diff options
Diffstat (limited to 'src/python/gudhi/representations')
| -rw-r--r-- | src/python/gudhi/representations/kernel_methods.py | 41 | ||||
| -rw-r--r-- | src/python/gudhi/representations/metrics.py | 71 | ||||
| -rw-r--r-- | src/python/gudhi/representations/preprocessing.py | 57 | ||||
| -rw-r--r-- | src/python/gudhi/representations/vector_methods.py | 563 |
4 files changed, 530 insertions, 202 deletions
diff --git a/src/python/gudhi/representations/kernel_methods.py b/src/python/gudhi/representations/kernel_methods.py index 596f4f07..23fd23c7 100644 --- a/src/python/gudhi/representations/kernel_methods.py +++ b/src/python/gudhi/representations/kernel_methods.py @@ -10,7 +10,7 @@ import numpy as np from sklearn.base import BaseEstimator, TransformerMixin from sklearn.metrics import pairwise_distances, pairwise_kernels -from .metrics import SlicedWassersteinDistance, PersistenceFisherDistance, _sklearn_wrapper, pairwise_persistence_diagram_distances, _sliced_wasserstein_distance, _persistence_fisher_distance +from .metrics import SlicedWassersteinDistance, PersistenceFisherDistance, _sklearn_wrapper, _pairwise, pairwise_persistence_diagram_distances, _sliced_wasserstein_distance, _persistence_fisher_distance from .preprocessing import Padding ############################################# @@ -60,7 +60,7 @@ def _persistence_scale_space_kernel(D1, D2, kernel_approx=None, bandwidth=1.): weight_pss = lambda x: 1 if x[1] >= x[0] else -1 return 0.5 * _persistence_weighted_gaussian_kernel(DD1, DD2, weight=weight_pss, kernel_approx=kernel_approx, bandwidth=bandwidth) -def pairwise_persistence_diagram_kernels(X, Y=None, kernel="sliced_wasserstein", **kwargs): +def pairwise_persistence_diagram_kernels(X, Y=None, kernel="sliced_wasserstein", n_jobs=None, **kwargs): """ This function computes the kernel matrix between two lists of persistence diagrams given as numpy arrays of shape (nx2). @@ -68,38 +68,41 @@ def pairwise_persistence_diagram_kernels(X, Y=None, kernel="sliced_wasserstein", X (list of n numpy arrays of shape (numx2)): first list of persistence diagrams. Y (list of m numpy arrays of shape (numx2)): second list of persistence diagrams (optional). If None, pairwise kernel values are computed from the first list only. kernel: kernel to use. It can be either a string ("sliced_wasserstein", "persistence_scale_space", "persistence_weighted_gaussian", "persistence_fisher") or a function taking two numpy arrays of shape (nx2) and (mx2) as inputs. If it is a function, make sure that it is symmetric. + n_jobs (int): number of jobs to use for the computation. This uses joblib.Parallel(prefer="threads"), so kernels that do not release the GIL may not scale unless run inside a `joblib.parallel_backend <https://joblib.readthedocs.io/en/latest/parallel.html#joblib.parallel_backend>`_ block. **kwargs: optional keyword parameters. Any further parameters are passed directly to the kernel function. See the docs of the various kernel classes in this module. Returns: numpy array of shape (nxm): kernel matrix. """ XX = np.reshape(np.arange(len(X)), [-1,1]) - YY = None if Y is None else np.reshape(np.arange(len(Y)), [-1,1]) + YY = None if Y is None or Y is X else np.reshape(np.arange(len(Y)), [-1,1]) if kernel == "sliced_wasserstein": - return np.exp(-pairwise_persistence_diagram_distances(X, Y, metric="sliced_wasserstein", num_directions=kwargs["num_directions"]) / kwargs["bandwidth"]) + return np.exp(-pairwise_persistence_diagram_distances(X, Y, metric="sliced_wasserstein", num_directions=kwargs["num_directions"], n_jobs=n_jobs) / kwargs["bandwidth"]) elif kernel == "persistence_fisher": - return np.exp(-pairwise_persistence_diagram_distances(X, Y, metric="persistence_fisher", kernel_approx=kwargs["kernel_approx"], bandwidth=kwargs["bandwidth"]) / kwargs["bandwidth_fisher"]) + return