)data(COKMexico)
data.frame of measurement 'NO2'
Mexico
Particular material 10 (PM10) of Bogota measure in 10 stations in the city.
data(AirQualityBogota)data(AirQualityBogota)
data.frame of measurements 'PM10'
Secretaria de Ambiente de Bogotá
Monitor network of air quality of Bogota http://rmcab.ambientebogota.gov.co
This functions prints a summary of the main objects of OptimalSpatialDesign objects.
## S3 method for class 'OptimalSpatialDesign' print(x, ...)## S3 method for class 'OptimalSpatialDesign' print(x, ...)
x |
Object of class 'OptimalSpatialDesign'. |
... |
arguments from print |
Shows the amount of fixed stations, new stations and the first six new coordinates.
Samuel Sánchez Gutiérrez [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Optimal sampling for spatial prediction of functional data. Statistical Methods & Applications, 25(1), 39-54.
library(gstat) data(AirQualityBogota) vgm_model <- gstat::vgm(psill = 5.665312, model = "Exc", range = 8000, kappa = 1.62, add.to = vgm(psill = 0.893, model = "Nug", range = 0, kappa = 0)) my.CRS <- sp::CRS("EPSG:21899") # https://epsg.io/21899 map <- as(map, "Spatial") bogota_shp <- sp::spTransform(map,my.CRS) target <- sp::spsample(bogota_shp,n = 100, type = "random") # The set of points in which we want to predict optimally. old_stations <- sp::spsample(bogota_shp,n = 3, type = "random") # The set of stations that are already fixed. FD_optimal_design(k = 10, s0 = target,model = vgm_model, map = map,plt = TRUE,#method = "scores", fixed_stations = old_stations) -> res print(res)library(gstat) data(AirQualityBogota) vgm_model <- gstat::vgm(psill = 5.665312, model = "Exc", range = 8000, kappa = 1.62, add.to = vgm(psill = 0.893, model = "Nug", range = 0, kappa = 0)) my.CRS <- sp::CRS("EPSG:21899") # https://epsg.io/21899 map <- as(map, "Spatial") bogota_shp <- sp::spTransform(map,my.CRS) target <- sp::spsample(bogota_shp,n = 100, type = "random") # The set of points in which we want to predict optimally. old_stations <- sp::spsample(bogota_shp,n = 3, type = "random") # The set of stations that are already fixed. FD_optimal_design(k = 10, s0 = target,model = vgm_model, map = map,plt = TRUE,#method = "scores", fixed_stations = old_stations) -> res print(res)
This is an internal function for functional kriging and cokriging. To perform the linear combinations to obtain functional kriging and cokriging. Once optimization process is finished and scores or lambda are obtained, this function builds the prediction, performing the linear combination between coefficients and basis functions.
recons_fd(X,name = NULL)recons_fd(X,name = NULL)
X |
A 'KS_pred' or 'COKS_pred' object obtained with function |
name |
Name of the variable of interest. Default 1, the first variable. |
Spatial functional predictions. The fd object based on the two functional kriging methods described in Bohorquez, M., Giraldo, R., & Mateu, J. (2016). List of
fd_scores |
|
fd_lambda |
Diego Sandoval [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Optimal sampling for spatial prediction of functional data. Statistical Methods & Applications, 25(1), 39-54.
