View source: R/depth.simplicialVolume.r
depth.simplicialVolume | R Documentation |
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 |
data |
Matrix of data where each row contains a |
exact |
|
k |
Number ( |
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")
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