np.exp(-pairwise_persistence_diagram_distances(X, Y, metric="persistence_fisher", kernel_approx=kwargs["kernel_approx"], bandwidth=kwargs["bandwidth"], n_jobs=n_jobs) / kwargs["bandwidth_fisher"]) elif kernel == "persistence_scale_space": - return pairwise_kernels(XX, YY, metric=_sklearn_wrapper(_persistence_scale_space_kernel, X, Y, **kwargs)) + return _pairwise(pairwise_kernels, False, XX, YY, metric=_sklearn_wrapper(_persistence_scale_space_kernel, X, Y, **kwargs), n_jobs=n_jobs) elif kernel == "persistence_weighted_gaussian": - return pairwise_kernels(XX, YY, metric=_sklearn_wrapper(_persistence_weighted_gaussian_kernel, X, Y, **kwargs)) + return _pairwise(pairwise_kernels, False, XX, YY, metric=_sklearn_wrapper(_persistence_weighted_gaussian_kernel, X, Y, **kwargs), n_jobs=n_jobs) else: - return pairwise_kernels(XX, YY, metric=_sklearn_wrapper(metric, **kwargs)) + return _pairwise(pairwise_kernels, False, XX, YY, metric=_sklearn_wrapper(metric, **kwargs), n_jobs=n_jobs) class SlicedWassersteinKernel(BaseEstimator, TransformerMixin): """ This is a class for computing the sliced Wasserstein kernel matrix from a list of persistence diagrams. The sliced Wasserstein kernel is computed by exponentiating the corresponding sliced Wasserstein distance with a Gaussian kernel. See http://proceedings.mlr.press/v70/carriere17a.html for more details. """ - def __init__(self, num_directions=10, bandwidth=1.0): + def __init__(self, num_directions=10, bandwidth=1.0, n_jobs=None): """ Constructor for the SlicedWassersteinKernel class. Parameters: bandwidth (double): bandwidth of the Gaussian kernel applied to the sliced Wasserstein distance (default 1.). num_directions (int): number of lines evenly sampled from [-pi/2,pi/2] in order to approximate and speed up the kernel computation (default 10). + n_jobs (int): number of jobs to use for the computation. See :func:`pairwise_persistence_diagram_kernels` for details. """ self.bandwidth = bandwidth self.num_directions = num_directions + self.n_jobs = n_jobs def fit(self, X, y=None): """ @@ -122,7 +125,7 @@ class SlicedWassersteinKernel(BaseEstimator, TransformerMixin): Returns: numpy array of shape (number of diagrams in **diagrams**) x (number of diagrams in X): matrix of pairwise sliced Wasserstein kernel values. """ - return pairwise_persistence_diagram_kernels(X, self.diagrams_, kernel="sliced_wasserstein", bandwidth=self.bandwidth, num_directions=self.num_directions) + return pairwise_persistence_diagram_kernels(X, self.diagrams_, kernel="sliced_wasserstein", bandwidth=self.bandwidth, num_directions=self.num_directions, n_jobs=self.n_jobs) def __call__(self, diag1, diag2): """ @@ -141,7 +144,7 @@ class PersistenceWeightedGaussianKernel(BaseEstimator, TransformerMixin): """ This is a class for computing the persistence weighted Gaussian kernel matrix from a list of persistence diagrams. The persistence weighted Gaussian kernel is computed by convolving the persistence diagram points with weighted Gaussian kernels. See http://proceedings.mlr.press/v48/kusano16.html for more details. """ - def __init__(self, bandwidth=1., weight=lambda x: 1, kernel_approx=None): + def __init__(self, bandwidth=1., weight=lambda x: 1, kernel_approx=None, n_jobs=None): """ Constructor for the PersistenceWeightedGaussianKernel class. @@ -149,9 +152,11 @@ class PersistenceWeightedGaussianKernel(BaseEstimator, TransformerMixin): bandwidth (double): bandwidth of the Gaussian kernel with which persistence diagrams will be convolved (default 1.) weight (function): weight function for the persistence diagram points (default constant function, ie lambda x: 1). This function must be defined on 2D points, ie lists or numpy arrays of the form [p_x,p_y]. kernel_approx (class): kernel approximation class used to speed up computation (default None). Common kernel approximations classes can be found in the scikit-learn