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fdars.metric

Distance metrics for functional data. "Self" functions compute an n-by-n distance matrix from a single dataset. "Cross" functions compute an n1-by-n2 matrix between two datasets.

Functions

Function Description
lp_self_1d Lp self-distance matrix, 1D
lp_cross_1d Lp cross-distance matrix, 1D
lp_self_2d Lp self-distance matrix, 2D
lp_cross_2d Lp cross-distance matrix, 2D
hausdorff_self_1d Hausdorff self-distance, 1D
hausdorff_cross_1d Hausdorff cross-distance, 1D
hausdorff_self_2d Hausdorff self-distance, 2D
hausdorff_cross_2d Hausdorff cross-distance, 2D
dtw_self_1d Dynamic time warping self-distance
dtw_cross_1d Dynamic time warping cross-distance
soft_dtw_self_1d Soft-DTW self-distance
soft_dtw_cross_1d Soft-DTW cross-distance
soft_dtw_div_self_1d Soft-DTW divergence self-distance
soft_dtw_div_cross_1d Soft-DTW divergence cross-distance
fourier_self_1d Fourier coefficient self-distance
fourier_cross_1d Fourier coefficient cross-distance
hshift_self_1d Horizontal shift self-distance
hshift_cross_1d Horizontal shift cross-distance

lp_self_1d

fdars.lp_self_1d(data, argvals, p=2.0)

Lp distance matrix for a single 1D functional dataset.

Parameter Type Default Description
data ndarray (n, m) Functional data matrix
argvals ndarray (m,) Evaluation points for integration
p float 2.0 Lp exponent; use float('inf') for L-infinity
Returns Type Description
dist ndarray (n, n) Symmetric distance matrix 
t = np.linspace(0, 1, 100)
D = fdars.lp_self_1d(data, t, p=2.0)

lp_cross_1d

fdars.lp_cross_1d(data1, data2, argvals, p=2.0)

Lp distance matrix between two 1D functional datasets.

Parameter Type Default Description
data1 ndarray (n1, m) First dataset
data2 ndarray (n2, m) Second dataset
argvals ndarray (m,) Evaluation points
p float 2.0 Lp exponent
Returns Type Description
dist ndarray (n1, n2) Distance matrix 
D = fdars.lp_cross_1d(train, test, t, p=2.0)

lp_self_2d

fdars.lp_self_2d(data, argvals_s, argvals_t, p=2.0)

Lp self-distance matrix for 2D functional data.

Parameter Type Default Description
data ndarray (n, m1*m2) Flattened 2D data
argvals_s ndarray (m1,) First dimension grid
argvals_t ndarray (m2,) Second dimension grid
p float 2.0 Lp exponent
Returns Type Description
dist ndarray (n, n) Distance matrix 
D = fdars.lp_self_2d(data, s_grid, t_grid, p=2.0)

lp_cross_2d

fdars.lp_cross_2d(data1, data2, argvals_s, argvals_t, p=2.0)

Lp cross-distance matrix for 2D functional data.

Parameter Type Default Description
data1 ndarray (n1, m1*m2) First dataset
data2 ndarray (n2, m1*m2) Second dataset
argvals_s ndarray (m1,) First dimension grid
argvals_t ndarray (m2,) Second dimension grid
p float 2.0 Lp exponent
Returns Type Description
dist ndarray (n1, n2) Distance matrix

hausdorff_self_1d

fdars.hausdorff_self_1d(data, argvals)

Hausdorff distance matrix for 1D functional data. Treats each curve as a set of (t, y(t)) points.

Parameter Type Description
data ndarray (n, m) Functional data
argvals ndarray (m,) Evaluation points
Returns Type Description
dist ndarray (n, n) Distance matrix 
D = fdars.hausdorff_self_1d(data, t)

hausdorff_cross_1d

fdars.hausdorff_cross_1d(data1, data2, argvals)

Hausdorff cross-distance for 1D data.

Parameter Type Description
data1 ndarray (n1, m) First dataset
data2 ndarray (n2, m) Second dataset
argvals ndarray (m,) Evaluation points
Returns Type Description
dist ndarray (n1, n2) Distance matrix

hausdorff_self_2d

fdars.hausdorff_self_2d(data, argvals_s, argvals_t)

Hausdorff self-distance for 2D data.

Parameter Type Description
data ndarray (n, m1*m2) Flattened 2D data
argvals_s ndarray (m1,) First dimension grid
argvals_t ndarray (m2,) Second dimension grid
Returns Type Description
dist ndarray (n, n) Distance matrix

hausdorff_cross_2d

fdars.hausdorff_cross_2d(data1, data2, argvals_s, argvals_t)

Hausdorff cross-distance for 2D data.

