multipers.filtrations package

Submodules

multipers.filtrations.density module

class multipers.filtrations.density.DTM(masses, metric='euclidean', **_kdtree_kwargs)

Bases: object

Distance To Measure

Parameters:: metric (str)

fit(X, sample_weights=None, y=None)

score_samples(Y, X=None)

Returns the kernel density estimates of each point in Y.

Parameters

Ytensor (m, d): m points with d dimensions for which the probability density will be calculated

Returns

the DTMs of Y, for each mass in masses.

score_samples_diff(Y)

Returns the kernel density estimates of each point in Y.

Parameters

Ytensor (m, d): m points with d dimensions for which the probability density will be calculated
Xtensor (n, d), optional: n points with d dimensions to which KDE will be fit. Provided to allow batch calculations in log_prob. By default, X is None and all points used to initialize KernelDensityEstimator are included.

Returns

log_probstensor (m): log probability densities for each of the queried points in Y

class multipers.filtrations.density.KDE(bandwidth=1, kernel='gaussian', return_log=False)

Bases: object

Fast, scikit-style, and differentiable kernel density estimation, using PyKeops.

Parameters:

bandwidth (Any)
kernel (Literal['gaussian', 'exponential', 'exponential_kernel', 'multivariate_gaussian', 'sinc'] | ~collections.abc.Callable)
return_log (bool)

fit(X, sample_weights=None, y=None)

score_samples(Y, X=None, return_kernel=False)

Returns the kernel density estimates of each point in Y.

Parameters

Ytensor (m, d): m points with d dimensions for which the probability density will be calculated
Xtensor (n, d), optional: n points with d dimensions to which KDE will be fit. Provided to allow batch calculations in log_prob. By default, X is None and all points used to initialize KernelDensityEstimator are included.

Returns

log_probstensor (m): log probability densities for each of the queried points in Y

static to_lazy(X, Y, x_weights)

class multipers.filtrations.density.KNNmean(k, metric='euclidean')

Bases: object

Parameters:

k (int)
metric (str)

fit(x)

score_samples(x)

multipers.filtrations.density._kernel(kernel='gaussian')

Parameters:: kernel (Literal['gaussian', 'exponential', 'exponential_kernel', 'multivariate_gaussian', 'sinc'] | ~collections.abc.Callable)

multipers.filtrations.density._pts_convolution_pykeops(pts, pts_weights, grid_iterator, kernel='gaussian', bandwidth=0.1, **more_kde_args)

Pykeops convolution

Parameters:

pts (ndarray)
pts_weights (ndarray)
kernel (Literal['gaussian', 'exponential', 'exponential_kernel', 'multivariate_gaussian', 'sinc'] | ~collections.abc.Callable)

multipers.filtrations.density._pts_convolution_sparse_old(pts, pts_weights, grid_iterator, kernel='gaussian', bandwidth=0.1, **more_kde_args)

Old version of convolution_signed_measures. Scikitlearn’s convolution is slower than the code above.

Parameters:

pts (ndarray)
pts_weights (ndarray)
kernel (Literal['gaussian', 'exponential', 'exponential_kernel', 'multivariate_gaussian', 'sinc'] | ~collections.abc.Callable)

multipers.filtrations.density.batch_signed_measure_convolutions(signed_measures, x, bandwidth, kernel)

Input

signed_measures: unragged, of shape (num_data, num_pts, D+1) where last coord is weights, (0 for dummy points)

x : the points to convolve (num_x,D)

bandwidth : the bandwidths or covariance matrix inverse or … of the kernel

kernel : “gaussian”, “multivariate_gaussian”, “exponential”, or Callable (x_i, y_i, bandwidth)->float

Output

Array of shape (num_convolutions, (num_axis), num_data, Array of shape (num_convolutions, (num_axis), num_data, max_x_size)

Parameters:: kernel (Literal['gaussian', 'exponential', 'exponential_kernel', 'multivariate_gaussian', 'sinc'] | ~collections.abc.Callable)

multipers.filtrations.density.convolution_signed_measures(iterable_of_signed_measures, filtrations, bandwidth, flatten=True, n_jobs=1, backend='pykeops', kernel='gaussian', **kwargs)

Evaluates the convolution of the signed measures Iterable(pts, weights) with a gaussian measure of bandwidth bandwidth, on a grid given by the filtrations

Parameters

iterable_of_signed_measures : (num_signed_measure) x [ (npts) x (num_parameters), (npts)]

filtrations : (num_parameter) x (filtration values)

flatten : bool

n_jobs : int

Outputs

The concatenated images, for each signed measure (num_signed_measures) x (len(f) for f in filtration_values)