library (such as RBFSampler for instance). + n_jobs (int): number of jobs to use for the computation. See :func:`pairwise_persistence_diagram_kernels` for details. """ self.bandwidth, self.weight = bandwidth, weight self.kernel_approx = kernel_approx + self.n_jobs = n_jobs def fit(self, X, y=None): """ @@ -174,7 +179,7 @@ class PersistenceWeightedGaussianKernel(BaseEstimator, TransformerMixin): Returns: numpy array of shape (number of diagrams in **diagrams**) x (number of diagrams in X): matrix of pairwise persistence weighted Gaussian kernel values. """ - return pairwise_persistence_diagram_kernels(X, self.diagrams_, kernel="persistence_weighted_gaussian", bandwidth=self.bandwidth, weight=self.weight, kernel_approx=self.kernel_approx) + return pairwise_persistence_diagram_kernels(X, self.diagrams_, kernel="persistence_weighted_gaussian", bandwidth=self.bandwidth, weight=self.weight, kernel_approx=self.kernel_approx, n_jobs=self.n_jobs) def __call__(self, diag1, diag2): """ @@ -193,15 +198,17 @@ class PersistenceScaleSpaceKernel(BaseEstimator, TransformerMixin): """ This is a class for computing the persistence scale space kernel matrix from a list of persistence diagrams. The persistence scale space kernel is computed by adding the symmetric to the diagonal of each point in each persistence diagram, with negative weight, and then convolving the points with a Gaussian kernel. See https://www.cv-foundation.org/openaccess/content_cvpr_2015/papers/Reininghaus_A_Stable_Multi-Scale_2015_CVPR_paper.pdf for more details. """ - def __init__(self, bandwidth=1., kernel_approx=None): + def __init__(self, bandwidth=1., kernel_approx=None, n_jobs=None): """ Constructor for the PersistenceScaleSpaceKernel class. Parameters: bandwidth (double): bandwidth of the Gaussian kernel with which persistence diagrams will be convolved (default 1.) kernel_approx (class): kernel approximation class used to speed up computation (default None). Common kernel approximations classes can be found in the scikit-learn library (such as RBFSampler for instance). + n_jobs (int): number of jobs to use for the computation. See :func:`pairwise_persistence_diagram_kernels` for details. """ self.bandwidth, self.kernel_approx = bandwidth, kernel_approx + self.n_jobs = n_jobs def fit(self, X, y=None): """ @@ -224,7 +231,7 @@ class PersistenceScaleSpaceKernel(BaseEstimator, TransformerMixin): Returns: numpy array of shape (number of diagrams in **diagrams**) x (number of diagrams in X): matrix of pairwise persistence scale space kernel values. """ - return pairwise_persistence_diagram_kernels(X, self.diagrams_, kernel="persistence_scale_space", bandwidth=self.bandwidth, kernel_approx=self.kernel_approx) + return pairwise_persistence_diagram_kernels(X, self.diagrams_, kernel="persistence_scale_space", bandwidth=self.bandwidth, kernel_approx=self.kernel_approx, n_jobs=self.n_jobs) def __call__(self, diag1, diag2): """ @@ -243,7 +250,7 @@ class PersistenceFisherKernel(BaseEstimator, TransformerMixin): """ This is a class for computing the persistence Fisher kernel matrix from a list of persistence diagrams. The persistence Fisher kernel is computed by exponentiating the corresponding persistence Fisher distance with a Gaussian kernel. See papers.nips.cc/paper/8205-persistence-fisher-kernel-a-riemannian-manifold-kernel-for-persistence-diagrams for more details. """ - def __init__(self, bandwidth_fisher=1., bandwidth=1., kernel_approx=None): + def __init__(self, bandwidth_fisher=1., bandwidth=1., kernel_approx=None, n_jobs=None): """ Constructor for the PersistenceFisherKernel class. @@ -251,9 +258,11 @@ class PersistenceFisherKernel(BaseEstimator, TransformerMixin): bandwidth (double): bandwidth of the Gaussian kernel applied to the persistence Fisher distance (default 1.). bandwidth_fisher (double): bandwidth of the Gaussian kernel used to