depth.space.spatial {ddalpha}

Calculate Depth Space using Spatial Depth

Description

Calculates the representation of the training classes in depth space using spatial depth.

Usage

depth.space.spatial(data, cardinalities, mah.estimate = "moment", mah.parMcd = 0.75)

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.

mah.estimate

is a character string specifying which estimates to use when calculating sample covariance matrix; can be "none", "moment" or "MCD", determining whether traditional moment or Minimum Covariance Determinant (MCD) (see covMcd) estimates for mean and covariance are used. By default "moment" is used. With "none" the non-affine invariant version of Spatial depth is calculated

mah.parMcd

is the value of the argument alpha for the function covMcd; is used when mah.estimate = "MCD".

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 Association 91 862–872.

Koltchinskii, V.I. (1997). M-estimation, convexity and quantiles. The Annals of Statistics 25 435–477.

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)