Simplicial volume depth#

DepthEucl.simplicialVolume(x: ndarray | None = None, exact: bool = True, k: float = 0.05, mah_estimate: str = 'moment', mah_parMCD: float = 0.75, evaluate_dataset: bool = False) → ndarray[source]

Calculates the simpicial volume 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.

exactbool, default=True

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

k: float or int, default=0.05
Number (k > 1) or portion (if 0 < k < 1) of simplices that are considered if exact = F.
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.
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

  • Oja, H. (1983). Descriptive statistics for multivariate distributions. Statistics and Probability Letters, 1, 327–332.

Examples
>>> import numpy as np
>>> from depth.model import DepthEucl
>>> mat1=[[1, 0, 0],[0, 2, 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, 20)
>>> model=DepthEucl().load_dataset(data)
>>> model.simplicalVolume(x, exact=True)
[0.45749049 0.34956166 0.2263421  0.68742137 0.94796538 0.51112415
 0.85250931 0.67914988 0.79165292 0.33192247]
>>> model.simplicalVolume(x, exact=False, k=0.2)
[0.46826813 0.40138917 0.23189724 0.69025277 0.938543   0.56005713
 0.8113647  0.72220103 0.82036139 0.33908597]

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