Simplicial depth#

simplicial(x, data, exact=True, k=0.05, seed=0)[source]#

Description

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

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=True (by default) implies the exact algorithm, exact=False implies the approximative algorithm, considering k simplices.

k

Number (k > 1) or portion (if 0 < k < 1) of simplices that are considered if exact=False.

If k > 1, then the algorithmic complexity is polynomial in d but is independent of the number of observations in data, given k.

If 0 < k < 1,then the algorithmic complexity is exponential in the number of observations in data, but the calculation precision stays approximately the same.

seed

The random seed. The default value seed=0 makes no change.

References

• Liu , R. Y. (1990). On a notion of data depth based on random simplices. The Annals of Statistics, 18, 405–414.

Examples

>>> import numpy as np
>>> from depth.multivariate import *
>>> mat1=[[1, 0, 0],[0, 1, 0],[0, 0, 1]]
>>> mat2=[[1, 0, 0],[0, 1, 0],[0, 0, 1]]
>>> x = np.random.multivariate_normal([1,1,1], mat2, 10)
>>> data = np.random.multivariate_normal([0,0,0], mat1, 25)
>>> simplicial(x, data,)
[0.04458498 0.         0.         0.         0.         0.
 0.         0.         0.         0.        ]