Calculate Depth Space using Mahalanobis Depth
Calculates the representation of the training classes in depth space using Mahalanobis depth.
depth.space.Mahalanobis(data, cardinalities, mah.estimate = "moment", mah.parMcd = 0.75)
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 |
mah.estimate |
is a character string specifying which estimates to use when calculating the Mahalanobis depth; can be |
mah.parMcd |
is the value of the argument |
The depth representation is calculated in the same way as in depth.Mahalanobis, see 'References' for more information and details.
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.
Mahalanobis, P. (1936). On the generalized distance in statistics. Proceedings of the National Academy India 12 49–55.
Liu, R.Y. (1992). Data depth and multivariate rank tests. In: Dodge, Y. (ed.), L1-Statistics and Related Methods, North-Holland (Amsterdam), 279–294.
Lopuhaa, H.P. and Rousseeuw, P.J. (1991). Breakdown points of affine equivariant estimators of multivariate location and covariance matrices. The Annals of Statistics 19 229–248.
Rousseeuw, P.J. and Leroy, A.M. (1987). Robust Regression and Outlier Detection. John Wiley & Sons (New York).
Zuo, Y.J. and Serfling, R. (2000). General notions of statistical depth function. The Annals of Statistics 28 461–482.
ddalpha.train and ddalpha.classify for application, depth.Mahalanobis for calculation of Mahalanobis depth.
# 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 Mahalanobis depth
depth.space.Mahalanobis(data, c(10, 10))
depth.space.Mahalanobis(data, c(10, 10), mah.estimate = "MCD", mah.parMcd = 0.75)
data <- getdata("hemophilia")
cardinalities = c(sum(data$gr == "normal"), sum(data$gr == "carrier"))
depth.space.Mahalanobis(data[,1:2], cardinalities)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.