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
Bohorquez M.; Giraldo R. and Mateu J. Spatial prediction and optimal sampling of functional data in Geostatistical Functional Data Analysis: Theory and Methods (2021). John Wiley Sons, Chichester, UK. ISBN: 978-1-119-38784-8. https://www.wiley.com/en-us/Geostatistical+Functional+Data+Analysis-p-9781119387848. ~
library(gstat) data(AirQualityBogota) newcoorden=data.frame(X=110000,Y=125000) SFD_PM10 <- SpatFD(PM10, coords = coord[,2:3], basis = "Bsplines", nbasis = 17, norder=5, lambda = 0.00002, nharm=3) modelos <- list(vgm(psill = 2634000, "Exp", range = 2103.25, nugget = 0), vgm(psill = 101494.96, "Exp", range = 1484.57, nugget = 0), vgm(psill =53673, "Exp", range = 42406, nugget = 0)) #method = "lambda" KS_SFD_PM10_l <- KS_scores_lambdas(SFD_PM10, newcoorden ,method = "lambda", model = modelos) curves_PM10_l <- recons_fd(KS_SFD_PM10_l) plot(curves_PM10_l) #method = "scores" KS_SFD_PM10_sc <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "scores", model = modelos) curves_PM10_sc <- recons_fd(KS_SFD_PM10_sc) plot(curves_PM10_sc)library(gstat) data(AirQualityBogota) newcoorden=data.frame(X=110000,Y=125000) SFD_PM10 <- SpatFD(PM10, coords = coord[,2:3], basis = "Bsplines", nbasis = 17, norder=5, lambda = 0.00002, nharm=3) modelos <- list(vgm(psill = 2634000, "Exp", range = 2103.25, nugget = 0), vgm(psill = 101494.96, "Exp", range = 1484.57, nugget = 0), vgm(psill =53673, "Exp", range = 42406, nugget = 0)) #method = "lambda" KS_SFD_PM10_l <- KS_scores_lambdas(SFD_PM10, newcoorden ,method = "lambda", model = modelos) curves_PM10_l <- recons_fd(KS_SFD_PM10_l) plot(curves_PM10_l) #method = "scores" KS_SFD_PM10_sc <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "scores", model = modelos) curves_PM10_sc <- recons_fd(KS_SFD_PM10_sc) plot(curves_PM10_sc)
Creates a list of P data-frames, one for each of the P spatial functional variables in the SpatFD-object. Each data-frame contains one column for each harmonic selected with its respective n_p-score values, and two additional columns for horizontal and vertical spatial coordinates.
scores(X)scores(X)
X |
An object of class SpatFD. |
For a SpatFD object with P spatial functional variables measured on n_p locations each, and nharm=k_p, p=1,..., P. The scores-function builds a data-frame with n_p rows and k_p+2 columns. The first two columns are the horizontal and vertical spatial coordinates x,y. The rest of the columns are the score values for each of the first k_p harmonics selected for the p variable, at each of the n_p locations.
A list with P data-frames, with dimension , each. p=1,…,P.
Functional principal components (FPCA) are applied to the centered data. The scores are scalar second order stationary Random fields, in virtue of the requirements for FPCA. Hence, the covariance function exists, that is, models are bounded, and always have sill and range parameters. Of course, some models have additional parameters, such as smoothing parameters. From the theoretical perspective, in this case, there is no possibility of non-bounded variogram models. The spatial covariance between two curves is determined by the sum of the covariance between spatial score vectors associated, see Bohorquez, Giraldo and Mateu 2016 and Bohorquez, Giraldo and Mateu 2021. This covariance can be modeled using the usual packages for geostatistical analysis, such as geoR and gstat. Finally, the sill of the variogram model for each dimension is bounded for the respective eigenvalue. Actually, an adequate option is to use this eigenvalue as sill and estimate the rest of the parameters.
Diego Sandoval [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Optimal sampling for spatial prediction of functional data. Statistical Methods & Applications, 25(1), 39-54.
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
data(AirQualityBogota) newcoorden=data.frame(X=seq(93000,105000,len=100),Y=seq(97000,112000,len=100)) # Building the SpatFD object SFD_PM10 <- SpatFD(PM10, coords = coord[, -1], basis = "Bsplines", nbasis = 17, norder=5, lambda = 0.00002, nharm=3) scores(SFD_PM10)data(AirQualityBogota) newcoorden=data.frame(X=seq(93000,105000,len=100),Y=seq(97000,112000,len=100)) # Building the SpatFD object SFD_PM10 <- SpatFD(PM10, coords = coord[, -1], basis = "Bsplines", nbasis = 17, norder=5, lambda = 0.00002, nharm=3) scores(SFD_PM10)
Given a variogram model, this functions simulates several realizations of a functional spatial process. This simulation can be conditioned to observed data.