Parameter Type Description
data1 ndarray (n1, m1*m2) First dataset
data2 ndarray (n2, m1*m2) Second dataset
argvals_s ndarray (m1,) First dimension grid
argvals_t ndarray (m2,) Second dimension grid
Returns Type Description
dist ndarray (n1, n2) Distance matrix

dtw_self_1d

fdars.dtw_self_1d(data, p=2.0, w=0)

Dynamic Time Warping self-distance matrix for 1D data.

Parameter Type Default Description
data ndarray (n, m) Functional data
p float 2.0 Lp exponent for pointwise cost
w int 0 Sakoe-Chiba band width; 0 means no constraint
Returns Type Description
dist ndarray (n, n) Distance matrix 
D = fdars.dtw_self_1d(data, p=2.0, w=10)

dtw_cross_1d

fdars.dtw_cross_1d(data1, data2, p=2.0, w=0)

DTW cross-distance for 1D data (curves may have different lengths).

Parameter Type Default Description
data1 ndarray (n1, m1) First dataset
data2 ndarray (n2, m2) Second dataset
p float 2.0 Lp exponent
w int 0 Sakoe-Chiba band width
Returns Type Description
dist ndarray (n1, n2) Distance matrix

soft_dtw_self_1d

fdars.soft_dtw_self_1d(data, gamma=1.0)

Soft-DTW distance matrix (differentiable approximation to DTW).

Parameter Type Default Description
data ndarray (n, m) Functional data
gamma float 1.0 Smoothing parameter (smaller = closer to DTW)
Returns Type Description
dist ndarray (n, n) Distance matrix 
D = fdars.soft_dtw_self_1d(data, gamma=0.1)

soft_dtw_cross_1d

fdars.soft_dtw_cross_1d(data1, data2, gamma=1.0)

Soft-DTW cross-distance for 1D data.

Parameter Type Default Description
data1 ndarray (n1, m) First dataset
data2 ndarray (n2, m) Second dataset
gamma float 1.0 Smoothing parameter
Returns Type Description
dist ndarray (n1, n2) Distance matrix

soft_dtw_div_self_1d

fdars.soft_dtw_div_self_1d(data, gamma=1.0)

Soft-DTW divergence self-distance. Bias-corrected version of Soft-DTW that is a proper divergence.

Parameter Type Default Description
data ndarray (n, m) Functional data
gamma float 1.0 Smoothing parameter
Returns Type Description
dist ndarray (n, n) Divergence matrix 
D = fdars.soft_dtw_div_self_1d(data, gamma=1.0)

soft_dtw_div_cross_1d

fdars.soft_dtw_div_cross_1d(data1, data2, gamma=1.0)

Soft-DTW divergence cross-distance.

Parameter Type Default Description
data1 ndarray (n1, m) First dataset
data2 ndarray (n2, m) Second dataset
gamma float 1.0 Smoothing parameter
Returns Type Description
dist ndarray (n1, n2) Divergence matrix

fourier_self_1d

fdars.fourier_self_1d(data, n_basis=5)

Distance based on Fourier coefficients. Projects curves onto a Fourier basis and computes Euclidean distances in coefficient space.

Parameter Type Default Description
data ndarray (n, m) Functional data
n_basis int 5 Number of Fourier basis functions
Returns Type Description
dist ndarray (n, n) Distance matrix 
D = fdars.fourier_self_1d(data, n_basis=7)

fourier_cross_1d

fdars.fourier_cross_1d(data1, data2, n_basis=5)

Fourier coefficient cross-distance.

Parameter Type Default Description
data1 ndarray (n1, m) First dataset
data2 ndarray (n2, m) Second dataset
n_basis int 5 Number of Fourier basis functions
Returns Type Description
dist ndarray (n1, n2) Distance matrix

hshift_self_1d

fdars.hshift_self_1d(data, argvals, max_shift=0)

Horizontal shift distance. Finds the optimal horizontal translation minimizing L2 distance.

Parameter Type Default Description
data ndarray (n, m) Functional data
argvals ndarray (m,) Evaluation points
max_shift int 0 Maximum shift in grid points; 0 means m/4
Returns Type Description
dist ndarray (n, n) Distance matrix 
D = fdars.hshift_self_1d(data, t, max_shift=20)

hshift_cross_1d

fdars.hshift_cross_1d(data1, data2, argvals, max_shift=0)

Horizontal shift cross-distance.

Parameter Type Default Description
data1 ndarray (n1, m) First dataset
data2 ndarray (n2, m) Second dataset
argvals ndarray (m,) Evaluation points
max_shift int 0 Maximum shift in grid points; 0 means m/4
Returns Type Description
dist ndarray (n1, n2) Distance matrix