turn persistence diagrams into probability distributions by PersistenceFisherDistance class (default 1.). kernel_approx (class): kernel approximation class used to speed up computation (default None). Common kernel approximations classes can be found in the scikit-learn library (such as RBFSampler for instance). + n_jobs (int): number of jobs to use for the computation. See :func:`pairwise_persistence_diagram_kernels` for details. """ self.bandwidth = bandwidth self.bandwidth_fisher, self.kernel_approx = bandwidth_fisher, kernel_approx + self.n_jobs = n_jobs def fit(self, X, y=None): """ @@ -276,7 +285,7 @@ class PersistenceFisherKernel(BaseEstimator, TransformerMixin): Returns: numpy array of shape (number of diagrams in **diagrams**) x (number of diagrams in X): matrix of pairwise persistence Fisher kernel values. """ - return pairwise_persistence_diagram_kernels(X, self.diagrams_, kernel="persistence_fisher", bandwidth=self.bandwidth, bandwidth_fisher=self.bandwidth_fisher, kernel_approx=self.kernel_approx) + return pairwise_persistence_diagram_kernels(X, self.diagrams_, kernel="persistence_fisher", bandwidth=self.bandwidth, bandwidth_fisher=self.bandwidth_fisher, kernel_approx=self.kernel_approx, n_jobs=self.n_jobs) def __call__(self, diag1, diag2): """ diff --git a/src/python/gudhi/representations/metrics.py b/src/python/gudhi/representations/metrics.py index 8a32f7e9..142ddef1 100644 --- a/src/python/gudhi/representations/metrics.py +++ b/src/python/gudhi/representations/metrics.py @@ -12,6 +12,7 @@ from sklearn.base import BaseEstimator, TransformerMixin from sklearn.metrics import pairwise_distances from gudhi.hera import wasserstein_distance as hera_wasserstein_distance from .preprocessing import Padding +from joblib import Parallel, delayed ############################################# # Metrics ################################### @@ -116,6 +117,20 @@ def _persistence_fisher_distance(D1, D2, kernel_approx=None, bandwidth=1.): vectorj = vectorj/vectorj_sum return np.arccos( min(np.dot(np.sqrt(vectori), np.sqrt(vectorj)), 1.) ) +def _pairwise(fallback, skipdiag, X, Y, metric, n_jobs): + if Y is not None: + return fallback(X, Y, metric=metric, n_jobs=n_jobs) + triu = np.triu_indices(len(X), k=skipdiag) + tril = (triu[1], triu[0]) + par = Parallel(n_jobs=n_jobs, prefer="threads") + d = par(delayed(metric)([triu[0][i]], [triu[1][i]]) for i in range(len(triu[0]))) + m = np.empty((len(X), len(X))) + m[triu] = d + m[tril] = d + if skipdiag: + np.fill_diagonal(m, 0) + return m + def _sklearn_wrapper(metric, X, Y, **kwargs): """ This function is a wrapper for any metric between two persistence diagrams that takes two numpy arrays of shapes (nx2) and (mx2) as arguments. @@ -134,7 +149,7 @@ PAIRWISE_DISTANCE_FUNCTIONS = { "persistence_fisher": _persistence_fisher_distance, } -def pairwise_persistence_diagram_distances(X, Y=None, metric="bottleneck", **kwargs): +def pairwise_persistence_diagram_distances(X, Y=None, metric="bottleneck", n_jobs=None, **kwargs): """ This function computes the distance matrix between two lists of persistence diagrams given as numpy arrays of shape (nx2). @@ -142,48 +157,51 @@ def pairwise_persistence_diagram_distances(X, Y=None, metric="bottleneck", **kwa X (list of n numpy arrays of shape (numx2)): first list of persistence diagrams. Y (list of m numpy arrays of shape (numx2)): second list of persistence diagrams (optional). If None, pairwise distances are computed from the first list only. metric: distance to use. It can be either a string ("sliced_wasserstein", "wasserstein", "hera_wasserstein" (Wasserstein distance computed with Hera---note that Hera is also used for the default option "wasserstein"), "pot_wasserstein" (Wasserstein distance computed with POT), "bottleneck", "persistence_fisher") or a function taking two numpy arrays of shape (nx2) and (mx2) as inputs. If