depth.simplicialVolume: Calculate Simplicial Volume Depth In ddalpha: Depth-Based Classification and Calculation of Data Depth

 depth.simplicialVolume R Documentation

Calculate Simplicial Volume Depth

Description

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

Usage

```depth.simplicialVolume(x, data, exact = F, k = 0.05, mah.estimate = "moment",
mah.parMcd = 0.75, 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 Oja depth (also: Simplicial volume depth). At first the Oja outlyingness function `O(x,data)` is calculated as the average of the volumes of simplices built on d data points and the measurement point `x` (Oja, 1983).

Zuo and Serfling (2000) proposed Oja depth based on the Oja outlyingness function as `1/(1 + O(x,data)/S)`, where S is a square root of the determinant of `cov(data)`, which makes the depth function affine-invariant.

Value

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

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.

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

`depth.Mahalanobis` for calculation of Mahalanobis depth.

`depth.projection` for calculation of projection depth.

`depth.simplicial` for calculation of simplicial 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.simplicialVolume(x, data, exact = TRUE)
cat("Depths: ", depths, "\n")

#approximative
depths <- depth.simplicialVolume(x, data, exact = FALSE, k = 0.2)
cat("Depths: ", depths, "\n")
```

ddalpha documentation built on March 23, 2022, 9:07 a.m.