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

 depth.simplicial R Documentation

## Calculate Simplicial Depth

### Description

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

### Usage

``````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

``````# 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")
``````

ddalpha documentation built on May 29, 2024, 1:12 a.m.