Spatial depth#

DepthEucl.spatial(x: ndarray | None = None, mah_estimate: str = 'moment', mah_parMcd: float = 0.75, evaluate_dataset: bool = False) → ndarray[source]

Calculates the spatial 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.

mah_estimatestr, {“moment”, “mcd”}, default=”moment”

A character string specifying which estimates to use when calculating the Mahalanobis depth; can be “‘moment’” or 'MCD', determining whether traditional moment or Minimum Covariance Determinant (MCD) estimates for mean and covariance are used.

mah_parMcdfloat, default=0.75

is the value of the argument alpha for the function covMcd; is used when mah.estimate = 'MCD'.

evaluate_datasetbool, default=False

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

References

  • Serfling, R. (2002). A depth function and a scale curve based on spatial quantiles. In Dodge, Y. (Ed.), Statistical Data Analysis Based on the L1-Norm and Related Methods, Statisctics in Industry and Technology, Birkhäuser, Basel, 25–38.

Examples
>>> import numpy as np
>>> from depth.model import DepthEucl
>>> mat1=[[1, 0, 0, 0, 0],[0, 2, 0, 0, 0],[0, 0, 3, 0, 0],[0, 0, 0, 2, 0],[0, 0, 0, 0, 1]]
>>> mat2=[[1, 0, 0, 0, 0],[0, 1, 0, 0, 0],[0, 0, 1, 0, 0],[0, 0, 0, 1, 0],[0, 0, 0, 0, 1]]
>>> x = np.random.multivariate_normal([1,1,1,1,1], mat2, 10)
>>> data = np.random.multivariate_normal([0,0,0,0,0], mat1, 1000)
>>> model=DepthEucl().load_dataset(data)
>>> model.spatial(x, )
[0.22548919451212823, 0.14038895785356165, 0.2745517635029123, 0.35450156620496354,
0.42373722245348566, 0.34562025044812095, 0.3585616673301636, 0.16916309940691643,
0.573349631625784, 0.32017213635679687]

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