# Cross validation, n-fold and leave-one-out for the hybrid method of support vector machine ('svm') regression and 'krige' (svmkrige) This function is a cross validation function for the hybrid method of 'svm' regression and 'krige' (svmkrige), where the data splitting is based on a stratified random sampling method (see the 'datasplit' function for details). ```r svmkrigecv( formula.svm = NULL, longlat, trainxy, y, scale = TRUE, type = NULL, kernel = "radial", degree = 3, gamma = if (is.vector(trainxy)) 1 else 1/ncol(trainxy), coef0 = 0, cost = 1, nu = 0.5, tolerance = 0.001, epsilon = 0.1, transformation = "none", delta = 1, formula.krige = res1 ~ 1, vgm.args = c("Sph"), anis = c(0, 1), alpha = 0, block = 0, beta, nmaxkrige = 12, validation = "CV", cv.fold = 10, predacc = "VEcv", ... ) ``` ## Arguments - `formula.svm`: a formula defining the response variable and predictive variables for 'svm'. - `longlat`: a dataframe contains longitude and latitude of point samples. - `trainxy`: a dataframe contains longitude (long), latitude (lat), predictive variables and the response variable of point samples. That is, the location information must be named as 'long' and 'lat'. - `y`: a vector of the response variable in the formula.svm, that is, the left part of the formula.svm. - `scale`: A logical vector indicating the variables to be scaled (default: TRUE). - `type`: the default setting is 'NULL'. See '?svm' for various options. - `kernel`: the default setting is 'radial'. See '?svm' for other options. - `degree`: a parameter needed for kernel of type polynomial (default: 3). - `gamma`: a parameter needed for all 'kernels' except 'linear' (default: 1/(data dimension)). - `coef0`: a parameter needed for kernels of type 'polynomial' and 'sigmoid'(default: 0). - `cost`: cost of constraints violation (default: 1). - `nu`: a parameter needed for 'nu-classification', 'nu-regression', and 'one-classification' (default: 0.5). - `tolerance`: tolerance of termination criterion (default: 0.001). - `epsilon`: 'epsilon' in the insensitive-loss function (default: 0.1). - `transformation`: transform the residuals of 'svm' to normalise the data; can be "sqrt" for square root, "arcsine" for arcsine, "log" or "none" for non transformation. By default, "none" is used. - `delta`: numeric; to avoid log(0) in the log transformation. The default is 1. - `formula.krige`: formula defining the response vector and (possible) regressor. an object (i.e., 'variogram.formula') for 'variogram' or a formula for 'krige'. see 'variogram' and 'krige' in 'gstat' for details. - `vgm.args`: arguments for 'vgm', e.g. variogram model of response variable and anisotropy parameters. see 'vgm' in 'gstat' for details. By default, "Sph" is used. - `anis`: anisotropy parameters: see notes 'vgm' in 'gstat' for details. - `alpha`: direction in plane (x,y). see variogram in 'gstat' for details. - `block`: block size. see 'krige' in 'gstat' for details. - `beta`: for simple kriging. see 'krige' in 'gstat' for details. - `nmaxkrige`: for a local predicting: the number of nearest observations that should be used for a prediction or simulation, where nearest is defined in terms of the space of the spatial locations. By default, 12 observations are used. - `validation`: validation methods, include 'LOO': leave-one-out, and 'CV': cross-validation. - `cv.fold`: integer; number of folds in the cross-validation. if > 1, then apply n-fold cross validation; the default is 10, i.e., 10-fold cross validation that is recommended. - `predacc`: can be either "VEcv" for 'vecv' or "ALL" for all measures in function pred.acc. - `...`: other arguments passed on to 'svm' and 'krige'. ## Returns A list with the following components: me, rme, mae, rmae, mse, rmse, rrmse, vecv and e1; or vecv only ## Note This function is largely based on 'rfcv' in 'randomForest', 'krigecv' in 'spm2'and 'svm' in 'e1071'. ## Examples ```r library(spm) data(petrel) gravel <- petrel[, c(1, 2, 6:9, 5)] longlat <- petrel[, c(1, 2)] model <- log(gravel + 1) ~ lat + bathy + I(long^3) + I(lat^2) + I(lat^3) y <- log(gravel[, 7] +1) set.seed(1234) svmkrigecv1 <- svmkrigecv(formula.svm = model, longlat = longlat, trainxy = gravel, y = y, transformation = "none", formula.krige = res1 ~ 1, vgm.args = "Sph", nmaxkrige = 12, validation = "CV", predacc = "ALL") svmkrigecv1 # svmok for count data data(sponge2) model <- species.richness ~ . # use all predictive variables in the dataset longlat <- sponge2[, 1:2] set.seed(1234) n <- 20 # number of iterations,60 to 100 is recommended. VEcv <- NULL for (i in 1:n) { svmkrigecv1 <- svmkrigecv(formula.svm = model, longlat = longlat, trainxy = sponge2[, -4], y = sponge2[, 3], gamma = 0.01, cost = 3.5, scale = TRUE, formula.krige = res1 ~ 1, vgm.args = ("Sph"), nmaxkrige = 12, validation = "CV", predacc = "VEcv") VEcv [i] <- svmkrigecv1 } plot(VEcv ~ c(1:n), xlab = "Iteration for svm", ylab = "VEcv (%)") points(cumsum(VEcv) / c(1:n) ~ c(1:n), col = 2) abline(h = mean(VEcv), col = 'blue', lwd = 2) ``` ## References Li, J., Potter, A., Huang, Z., and Heap, A. (2012). Predicting Seabed Sand Content across the Australian Margin Using Machine Learning and Geostatistical Methods, Geoscience Australia, Record 2012/48, 115pp. Li, J., Heap, A., Potter, A., and Danilel, J.J. (2011). Predicting Seabed Mud Content across the Australian Margin II: Performance of Machine Learning Methods and Their Combination with Ordinary Kriging and Inverse Distance Squared, Geoscience Australia, Record 2011/07, 69pp. David Meyer, Evgenia Dimitriadou, Kurt Hornik, Andreas Weingessel and Friedrich Leisch (2020). e1071: Misc Functions of the Department of Statistics, Probability Theory Group (Formerly: E1071), TU Wien. R package version 1.7-4. https://CRAN.R-project.org/package=e1071. Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers & Geosciences, 30: 683-691. ## Author(s) Jin Li

svmkrigecv function