Calculate Depth Space using Projection Depth
Calculates the representation of the training classes in depth space using projection depth.
depth.space.projection(data, cardinalities,
method = "random", num.directions = 1000, seed = 0)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 |
method |
to be used in calculations.
|
num.directions |
Number of random directions to be generated for |
seed |
the random seed. The default value |
The depth representation is calculated in the same way as in depth.projection, 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.
Donoho, D.L. (1982). Breakdown properties of multivariate location estimators. Ph.D. qualifying paper. Department of Statistics, Harvard University.
Liu, R.Y. (1992). Data depth and multivariate rank tests. In: Dodge, Y. (ed.), L1-Statistics and Related Methods, North-Holland (Amsterdam), 279–294.
Liu, X. and Zuo, Y. (2014). Computing projection depth and its associated estimators. Statistics and Computing 24 51–63.
Stahel, W.A. (1981). Robust estimation: infinitesimal optimality and covariance matrix estimators. Ph.D. thesis (in German). Eidgenossische Technische Hochschule Zurich.
Zuo, Y.J. and Lai, S.Y. (2011). Exact computation of bivariate projection depth and the Stahel-Donoho estimator. Computational Statistics and Data Analysis 55 1173–1179.
ddalpha.train and ddalpha.classify for application, depth.projection for calculation of projection 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 projection depth
depth.space.projection(data, c(10, 10), method = "random", num.directions = 1000)
depth.space.projection(data, c(10, 10), method = "linearize")
data <- getdata("hemophilia")
cardinalities = c(sum(data$gr == "normal"), sum(data$gr == "carrier"))
depth.space.projection(data[,1:2], cardinalities)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.