Calculate Simplicial Volume Depth
Calculates the simpicial volume depth of points w.r.t. a multivariate data set.
depth.simplicialVolume(x, data, exact = F, k = 0.05, mah.estimate = "moment",
mah.parMcd = 0.75, seed = 0)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 |
Matrix of data where each row contains a d-variate point, w.r.t. which the depth is to be calculated. |
exact |
|
k |
Number (k>1) or portion (if 0<k<1) of simplices that are considered if |
mah.estimate |
A character string specifying affine-invariance adjustment; can be |
mah.parMcd |
The value of the argument |
seed |
The random seed. The default value |
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.
Numerical vector of depths, one for each row in x; or one depth value if x is a numerical vector.
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.
# 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")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.