Depth(-based) visualization#

depth_mesh(model: DepthEucl, notion: str = 'halfspace', freq: List[int] = [100, 100], xlim: List[int] | None = None, ylim: List[int] | None = None, mah_estimate: str = 'moment', mah_parMCD: float = 0.75, beta: int = 2, distance: str = 'Lp', Lp_p: int = 2, exact: bool = True, method: str = 'recursive', k: float = 0.05, solver: str = 'neldermead', NRandom: int = 1000, n_refinements: int = 10, sphcap_shrink: float = 0.5, alpha_Dirichlet: float = 1.25, cooling_factor: float = 0.95, cap_size: float | int = 1, start: str = 'mean', space: str = 'sphere', line_solver: str = 'goldensection', bound_gc: bool = True) → tuple[ndarray, ndarray, ndarray][source]

Computes the depth mesh

Parameters

notion: str, default=”halfspace”

Chosen notion for depth computation. The mesh will be computed using this notion to map the 2D space

freq: List[int], defaul=[100,100]

Amount of points to map depth in both dimensions.

xlim: List[int], default=None

Limits for x value computation. If None, value is determined based on dataset values.

ylim: List[int], default=None

Limits for y value computation. If None, value is determined based on dataset values.

Results

xs: np.ndarray

x coordinate for plotting

ys: np.ndarray

y coordinate for plotting

depth_grid: np.ndarray

depth values for the grid

depth_plot2d(model: DepthEucl, notion: str = 'halfspace', freq: list = [100, 100], xlim: List[int] | List[float] = None, ylim: List[int] | List[float] = None, cmap: str = 'YlOrRd', ret_depth_mesh: bool = False, xs=None, ys=None, val_mesh=None, mah_estimate='moment', mah_parMCD=0.75, beta=2, distance='Lp', Lp_p=2, exact=True, method='recursive', k=0.05, solver='neldermead', NRandom=1000, n_refinements=10, sphcap_shrink=0.5, alpha_Dirichlet=1.25, cooling_factor=0.95, cap_size=1, start='mean', space='sphere', line_solver='goldensection', bound_gc=True)[source]

Plots the 2D view of the depth

Parameters

model: Euclidean Depth model

Model with loaded dataset

notion: str, default=”halfspace”

Chosen notion for depth computation. The mesh will be computed using this notion to map the 2D space

freq: List[int], defaul=[100,100]

Amount of points to map depth in both dimensions.

xlim: List[int], default=None

Limits for x value computation. If None, value is determined based on dataset values.

ylim: List[int], default=None

Limits for y value computation. If None, value is determined based on dataset values.

exactbool, delfaut=True

Whether the depth computation is exact.

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

Specifying which estimates to use when calculating the depth

mah_parMcdfloat, default=0.75

Value of the argument alpha for the function covMcd

solverstr, default=”neldermead”

The type of solver used to approximate the depth.

NRandomint, default=1000

Total number of directions used for approximate depth

n_refinementsint, default = 10

Number of iterations used to approximate the depth For solver='refinedrandom' or 'refinedgrid'

sphcap_shrinkfloat, default = 0.5

For solver = refinedrandom or refinedgrid, it’s the shrinking of the spherical cap.

alpha_Dirichletfloat, default = 1.25

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

cooling_factorfloat, default = 0.95

For solver = randomsimplices, it’s the cooling factor.

cap_sizeint | float, default = 1

For solver = simulatedannealing or neldermead, it’s the size of the spherical cap.

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

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 hemispher

pretransform: str, default=”1Mom” The method of data scaling.

'1Mom' or 'NMom' for scaling using data moments. '1MCD' or 'NMCD' for scaling using robust data moments (Minimum Covariance Determinant (MCD).

kernel: str, default=”EDKernel”

'EDKernel' for the kernel of type 1/(1+kernel.bandwidth*EuclidianDistance2(x,y)), 'GKernel' [default and recommended] for the simple Gaussian kernel, 'EKernel' exponential kernel: exp(-kernel.bandwidth*EuclidianDistance(x, y)), 'VarGKernel' variable Gaussian kernel, where kernel.bandwidth is proportional to the depth.zonoid of a point.

kernel_bandwidth: int, default=0

the single bandwidth parameter of the kernel. If 0 - the Scott`s rule of thumb is used.

k: float, 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.

Returns

fig, ax, im