depth.qhpeeling {ddalpha}

Calculate Convex Hull Peeling Depth

Description

Calculates the convex hull peeling depth of points w.r.t. a multivariate data set.

Usage

depth.qhpeeling(x, data)

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.

Details

Calculates the convex hull peeling depth (Eddy, 1982; see also Cascos, 2009).

Value

Numerical vector of depths, one for each row in x; or one depth value if x is a numerical vector. Each depth value equals the number of the convex hulls to be peeled from data so that (the corresponding row of) x is not contained in the convex hull of the rest of the data; the depths are normalized by the number of points in data.

References

Eddy, W.F. (1982). Convex hull peeling. In: Caussinus, H., Ettinger, P. and Tomassone, R. (eds), COMPSTAT 1982. Proceedings in computational statistics, Physica-Verlag (Vienna), 42–47.

Cascos, I. (2009). Data depth: multivariate statistics and geometry. In: Kendall, W.S. and Molchanov, I. (eds) New Perspectives in Stochastic Geometry, Clarendon/Oxford University Press (Oxford).

See Also

depth.halfspace for calculation of the Tukey depth.

depth.L2 for calculation of L2-depth.

depth.Mahalanobis for calculation of Mahalanobis depth.

depth.projection for calculation of projection depth.

depth.simplicial for calculation of simplicial depth.

depth.simplicialVolume for calculation of simplicial volume depth.

depth.spatial for calculation of spatial depth.

depth.potential for calculation of data potential.

depth.zonoid for calculation of zonoid depth.

Examples

# Mixture of 3-variate normal distributions
data <- mvrnorm(25, rep(0, 3), diag(3))
x <- rbind(mvrnorm(10, rep(1, 3), diag(3)), data)
depths <- depth.qhpeeling(x, data)
cat("Depths:", depths, "\n")