sim_functional_process(nsims,variograms,nbasis,coords,data = NULL, data_coords = NULL,basis = NULL,mu = NULL,L = NULL)sim_functional_process(nsims,variograms,nbasis,coords,data = NULL, data_coords = NULL,basis = NULL,mu = NULL,L = NULL)
nsims |
Integer giving the number of curves to simulate. |
variograms |
|
nbasis |
Integer giving the number of basis functions on which the process is going to be projected. |
coords |
Gridded |
data |
|
data_coords |
|
basis |
Character giving the basis of functions (only for inconditional simulation) (nbasis must be provided). |
mu |
|
L |
Limits of the symetric interval centered on zero that is the domain of the basis that is going to be created in unconditional simulation case. |
When data is passed, conditional simulation is performed. That means that each simulated realization of the process interpolated the observed curves in data. If data is NULL, the realizations of the process are simulated without imterpolation restrictions.
A list of nsims SpatFD objects each one with as much curves as points are in coords.
Samuel Sánchez Gutiérrez [email protected].
Bohorquez, M., Giraldo, R. & Mateu, J. Multivariate functional random fields: prediction and optimal sampling. Stoch Environ Res Risk Assess 31, 53–70 (2017). https://doi.org/10.1007/s00477-016-1266-y
library(gstat) library(fda) library(sp) data("CanadianWeather") canada.CRS <- CRS("+init=epsg:4608") coords <- SpatialPoints(CanadianWeather$coordinates, proj4string = CRS("+init=epsg:4326")) coords <- spTransform(coords,canada.CRS) obs <- CanadianWeather$dailyAv[,,1] # Temperature Lfd_obj <- int2Lfd(m = 2) create.bspline.basis(rangeval = c(1,365), nbasis = 40, norder = 4) -> mi.base mi.fdPar <- fdPar(mi.base, Lfd_obj, lambda = 7.389) mi.fd <- smooth.basis(argvals = 1:365, y = obs, fdParobj = mi.fdPar) nbasis <- 5 canada <- mi.fd$fd canada.pca <- pca.fd(canada,nharm = 10) base_ort <- canada.pca$harmonics[1:nbasis] canada_mean <- canada.pca$meanfd formula2fd <- function(rango, expresion) { # Generate grid n <- 500 # length of the grid x <- seq(rango[1], rango[2], length.out = n) # evaluate expression on the grid y_vals <- eval(parse(text = expresion)) # convert to fd basis <- create.bspline.basis(rangeval = rango, nbasis = 30) fd_obj <- Data2fd(x, y_vals,basisobj = basis) return(fd_obj) } media <- formula2fd(c(-1,1),"3*sin(x*4)") # No conditional vario <- vgm(.25, "Exp", .5, .05) nbasis <- 6 sims <- sim_functional_process(10,vario,nbasis,coords,basis = 'Legendre',mu = media) class(sims) length(sims) class(sims[[1]]) # plot(sims[[3]][[1]]$data_fd) sims <- sim_functional_process(10,vario,nbasis,coords,basis = 'Legendre') class(sims) length(sims) class(sims[[1]]) # plot(sims[[3]][[1]]$data_fd) # Conditional vario <- vgm(100, "Exp", 900, 10) new_coords <- spsample(coords,100,type = "regular") gridded(new_coords) <- TRUE length(new_coords) a <- sim_functional_process(10,vario,nbasis,new_coords,canada,coords) class(a) length(a) class(a[[1]]) #plot(a[[1]][[1]]$data_fd) vario <- vgm(100, "Wav", 900, 10) a <- sim_functional_process(10,vario,nbasis,new_coords,canada,coords) class(a) length(a) class(a[[1]]) #plot(a[[1]][[1]]$data_fd)library(gstat) library(fda) library(sp) data("CanadianWeather") canada.CRS <- CRS("+init=epsg:4608") coords <- SpatialPoints(CanadianWeather$coordinates, proj4string = CRS("+init=epsg:4326")) coords <- spTransform(coords,canada.CRS) obs <- CanadianWeather$dailyAv[,,1] # Temperature Lfd_obj <- int2Lfd(m = 2) create.bspline.basis(rangeval = c(1,365), nbasis = 40, norder = 4) -> mi.base mi.fdPar <- fdPar(mi.base, Lfd_obj, lambda = 7.389) mi.fd <- smooth.basis(argvals = 1:365, y = obs, fdParobj = mi.fdPar) nbasis <- 5 canada <- mi.fd$fd canada.pca <- pca.fd(canada,nharm = 10) base_ort <- canada.pca$harmonics[1:nbasis] canada_mean <- canada.pca$meanfd formula2fd <- function(rango, expresion) { # Generate grid n <- 500 # length of the grid x <- seq(rango[1], rango[2], length.out = n) # evaluate expression on the grid y_vals <- eval(parse(text = expresion)) # convert to fd basis <- create.bspline.basis(rangeval = rango, nbasis = 30) fd_obj <- Data2fd(x, y_vals,basisobj = basis) return(fd_obj) } media <- formula2fd(c(-1,1),"3*sin(x*4)") # No conditional vario <- vgm(.25, "Exp", .5, .05) nbasis <- 6 sims <- sim_functional_process(10,vario,nbasis,coords,basis = 'Legendre',mu = media) class(sims) length(sims) class(sims[[1]]) # plot(sims[[3]][[1]]$data_fd) sims <- sim_functional_process(10,vario,nbasis,coords,basis = 'Legendre') class(sims) length(sims) class(sims[[1]]) # plot(sims[[3]][[1]]$data_fd) # Conditional vario <- vgm(100, "Exp", 900, 10) new_coords <- spsample(coords,100,type = "regular") gridded(new_coords) <- TRUE length(new_coords) a <- sim_functional_process(10,vario,nbasis,new_coords,canada,coords) class(a) length(a) class(a[[1]]) #plot(a[[1]][[1]]$data_fd) vario <- vgm(100, "Wav", 900, 10) a <- sim_functional_process(10,vario,nbasis,new_coords,canada,coords) class(a) length(a) class(a[[1]]) #plot(a[[1]][[1]]$data_fd)
Creates an object of the class SpatFD from spatial coordinates, and functions or time-series observed at each spatial location. Time series is a generic term. In fact, observations might be across the frequency or across another spatial dimension such as depth, instead of time.
SpatFD(data, coords, basis = "Bsplines", nbasis = 4, lambda = 0, nharm = NULL, name = NULL, add = NULL, ...)SpatFD(data, coords, basis = "Bsplines", nbasis = 4, lambda = 0, nharm = NULL, name = NULL, add = NULL, ...)
data |
Data must be provided in a data-frame or a matrix where each column corresponds to a location, and the rows are a sequence of data points, that is, the rows are ordered according to time, frequency, depth, …. Data can also be an fd-object from the fda package. |
coords |
A data-frame or a matrix with spatial coordinates (x,y). The number of columns in data must coincide with the number of rows in coords for each variable. |
basis |
Basis functions. "Fourier" or "Bsplines". By default, "Bsplines". |
nbasis |
The number of basis functions. |
lambda |
The value of the smoothing parameter. |
nharm |
The number of harmonics or eigenfunctions to be reported in the Functional Principal Components results if vp is not given. |
name |
A new name for data can be assigned. |
add |
Other variables can be added for spatial multivariate functional prediction, that is, for functional cokriging. It is not necessary that all variables are observed at the same spatial locations. |
... |
arguments from fda create.bspline.basis or create.fourier.basis. |
The SpatFD-objects storage the functional data, its parameters, the functional principal component analysis results, and the spatial coordinates for each variable. Each variable has its own functional data, data-frame or matrix and its spatial coordinates file.