it is a function, make sure that it is symmetric and that it outputs 0 if called on the same two arrays. + n_jobs (int): number of jobs to use for the computation. This uses joblib.Parallel(prefer="threads"), so metrics that do not release the GIL may not scale unless run inside a `joblib.parallel_backend <https://joblib.readthedocs.io/en/latest/parallel.html#joblib.parallel_backend>`_ block. **kwargs: optional keyword parameters. Any further parameters are passed directly to the distance function. See the docs of the various distance classes in this module. Returns: numpy array of shape (nxm): distance matrix """ XX = np.reshape(np.arange(len(X)), [-1,1]) - YY = None if Y is None else np.reshape(np.arange(len(Y)), [-1,1]) + YY = None if Y is None or Y is X else np.reshape(np.arange(len(Y)), [-1,1]) if metric == "bottleneck": try: from .. import bottleneck_distance - return pairwise_distances(XX, YY, metric=_sklearn_wrapper(bottleneck_distance, X, Y, **kwargs)) + return _pairwise(pairwise_distances, True, XX, YY, metric=_sklearn_wrapper(bottleneck_distance, X, Y, **kwargs), n_jobs=n_jobs) except ImportError: print("Gudhi built without CGAL") raise elif metric == "pot_wasserstein": try: from gudhi.wasserstein import wasserstein_distance as pot_wasserstein_distance - return pairwise_distances(XX, YY, metric=_sklearn_wrapper(pot_wasserstein_distance, X, Y, **kwargs)) + return _pairwise(pairwise_distances, True, XX, YY, metric=_sklearn_wrapper(pot_wasserstein_distance, X, Y, **kwargs), n_jobs=n_jobs) except ImportError: print("POT (Python Optimal Transport) is not installed. Please install POT or use metric='wasserstein' or metric='hera_wasserstein'") raise elif metric == "sliced_wasserstein": Xproj = _compute_persistence_diagram_projections(X, **kwargs) Yproj = None if Y is None else _compute_persistence_diagram_projections(Y, **kwargs) - return pairwise_distances(XX, YY, metric=_sklearn_wrapper(_sliced_wasserstein_distance_on_projections, Xproj, Yproj)) + return _pairwise(pairwise_distances, True, XX, YY, metric=_sklearn_wrapper(_sliced_wasserstein_distance_on_projections, Xproj, Yproj), n_jobs=n_jobs) elif type(metric) == str: - return pairwise_distances(XX, YY, metric=_sklearn_wrapper(PAIRWISE_DISTANCE_FUNCTIONS[metric], X, Y, **kwargs)) + return _pairwise(pairwise_distances, True, XX, YY, metric=_sklearn_wrapper(PAIRWISE_DISTANCE_FUNCTIONS[metric], X, Y, **kwargs), n_jobs=n_jobs) else: - return pairwise_distances(XX, YY, metric=_sklearn_wrapper(metric, X, Y, **kwargs)) + return _pairwise(pairwise_distances, True, XX, YY, metric=_sklearn_wrapper(metric, X, Y, **kwargs), n_jobs=n_jobs) class SlicedWassersteinDistance(BaseEstimator, TransformerMixin): """ This is a class for computing the sliced Wasserstein distance matrix from a list of persistence diagrams. The Sliced Wasserstein distance is computed by projecting the persistence diagrams onto lines, comparing the projections with the 1-norm, and finally integrating over all possible lines. See http://proceedings.mlr.press/v70/carriere17a.html for more details. """ - def __init__(self, num_directions=10): + def __init__(self, num_directions=10, n_jobs=None): """ Constructor for the SlicedWassersteinDistance class. Parameters: num_directions (int): number of lines evenly sampled from [-pi/2,pi/2] in order to approximate and speed up the distance computation (default 10). + n_jobs (int): number of jobs to use for the computation. See :func:`pairwise_persistence_diagram_distances` for details. """ self.num_directions = num_directions + self.n_jobs = n_jobs def fit(self, X, y=None): """ @@ -206,7 +224,7 @@ class SlicedWassersteinDistance(BaseEstimator, TransformerMixin): Returns: numpy array of shape (number of diagrams in **diagrams**) x (number of diagrams in X): matrix of pairwise sliced Wasserstein distances. """ - return