R/svmidwpred.R

In spm2: Spatial Predictive Modeling

#' @title Generate spatial predictions using the hybrid method of support vector machine ('svm')
#'  regression and inverse distance weighted ('IDW') ('svmidw')
#'
#' @description This function is for generating spatial predictions using the hybrid
#' method of 'svm' and 'idw' ('svmidw').
#'
#' @param formula a formula defining the response variable and predictive variables
#'  for 'svm'.
#' @param longlat	a dataframe contains longitude and latitude of point samples. The
#'  location information must be named as 'long' and 'lat'.
#' @param trainxy a dataframe contains longitude (long), latitude (lat),
#' predictive variables and the response variable of point samples.
#' @param y a vector of the response variable in the formula, that is, the left
#' part of the formula.
#' @param longlatpredx	a dataframe contains longitude and latitude of point locations
#' (i.e., the centers of grids) to be predicted.
#' @param predx	a dataframe or matrix contains columns of predictive variables
#' for the grids to be predicted.
#' @param scale A logical vector indicating the variables to be scaled (default: TRUE).
#' @param type the default setting is 'NULL'. See '?svm' for various options.
#' @param kernel the default setting is 'radial'. See '?svm' for other options.
#' @param degree a parameter needed for kernel of type polynomial (default: 3).
#' @param gamma a parameter needed for all 'kernels' except 'linear'
#' (default: 1/(data dimension)).
#' @param coef0 a parameter needed for kernels of type 'polynomial' and 'sigmoid'(default: 0).
#' @param cost cost of constraints violation (default: 1).
#' @param nu a parameter needed for 'nu-classification', 'nu-regression', and 'one-classification' (default: 0.5).
#' @param tolerance tolerance of termination criterion (default: 0.001).
#' @param epsilon 'epsilon' in the insensitive-loss function (default: 0.1).
#'  See '?svm' for details.
#' @param idp	 a numeric number specifying the inverse distance weighting power.
#' @param nmaxidw 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.
#' @param ... other arguments passed on to 'svm'.
#'
#' @return A dataframe of longitude, latitude, and predictions.
#'
#' @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 Jin Li
#' @examples
#' \donttest{
#' library(spm)
#' data(petrel)
#' data(petrel.grid)
#'
#' 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)
#'
#' svmidwpred1 <- svmidwpred(formula = model, longlat = longlat, trainxy =  gravel,
#' y = y, longlatpredx = petrel.grid[, c(1:2)], predx = petrel.grid, idp = 2,
#'  nmaxidw = 12)
#'
#' names(svmidwpred1)
#'
#' # Back transform 'svmidwpred$predictions' to generate the final predictions
#' svmidw.predictions <- exp(svmidwpred1$predictions) - 1
#' range(svmidw.predictions)
#'}
#'
#' @export
svmidwpred <- function (formula = NULL, longlat, trainxy, y, longlatpredx, predx, 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, idp = 2, nmaxidw = 12, ...) {

    names(longlat) <- c("long", "lat")
    names(longlatpredx) <- c("long", "lat")

    # svm modeling
    svm1 <- e1071::svm(formula, trainxy, scale = scale, type = type, kernel = kernel, degree = degree, gamma = gamma, coef0 = coef0, cost = cost, nu = nu, tolerance = tolerance, epsilon = epsilon)

    # svm predictions
    pred.svm1 <- stats::predict(svm1, predx, type = "response")

    # the residuals of svm for idw
    data.dev1 <- longlat
    data.pred1 <- longlatpredx
    dev.svm1 <- stats::predict(svm1, trainxy, type="response")
    data.dev1$res1 <- y - dev.svm1

    # idw of the residuals
    gstat1 <- gstat::gstat(id = "res1", formula = res1 ~ 1, locations = ~ long + lat, data = data.dev1, set = list(idp = idp), nmax = nmaxidw)

    # idw predictions
    pred.idw1<- stats::predict(gstat1, data.pred1)

    predictions <- pred.idw1$res1.pred + pred.svm1
    svmidw.pred <- cbind(longlatpredx, predictions)
    svmidw.pred
}