Parameters:

flatten (bool)
n_jobs (int)
kernel (Literal['gaussian', 'exponential', 'exponential_kernel', 'multivariate_gaussian', 'sinc'] | ~collections.abc.Callable)

multipers.filtrations.density.exponential_kernel(x_i, y_j, bandwidth)

multipers.filtrations.density.gaussian_kernel(x_i, y_j, bandwidth)

multipers.filtrations.density.multivariate_gaussian_kernel(x_i, y_j, covariance_matrix_inverse)

multipers.filtrations.density.sinc_kernel(x_i, y_j, bandwidth)

multipers.filtrations.filtrations module

multipers.filtrations.filtrations.CoreDelaunay(points, *, beta=1.0, ks=None, precision='safe', verbose=False, max_alpha_square=inf)

Computes the Delaunay core bifiltration of a point cloud presented in the paper “Core Bifiltration” https://arxiv.org/abs/2405.01214, and returns the (multi-critical) bifiltration as a SimplexTreeMulti. The Delaunay core bifiltration is an alpha complex version of the core bifiltration which is smaller in size. Moreover, along the horizontal line k=1, the Delaunay core bifiltration is identical to the alpha complex.

Input:

points: The point cloud as an ArrayLike of shape (n, d) where n is the number of points and d is the dimension of the points.
beta: The beta parameter for the Delaunay Core Bifiltration (default 1.0).
ks: The list of k-values to include in the bifiltration (default None). If None, the k-values are set to [1, 2, …, n] where n is the number of points in the point cloud. For large point clouds, it is recommended to set ks to a smaller list of k-values to reduce computation time. The values in ks must all be integers, positive, and less than or equal to the number of points in the point cloud.
precision: The precision of the computation of the AlphaComplex, one of [‘safe’, ‘exact’, ‘fast’] (default ‘safe’). See the GUDHI documentation for more information.
verbose: Whether to print progress messages (default False).
max_alpha_square: The maximum squared alpha value to consider when createing the alpha complex (default inf). See the GUDHI documentation for more information.

Parameters:

points (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])
beta (float)
ks (Sequence[int] | None)
precision (str)
verbose (bool)
max_alpha_square (float)

Return type:

multipers.filtrations.filtrations.Cubical(image, **slicer_kwargs)

Computes the cubical filtration of an image. The last axis dimention is interpreted as the number of parameters.

Input:

image: ArrayLike of shape (*image_resolution, num_parameters)
** args : specify non-default slicer parameters

Parameters:: image (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])

multipers.filtrations.filtrations.DegreeRips(*, points=None, distance_matrix=None, ks=None, threshold_radius=None): The DegreeRips filtration.

multipers.filtrations.filtrations.DelaunayCodensity(points, bandwidth=None, *, return_log=True, dtm_mass=None, kernel='gaussian', threshold_radius=None, reduce_degree=-1, vineyard=None, dtype=<class 'numpy.float64'>, verbose=False, clear=True, flagify=False)

TODO

Parameters:

points (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])
bandwidth (float | None)
return_log (bool)
dtm_mass (float | None)
kernel (Literal['gaussian', 'exponential', 'exponential_kernel', 'multivariate_gaussian', 'sinc'] | ~collections.abc.Callable)
threshold_radius (float | None)
reduce_degree (int)
vineyard (bool | None)
verbose (bool)
clear (bool)
flagify (bool)

multipers.filtrations.filtrations.DelaunayLowerstar(points, function, *, distance_matrix=None, threshold_radius=None, reduce_degree=-1, vineyard=None, dtype=<class 'numpy.float64'>, verbose=False, clear=True, flagify=False)

Computes the Function Delaunay bifiltration. Similar to RipsLowerstar, but most suited for low-dimensional euclidean data. See [Delaunay bifiltrations of functions on point clouds, Alonso et al] https://doi.org/10.1137/1.9781611977912.173

Input:

points or distance_matrix: ArrayLike
function : ArrayLike of shape (num_data, )
threshold_radius: max edge length of the rips. Defaults at min(max(distance_matrix, axis=1)).

Parameters:

points (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])
function (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])
distance_matrix (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None)
threshold_radius (float | None)
reduce_degree (int)
vineyard (bool | None)
verbose (bool)
clear (bool)
flagify (bool)

multipers.filtrations.filtrations.RipsCodensity(points, bandwidth=None, *, return_log=True, dtm_mass=None, kernel='gaussian', threshold_radius=None)

Computes the Rips density filtration.

Parameters:

points (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])
bandwidth (float | None)
return_log (bool)
dtm_mass (float | None)
kernel (Literal['gaussian', 'exponential', 'exponential_kernel', 'multivariate_gaussian', 'sinc'] | ~collections.abc.Callable)
threshold_radius (float | None)

multipers.filtrations.filtrations.RipsLowerstar(*, points=None, distance_matrix=None, function=None, threshold_radius=None)

Computes the Rips complex, with the usual rips filtration as a first parameter, and the lower star multi filtration as other parameter.

