Anomaly component analysis#

DepthEucl.ACA(dim: int = 2, sample_size: None = None, sample: None = None, notion: str = 'projection', solver: str = 'neldermead', NRandom: int = 100, n_refinements: int = 10, sphcap_shrink: float = 0.5, alpha_Dirichlet: float = 1.25, cooling_factor: float = 0.95, cap_size: int = 1, start: str = 'mean', space: str = 'sphere', line_solver: str = 'goldensection', bound_gc: bool = True)[source]

Computes the abnormal component analysis

Arguments
dim: int, default=2

Number of dimensions to keep in the reduction

sample_size: int, default=None

Size of the dataset (uniform sampling) to be used in the ACA calculation

sample: list[int], default=None

Indices for the dataset to be used in the computation

notion: str {'projection', 'halfspace'}, default=”projection”

Chosen notion for depth computation

solverstr {'refinedrandom', 'neldermead'}, default=”neldermead”

The type of solver used to approximate the depth.

NRandomint, default=1000

The total number of iterations to compute the depth. Some solvers are converging faster so they are run several time to achieve NRandom iterations.

n_refinementsint, default = 10

Set the maximum of iteration for computing the depth of one point. For solver='refinedrandom' or 'refinedgrid'.

sphcap_shrinkfloat, default = 0.5

It’s the shrinking of the spherical cap. For solver='refinedrandom' or 'refinedgrid'.

alpha_Dirichletfloat, default = 1.25

It’s the parameter of the Dirichlet distribution. For solver='randomsimplices'.

cooling_factorfloat, default = 0.95

It’s the cooling factor. For solver='simulatedannealing'.

cap_sizeint | float, default = 1

It’s the size of the spherical cap. For solver='simulatedannealing' or 'neldermead'.

startstr {‘mean’, ‘random’}, default = mean

For solver='simulatedannealing' or 'neldermead', it’s the method used to compute the first depth.

spacestr {‘sphere’, ‘euclidean’}, default = ‘sphere’

For solver='coordinatedescent' or 'neldermead', it’s the type of spacecin which the solver is running.

line_solverstr {‘uniform’, ‘goldensection’}, default = goldensection

For solver='coordinatedescent', it’s the line searh strategy used by this solver.

bound_gcbool, default = True

For solver='neldermead', it’s True if the search is limited to the closed hemisphere.

Results

ACA directions for dimensional reduction

References

  • Valla, R., Mozharovskyi, P., & d’Alché-Buc, F. (2023). Anomaly component analysis. arXiv preprint arXiv:2312.16139.

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]]
>>> np.random.seed(0)
>>> data1 = np.random.multivariate_normal([0,0,0,0,0], mat1, 990)
>>> data2 = np.random.multivariate_normal([0,1,1,0,0], mat2, 10)
>>> data=np.concat((data1,data2),axis=0)
>>> model = DepthEucl().load_dataset(data)
>>> model.ACA(dim=2, sample_size=900)
    array([[-0.13558675, -0.13558675],
            [ 2.65800844,  2.65800844],
            [-1.38230018, -1.38230018],
            [-0.11503065, -0.11503065],
            [ 0.55349281,  0.55349281]])

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