depth.space.simplicialVolume {ddalpha} | R Documentation

## Calculate Depth Space using Simplicial Volume Depth

### Description

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

### Usage

    depth.space.simplicialVolume(data, cardinalities, exact = F, k = 0.05,
                                 mah.estimate = "moment", mah.parMcd = 0.75, 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.
`mah.estimate` | A character string specifying affine-invariance adjustment; can be `"none"`, `"moment"` or `"MCD"`, determining whether no affine-invariance adjustemt or moment or Minimum Covariance Determinant (MCD) (see `covMcd`) estimates of the covariance are used. By default `"moment"` is used.
`mah.parMcd` | The value of the argument `alpha` for the function `covMcd`; is used when `mah.estimate =` `"MCD"`.
`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.simplicialVolume`, see References below 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

Oja, H. (1983). Descriptive statistics for multivariate distributions. Statistics & Probability Letters 1 327–332.

Zuo, Y.J. and Serfling, R. (2000). General notions of statistical depth function. The Annals of Statistics 28 461–482.

### See Also

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

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

[Package ddalpha version 1.3.9 Index]