Input:

points or distance_matrix: ArrayLike
function : ArrayLike of shape (num_data, num_parameters -1)
threshold_radius: max edge length of the rips. Defaults at min(max(distance_matrix, axis=1)).

Parameters:

points (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None)
distance_matrix (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None)
function (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None)
threshold_radius (float | None)

Module contents

multipers.filtrations.CoreDelaunay(points, *, beta=1.0, ks=None, precision='safe', verbose=False, max_alpha_square=inf)

Computes the Delaunay core bifiltration of a point cloud presented in the paper “Core Bifiltration” https://arxiv.org/abs/2405.01214, and returns the (multi-critical) bifiltration as a SimplexTreeMulti. The Delaunay core bifiltration is an alpha complex version of the core bifiltration which is smaller in size. Moreover, along the horizontal line k=1, the Delaunay core bifiltration is identical to the alpha complex.

Input:

points: The point cloud as an ArrayLike of shape (n, d) where n is the number of points and d is the dimension of the points.
beta: The beta parameter for the Delaunay Core Bifiltration (default 1.0).
ks: The list of k-values to include in the bifiltration (default None). If None, the k-values are set to [1, 2, …, n] where n is the number of points in the point cloud. For large point clouds, it is recommended to set ks to a smaller list of k-values to reduce computation time. The values in ks must all be integers, positive, and less than or equal to the number of points in the point cloud.
precision: The precision of the computation of the AlphaComplex, one of [‘safe’, ‘exact’, ‘fast’] (default ‘safe’). See the GUDHI documentation for more information.
verbose: Whether to print progress messages (default False).
max_alpha_square: The maximum squared alpha value to consider when createing the alpha complex (default inf). See the GUDHI documentation for more information.

Parameters:

points (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])
beta (float)
ks (Sequence[int] | None)
precision (str)
verbose (bool)
max_alpha_square (float)

Return type:

multipers.filtrations.Cubical(image, **slicer_kwargs)

Computes the cubical filtration of an image. The last axis dimention is interpreted as the number of parameters.

Input:

image: ArrayLike of shape (*image_resolution, num_parameters)
** args : specify non-default slicer parameters

Parameters:: image (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])

multipers.filtrations.DegreeRips(*, points=None, distance_matrix=None, ks=None, threshold_radius=None): The DegreeRips filtration.

multipers.filtrations.DelaunayCodensity(points, bandwidth=None, *, return_log=True, dtm_mass=None, kernel='gaussian', threshold_radius=None, reduce_degree=-1, vineyard=None, dtype=<class 'numpy.float64'>, verbose=False, clear=True, flagify=False)

TODO

Parameters:

points (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])
bandwidth (float | None)
return_log (bool)
dtm_mass (float | None)
kernel (Literal['gaussian', 'exponential', 'exponential_kernel', 'multivariate_gaussian', 'sinc'] | ~collections.abc.Callable)
threshold_radius (float | None)
reduce_degree (int)
vineyard (bool | None)
verbose (bool)
clear (bool)
flagify (bool)

multipers.filtrations.DelaunayLowerstar(points, function, *, distance_matrix=None, threshold_radius=None, reduce_degree=-1, vineyard=None, dtype=<class 'numpy.float64'>, verbose=False, clear=True, flagify=False)

Computes the Function Delaunay bifiltration. Similar to RipsLowerstar, but most suited for low-dimensional euclidean data. See [Delaunay bifiltrations of functions on point clouds, Alonso et al] https://doi.org/10.1137/1.9781611977912.173

Input:

points or distance_matrix: ArrayLike
function : ArrayLike of shape (num_data, )
threshold_radius: max edge length of the rips. Defaults at min(max(distance_matrix, axis=1)).

Parameters:

points (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])
function (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])
distance_matrix (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None)
threshold_radius (float | None)
reduce_degree (int)
vineyard (bool | None)
verbose (bool)
clear (bool)
flagify (bool)

multipers.filtrations.RipsCodensity(points, bandwidth=None, *, return_log=True, dtm_mass=None, kernel='gaussian', threshold_radius=None)

Computes the Rips density filtration.

Parameters:

points (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes])
bandwidth (float | None)
return_log (bool)
dtm_mass (float | None)
kernel (Literal['gaussian', 'exponential', 'exponential_kernel', 'multivariate_gaussian', 'sinc'] | ~collections.abc.Callable)
threshold_radius (float | None)

multipers.filtrations.RipsLowerstar(*, points=None, distance_matrix=None, function=None, threshold_radius=None)

Computes the Rips complex, with the usual rips filtration as a first parameter, and the lower star multi filtration as other parameter.

Input:

points or distance_matrix: ArrayLike
function : ArrayLike of shape (num_data, num_parameters -1)
threshold_radius: max edge length of the rips. Defaults at min(max(distance_matrix, axis=1)).

Parameters:

points (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None)
distance_matrix (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None)
function (Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] | None)
threshold_radius (float | None)