R: Calculate Depth Space using Zonoid Depth

depth.space.zonoid {ddalpha} | R Documentation

## Calculate Depth Space using Zonoid Depth

### Description

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

### Usage

    depth.space.zonoid(data, cardinalities, seed = 0)

### 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.
`seed` | the random seed. The default value `seed=0` makes no changes.

### Details

The depth representation is calculated in the same way as in `depth.zonoid`, 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

Dyckerhoff, R., Koshevoy, G., and Mosler, K. (1996). Zonoid data depth: theory and computation. In: Prat A. (ed), COMPSTAT 1996. Proceedings in computational statistics, Physica-Verlag (Heidelberg), 235–240.

Koshevoy, G. and Mosler, K. (1997). Zonoid trimming for multivariate distributions Annals of Statistics 25 1998–2017.

Mosler, K. (2002). Multivariate dispersion, central regions and depth: the lift zonoid approach Springer (New York).

### See Also

`ddalpha.train` and `ddalpha.classify` for application, `depth.zonoid` for calculation of zonoid 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 zonoid depth
    depth.space.zonoid(data, c(10, 10))

    data <- getdata("hemophilia")
    cardinalities = c(sum(data$gr == "normal"), sum(data$gr == "carrier"))
    depth.space.zonoid(data[,1:2], cardinalities)

[Package ddalpha version 1.3.11 Index]