1\name{depth.space.spatial} 2\alias{depth.space.spatial} 3\title{ 4Calculate Depth Space using Spatial Depth 5} 6\description{ 7Calculates the representation of the training classes in depth space using spatial depth. 8} 9\usage{ 10depth.space.spatial(data, cardinalities, mah.estimate = "moment", mah.parMcd = 0.75) 11} 12\arguments{ 13 \item{data}{ 14Matrix containing training sample where each row is a \eqn{d}-dimensional object, and objects of each class are kept together so that the matrix can be thought of as containing blocks of objects representing classes. 15} 16 \item{cardinalities}{ 17Numerical vector of cardinalities of each class in \code{data}, each entry corresponds to one class. 18} 19 \item{mah.estimate}{ is a character string specifying which estimates to use when calculating sample covariance matrix; can be \code{"none"}, \code{"moment"} or \code{"MCD"}, determining whether traditional moment or Minimum Covariance Determinant (MCD) (see \code{\link{covMcd}}) estimates for mean and covariance are used. By default \code{"moment"} is used. With \code{"none"} the non-affine invariant version of Spatial depth is calculated 20} 21 \item{mah.parMcd}{ 22is the value of the argument \code{alpha} for the function \code{\link{covMcd}}; is used when \code{mah.estimate =} \code{"MCD"}. 23} 24} 25\details{ 26The depth representation is calculated in the same way as in \code{\link{depth.spatial}}, see 'References' for more information and details. 27} 28\value{ 29Matrix of objects, each object (row) is represented via its depths (columns) w.r.t. each of the classes of the training sample; order of the classes in columns corresponds to the one in the argument \code{cardinalities}. 30} 31\references{ 32Chaudhuri, P. (1996). On a geometric notion of quantiles for multivariate data. \emph{Journal of the Americal Statistical Association} \bold{91} 862--872. 33 34Koltchinskii, V.I. (1997). M-estimation, convexity and quantiles. \emph{The Annals of Statistics} \bold{25} 435--477. 35 36Serfling, R. (2006). Depth functions in nonparametric multivariate inference. In: Liu, R., Serfling, R., Souvaine, D. (eds.), \emph{Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications}, American Mathematical Society, 1--16. 37 38Vardi, Y. and Zhang, C.H. (2000). The multivariate L1-median and associated data depth. \emph{Proceedings of the National Academy of Sciences, U.S.A.} \bold{97} 1423--1426. 39} 40\seealso{ 41\code{\link{ddalpha.train}} and \code{\link{ddalpha.classify}} for application, \code{\link{depth.spatial}} for calculation of spatial depth. 42} 43\examples{ 44# Generate a bivariate normal location-shift classification task 45# containing 20 training objects 46class1 <- mvrnorm(10, c(0,0), 47 matrix(c(1,1,1,4), nrow = 2, ncol = 2, byrow = TRUE)) 48class2 <- mvrnorm(10, c(2,2), 49 matrix(c(1,1,1,4), nrow = 2, ncol = 2, byrow = TRUE)) 50data <- rbind(class1, class2) 51# Get depth space using spatial depth 52depth.space.spatial(data, c(10, 10)) 53 54data <- getdata("hemophilia") 55cardinalities = c(sum(data$gr == "normal"), sum(data$gr == "carrier")) 56depth.space.spatial(data[,1:2], cardinalities) 57} 58\keyword{ robust } 59\keyword{ multivariate } 60\keyword{ nonparametric } 61