# depth.simplicial: Calculate Simplicial Depth In ddalpha: Depth-Based Classification and Calculation of Data Depth

## Description

Calculates the simplicial depth of points w.r.t. a multivariate data set.

## Usage

 `1` ```depth.simplicial(x, data, exact = F, k = 0.05, seed = 0) ```

## Arguments

 `x` Matrix of objects (numerical vector as one object) whose depth is to be calculated; each row contains a d-variate point. Should have the same dimension as `data`. `data` Matrix of data where each row contains a d-variate point, w.r.t. which the depth is to be calculated. `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 01, then the algorithmic complexity is polynomial in d but is independent of the number of observations in `data`, given k. If 0

## Details

Calculates simplicial depth. Simplicial depth is counted as a probability that a point lies in a simplex, built on d+1 data points.

## Value

Numerical vector of depths, one for each row in `x`; or one depth value if `x` is a numerical vector.

## 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.

`depth.halfspace` for calculation of the Tukey depth.

`depth.Mahalanobis` for calculation of Mahalanobis depth.

`depth.projection` for calculation of projection depth.

`depth.simplicialVolume` for calculation of simplicial volume depth.

`depth.spatial` for calculation of spatial depth.

`depth.zonoid` for calculation of zonoid depth.

`depth.potential` for calculation of data potential.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```# 3-dimensional normal distribution data <- mvrnorm(20, rep(0, 3), matrix(c(1, 0, 0, 0, 2, 0, 0, 0, 1), nrow = 3)) x <- mvrnorm(10, rep(1, 3), matrix(c(1, 0, 0, 0, 1, 0, 0, 0, 1), nrow = 3)) #exact depths <- depth.simplicial(x, data, exact = TRUE) cat("Depths: ", depths, "\n") #approximative depths <- depth.simplicial(x, data, exact = FALSE, k = 0.2) cat("Depths: ", depths, "\n") ```

### Example output

```Loading required package: MASS