Calculates the representation of the training classes in depth space using spatial depth.
Usage
depth.space.spatial(data, cardinalities)
Arguments
data
Matrix containing training sample where each row is a 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.
cardinalities
Numerical vector of cardinalities of each class in data, each entry corresponds to one class.
Details
The depth representation is calculated in the same way as in depth.spatial, see 'References' for more information and details.
Value
Matrix 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 cardinalities.
References
Chaudhuri, P. (1996). On a geometric notion of quantiles for multivariate data. Journal of the Americal Statistical Association91 862–872.
Koltchinskii, V.I. (1997). M-estimation, convexity and quantiles. The Annals of Statistics25 435–477.
Serfling, R. (2006). Depth functions in nonparametric multivariate inference. In: Liu, R.,
Serfling, R., Souvaine, D. (eds.), Data Depth: Robust Multivariate Analysis, Computational
Geometry and Applications, American Mathematical Society, 1–16
Vardi, Y. and Zhang, C.H. (2000). The multivariate L1
-median and associated data depth.
Proceedings of the National Academy of Sciences, U.S.A.97 1423–1426.
See Also
ddalpha.train and ddalpha.classify for application, depth.spatial for calculation of spatial depth.
Examples
# Generate a bivariate normal location-shift classification task
# containing 20 training objects
class1 <- mvrnorm(10, c(0,0),
matrix(c(1,1,1,4), nrow = 2, ncol = 2, byrow = TRUE))
class2 <- mvrnorm(10, c(2,2),
matrix(c(1,1,1,4), nrow = 2, ncol = 2, byrow = TRUE))
data <- rbind(class1, class2)
# Get depth space using spatial depth
depth.space.spatial(data, c(10, 10))
data <- getdata("hemophilia")
cardinalities = c(sum(data$gr == "normal"), sum(data$gr == "carrier"))
depth.space.spatial(data[,1:2], cardinalities)