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fdars.depth

Depth measures for functional data. All functions compute depth values for observations in data relative to a reference sample ref_data.

Functions

Function Description
fraiman_muniz_1d Fraiman-Muniz depth for 1D data
fraiman_muniz_2d Fraiman-Muniz depth for 2D data
modal_1d Modal depth for 1D data
modal_2d Modal depth for 2D data
random_projection_1d Random projection depth for 1D data
random_projection_2d Random projection depth for 2D data
random_tukey_1d Random Tukey depth for 1D data
random_tukey_2d Random Tukey depth for 2D data
band_1d Band depth for 1D data
modified_band_1d Modified band depth for 1D data
modified_epigraph_index_1d Modified epigraph index for 1D data
functional_spatial_1d Functional spatial depth for 1D data
functional_spatial_2d Functional spatial depth for 2D data
kernel_functional_spatial_1d Kernel functional spatial depth for 1D data
kernel_functional_spatial_2d Kernel functional spatial depth for 2D data

fraiman_muniz_1d

fdars.fraiman_muniz_1d(data, ref_data, scale=True)

Fraiman-Muniz integrated depth for 1D functional data.

Parameter Type Default Description
data ndarray (n, m) Data to compute depth for
ref_data ndarray (n_ref, m) Reference sample
scale bool True Whether to scale depth values
Returns Type Description
depth ndarray (n,) Depth values
depth = fdars.fraiman_muniz_1d(data, data)  # self-referencing

fraiman_muniz_2d

fdars.fraiman_muniz_2d(data, ref_data, scale=True)

Fraiman-Muniz depth for 2D (surface) functional data. Same interface as fraiman_muniz_1d.


fdars.modal_1d(data, ref_data, h=1.0)

Modal depth for 1D functional data. Uses kernel density estimation.

Parameter Type Default Description
data ndarray (n, m) Data to compute depth for
ref_data ndarray (n_ref, m) Reference sample
h float 1.0 Kernel bandwidth
Returns Type Description
depth ndarray (n,) Depth values
depth = fdars.modal_1d(data, data, h=0.5)

fdars.modal_2d(data, ref_data, h=1.0)

Modal depth for 2D data. Same interface as modal_1d.


random_projection_1d

fdars.random_projection_1d(data, ref_data, n_proj=50)

Random projection depth for 1D functional data. Projects onto random directions and averages univariate depth.

Parameter Type Default Description
data ndarray (n, m) Data to compute depth for
ref_data ndarray (n_ref, m) Reference sample
n_proj int 50 Number of random projections
Returns Type Description
depth ndarray (n,) Depth values
depth = fdars.random_projection_1d(data, data, n_proj=100)

random_projection_2d

fdars.random_projection_2d(data, ref_data, n_proj=50)

Random projection depth for 2D data. Same interface as random_projection_1d.


random_tukey_1d

fdars.random_tukey_1d(data, ref_data, n_proj=50)

Random Tukey (halfspace) depth for 1D functional data.

Parameter Type Default Description
data ndarray (n, m) Data to compute depth for
ref_data ndarray (n_ref, m) Reference sample
n_proj int 50 Number of random projections
Returns Type Description
depth ndarray (n,) Depth values
depth = fdars.random_tukey_1d(data, data, n_proj=50)

random_tukey_2d

fdars.random_tukey_2d(data, ref_data, n_proj=50)

Random Tukey depth for 2D data. Same interface as random_tukey_1d.


band_1d

fdars.band_1d(data, ref_data)

Band depth for 1D functional data. Measures the proportion of bands (defined by pairs of reference curves) that contain the target curve.

Parameter Type Description
data ndarray (n, m) Data to compute depth for
ref_data ndarray (n_ref, m) Reference sample
Returns Type Description
depth ndarray (n,) Depth values
depth = fdars.band_1d(data, data)

modified_band_1d

fdars.modified_band_1d(data, ref_data)

Modified band depth for 1D data. Relaxed version of band depth that measures the proportion of time a curve is inside each band.

Parameter Type Description
data ndarray (n, m) Data to compute depth for
ref_data ndarray (n_ref, m) Reference sample
Returns Type Description
depth ndarray (n,) Depth values
depth = fdars.modified_band_1d(data, data)

modified_epigraph_index_1d

fdars.modified_epigraph_index_1d(data, ref_data)

Modified epigraph index for 1D data. Measures how often each curve lies above the reference curves.

Parameter Type Description
data ndarray (n, m) Data to compute depth for
ref_data ndarray (n_ref, m) Reference sample
Returns Type Description
index ndarray (n,) Epigraph index values
mei = fdars.modified_epigraph_index_1d(data, data)

functional_spatial_1d

fdars.functional_spatial_1d(data, ref_data, argvals=None)

Functional spatial depth for 1D data. Extends multivariate spatial depth to functional setting.

Parameter Type Default Description
data ndarray (n, m) Data to compute depth for
ref_data ndarray (n_ref, m) Reference sample
argvals ndarray (m,) or None None Evaluation points; if None, uses uniform [0,1] grid
Returns Type Description
depth ndarray (n,) Depth values
t = np.linspace(0, 1, 100)
depth = fdars.functional_spatial_1d(data, data, argvals=t)

functional_spatial_2d

fdars.functional_spatial_2d(data, ref_data)

Functional spatial depth for 2D data.

Parameter Type Description
data ndarray (n, m) Data to compute depth for
ref_data ndarray (n_ref, m) Reference sample
Returns Type Description
depth ndarray (n,) Depth values
depth = fdars.functional_spatial_2d(data, data)

kernel_functional_spatial_1d

fdars.kernel_functional_spatial_1d(data, ref_data, argvals, h=1.0)

Kernel functional spatial depth for 1D data. Uses a Gaussian kernel with bandwidth h.

Parameter Type Default Description
data ndarray (n, m) Data to compute depth for
ref_data ndarray (n_ref, m) Reference sample
argvals ndarray (m,) Evaluation points
h float 1.0 Kernel bandwidth
Returns Type Description
depth ndarray (n,) Depth values
t = np.linspace(0, 1, 100)
depth = fdars.kernel_functional_spatial_1d(data, data, t, h=0.5)

kernel_functional_spatial_2d

fdars.kernel_functional_spatial_2d(data, ref_data, h=1.0)

Kernel functional spatial depth for 2D data.

Parameter Type Default Description
data ndarray (n, m) Data to compute depth for
ref_data ndarray (n_ref, m) Reference sample
h float 1.0 Kernel bandwidth
Returns Type Description
depth ndarray (n,) Depth values
depth = fdars.kernel_functional_spatial_2d(data, data, h=0.5)