R: Calculate Depth Space using Simplicial Depth

depth.space.simplicial {ddalpha} | R Documentation

## Calculate Depth Space using Simplicial Depth

### Description

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

### Usage

    depth.space.simplicial(data, cardinalities, exact = F, k = 0.05, 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.
`exact` | `exact=F` (by default) implies the approximative algorithm, considering `k` simplices, `exact=T` implies the exact algorithm.
`k` | Number (k>1) or portion (if 0<k<1) of simplices that are considered if `exact=F`. If k>1, then the algorithmic complexity is polynomial in d but is independent of the number of observations in `data`, given k. If 0<k<1, then the algorithmic complexity is exponential in the number of observations in `data`, but the calculation precision stays approximately the same.
`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.simplicial`, 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 American Statistical Association 91 862–872.

Liu, R. Y. (1990). On a notion of data depth based on random simplices. The Annals of Statistics 18 405–414.

Rousseeuw, P.J. and Ruts, I. (1996). Algorithm AS 307: Bivariate location depth. Journal of the Royal Statistical Society. Seriec C (Applied Statistics) 45 516–526.

### See Also

`ddalpha.train` and `ddalpha.classify` for application, `depth.simplicial` for calculation of simplicial 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(1,1),
                      matrix(c(1,1,1,4), nrow = 2, ncol = 2, byrow = TRUE))
    data <- rbind(class1, class2)
    # Get depth space using simplicial depth
    depth.space.simplicial(data, c(10, 10))

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

[Package ddalpha version 1.3.4 Index]