For each variable: The functional data and functional principal components linked with spatial coordinates.
1. Although there is no limit for the number of variables for functional cokriging, the real limitation is found on the constraints required to find a valid multivariate covariance model. So, it is highly recommended to apply the parsimony principle.
2. Locations must be in the same region of interest to make sense to include all of them in the same prediction model. However, each variable can be observed in different spatial locations and each can have a different number of observations. There is no limit for the number of variables to be included in this object.
Diego Sandoval [email protected] & Angie Villamil [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Optimal sampling for spatial prediction of functional data. Statistical Methods & Applications, 25(1), 39-54.
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
# Load data data(AirQualityBogota) # Create an univariate object using 2 nharm SFD_PM10 <- SpatFD(PM10, coords = coord[,2:3], basis = "Bsplines", nbasis = 91, lambda = 0.00002, nharm = 2) SFD_PM10# Load data data(AirQualityBogota) # Create an univariate object using 2 nharm SFD_PM10 <- SpatFD(PM10, coords = coord[,2:3], basis = "Bsplines", nbasis = 91, lambda = 0.00002, nharm = 2) SFD_PM10
This functions shows a summary of the main objects of COKS_pred objects.
## S3 method for class 'COKS_pred' summary(object, ...)## S3 method for class 'COKS_pred' summary(object, ...)
object |
Object of class 'COKS_pred'. |
... |
arguments from summary |
This functions prints according to method computed: eigenvalues, variance of prediction and each of the models.
Joan Nicolás Castro [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
data(COKMexico) SFD_PM10_NO2 <- SpatFD(Mex_PM10, coords = coord_PM10, basis = "Fourier", nbasis = 21, lambda = 0.000001, nharm = 2) SFD_PM10_NO2 <- SpatFD(NO2, coords = coord_NO2, basis = "Fourier", nbasis = 27, lambda = 0.000001, nharm = 2,add = SFD_PM10_NO2) model1 <- gstat::vgm(647677.1,"Gau",23317.05) model1 <- gstat::vgm(127633,"Wav",9408.63, add.to = model1) newcoords <- data.frame(x = 509926,y = 2179149) coks <- COKS_scores_lambdas(SFD_PM10_NO2,newcoords,model1) summary(coks)data(COKMexico) SFD_PM10_NO2 <- SpatFD(Mex_PM10, coords = coord_PM10, basis = "Fourier", nbasis = 21, lambda = 0.000001, nharm = 2) SFD_PM10_NO2 <- SpatFD(NO2, coords = coord_NO2, basis = "Fourier", nbasis = 27, lambda = 0.000001, nharm = 2,add = SFD_PM10_NO2) model1 <- gstat::vgm(647677.1,"Gau",23317.05) model1 <- gstat::vgm(127633,"Wav",9408.63, add.to = model1) newcoords <- data.frame(x = 509926,y = 2179149) coks <- COKS_scores_lambdas(SFD_PM10_NO2,newcoords,model1) summary(coks)
This functions shows a summary of the main objects of gfdata objects.
## S3 method for class 'gfdata' summary(object, ...)## S3 method for class 'gfdata' summary(object, ...)
object |
Object of class 'gfdata'. |
... |
arguments from summary. |
For each variable included in the gfdata object, this functions return: Head of data, Coordinates, Eigenvalues, Mean coefficients, Proportion of explained variance by each component
Joan Nicolás Castro [email protected], Venus Celeste Puertas [email protected]
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis) summary.gfdata(object=s4.gfdata)data(vowels) #### Create parameters and names for the data. p = 228 ; nelec = 21 ; nvow = 5 names_vowels = c("a","e","i","o","u") n.basis<-c(14,13,12,13,11) s4.gfdata = gfdata(data=vowels,p=p,names=names_vowels,coords=vowels_coords,nbasis=n.basis) summary.gfdata(object=s4.gfdata)
This functions shows a summary of the main objects of KS_pred objects.
