Simplicial depth#

DepthEucl.simplicial(x: ndarray | None = None, exact: bool = True, k: float = 0.05, evaluate_dataset: bool = False) → ndarray[source]

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

Arguments
x: array-like or None, default=None

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.

exact: bool, default=True

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

kfloat or int, default=0.05
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.
evaluate_datasetbool, default=False

Determines if dataset loaded will be evaluated. Automatically sets x to dataset

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.model import DepthEucl
>>> 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)
>>> model=DepthEucl().load_dataset(data)
>>> model.simplicial(x,)
[0.04458498 0.         0.         0.         0.         0.
 0.         0.         0.         0.        ]

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