## S3 method for class 'KS_pred' summary(object, ...)## S3 method for class 'KS_pred' summary(object, ...)
object |
Object of class 'KS_pred'. |
... |
arguments from summary |
This functions prints according to method computed: eigenvalues, variance of prediction and each of the models.
Joan Nicolás Castro [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
library(gstat) data(AirQualityBogota) newcoorden=data.frame(X=110000,Y=125000) # Recibir los datos, suavizarlos y ACP SFD_PM10 <- SpatFD(PM10, coords = coord[,2:3], basis = "Bsplines", nbasis = 17, norder=5, lambda = 0.00002, nharm=3) #Variogram model for each component modelos <- list(vgm(psill = 2634000, "Exp", range = 2103.25, nugget = 0), vgm(psill = 101494.96, "Exp", range = 1484.57, nugget = 0), vgm(psill =53673, "Exp", range = 42406, nugget = 0)) #Genera los scores y los lambdas para predecir en nuevas coordenadas #method = "lambda" KS_SFD_PM10_l <- KS_scores_lambdas(SFD_PM10, newcoorden ,method = "lambda", model = modelos) summary(KS_SFD_PM10_l)library(gstat) data(AirQualityBogota) newcoorden=data.frame(X=110000,Y=125000) # Recibir los datos, suavizarlos y ACP SFD_PM10 <- SpatFD(PM10, coords = coord[,2:3], basis = "Bsplines", nbasis = 17, norder=5, lambda = 0.00002, nharm=3) #Variogram model for each component modelos <- list(vgm(psill = 2634000, "Exp", range = 2103.25, nugget = 0), vgm(psill = 101494.96, "Exp", range = 1484.57, nugget = 0), vgm(psill =53673, "Exp", range = 42406, nugget = 0)) #Genera los scores y los lambdas para predecir en nuevas coordenadas #method = "lambda" KS_SFD_PM10_l <- KS_scores_lambdas(SFD_PM10, newcoorden ,method = "lambda", model = modelos) summary(KS_SFD_PM10_l)
This functions shows a summary of the main objects of SpatFD objects.
## S3 method for class 'SpatFD' summary(object, ...)## S3 method for class 'SpatFD' summary(object, ...)
object |
Object of class 'SpatFD'. |
... |
arguments from summary. |
For each variable included in the SpatFd object, this functions return: Head of data, Coordinates, Eigenvalues, Mean coefficients, Proportion of explained variance by each component
Joan Nicolás Castro [email protected].
Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).
# Load data data(AirQualityBogota) # Create an univariate object using 2 nharm SFD_PM10 <- SpatFD(PM10, coords = coord[,2:3], basis = "Bsplines", nbasis = 91, lambda = 0.00002, nharm = 2) summary(SFD_PM10)# Load data data(AirQualityBogota) # Create an univariate object using 2 nharm SFD_PM10 <- SpatFD(PM10, coords = coord[,2:3], basis = "Bsplines", nbasis = 91, lambda = 0.00002, nharm = 2) summary(SFD_PM10)
Data consist of EEG signals taken from 21 electrodes from imaginary thinking of the five Spanish vowels, to be applied into a BCI for a hand prosthesis.
data(vowels)data(vowels)
two data.frame of measurements 'vowels' and coordinates 'vowels_coords'.
https://github.com/carlos-sarmientov/DATABASE-IMAGINED-VOWELS-1
Classification techniques for imaginary speech brain signal through spatial functional data https://repositorio.unal.edu.co/handle/unal/85267
Coordinates of the electrodes from the vowels data set.
data(vowels)data(vowels)
matrix of coordinates
https://github.com/carlos-sarmientov/DATABASE-IMAGINED-VOWELS-1
Classification techniques for imaginary speech brain signal through spatial functional data https://repositorio.unal.edu.co/handle/unal/85267