pairwise_persistence_diagram_distances(X, self.diagrams_, metric="sliced_wasserstein", num_directions=self.num_directions) + return pairwise_persistence_diagram_distances(X, self.diagrams_, metric="sliced_wasserstein", num_directions=self.num_directions, n_jobs=self.n_jobs) def __call__(self, diag1, diag2): """ @@ -227,14 +245,16 @@ class BottleneckDistance(BaseEstimator, TransformerMixin): :Requires: `CGAL <installation.html#cgal>`_ :math:`\geq` 4.11.0 """ - def __init__(self, epsilon=None): + def __init__(self, epsilon=None, n_jobs=None): """ Constructor for the BottleneckDistance class. Parameters: epsilon (double): absolute (additive) error tolerated on the distance (default is the smallest positive float), see :func:`gudhi.bottleneck_distance`. + n_jobs (int): number of jobs to use for the computation. See :func:`pairwise_persistence_diagram_distances` for details. """ self.epsilon = epsilon + self.n_jobs = n_jobs def fit(self, X, y=None): """ @@ -257,7 +277,7 @@ class BottleneckDistance(BaseEstimator, TransformerMixin): Returns: numpy array of shape (number of diagrams in **diagrams**) x (number of diagrams in X): matrix of pairwise bottleneck distances. """ - Xfit = pairwise_persistence_diagram_distances(X, self.diagrams_, metric="bottleneck", e=self.epsilon) + Xfit = pairwise_persistence_diagram_distances(X, self.diagrams_, metric="bottleneck", e=self.epsilon, n_jobs=self.n_jobs) return Xfit def __call__(self, diag1, diag2): @@ -282,15 +302,17 @@ class PersistenceFisherDistance(BaseEstimator, TransformerMixin): """ This is a class for computing the persistence Fisher distance matrix from a list of persistence diagrams. The persistence Fisher distance is obtained by computing the original Fisher distance between the probability distributions associated to the persistence diagrams given by convolving them with a Gaussian kernel. See http://papers.nips.cc/paper/8205-persistence-fisher-kernel-a-riemannian-manifold-kernel-for-persistence-diagrams for more details. """ - def __init__(self, bandwidth=1., kernel_approx=None): + def __init__(self, bandwidth=1., kernel_approx=None, n_jobs=None): """ Constructor for the PersistenceFisherDistance class. Parameters: bandwidth (double): bandwidth of the Gaussian kernel used to turn persistence diagrams into probability distributions (default 1.). kernel_approx (class): kernel approximation class used to speed up computation (default None). Common kernel approximations classes can be found in the scikit-learn library (such as RBFSampler for instance). + n_jobs (int): number of jobs to use for the computation. See :func:`pairwise_persistence_diagram_distances` for details. """ self.bandwidth, self.kernel_approx = bandwidth, kernel_approx + self.n_jobs = n_jobs def fit(self, X, y=None): """ @@ -313,7 +335,7 @@ class PersistenceFisherDistance(BaseEstimator, TransformerMixin): Returns: numpy array of shape (number of diagrams in **diagrams**) x (number of diagrams in X): matrix of pairwise persistence Fisher distances. """ - return pairwise_persistence_diagram_distances(X, self.diagrams_, metric="persistence_fisher", bandwidth=self.bandwidth, kernel_approx=self.kernel_approx) + return pairwise_persistence_diagram_distances(X, self.diagrams_, metric="persistence_fisher", bandwidth=self.bandwidth, kernel_approx=self.kernel_approx, n_jobs=self.n_jobs) def __call__(self, diag1, diag2): """ @@ -328,23 +350,32 @@ class PersistenceFisherDistance(BaseEstimator, TransformerMixin): """ return _persistence_fisher_distance(diag1, diag2, bandwidth=self.bandwidth, kernel_approx=self.kernel_approx) + class WassersteinDistance(BaseEstimator, TransformerMixin): """ This is a class for computing the Wasserstein distance matrix from a list of persistence diagrams. """ - def __init__(self, order=2, internal_p=2, mode="pot", delta=0.01): + + def __init__(self, order=1, internal_p=np.inf, mode="hera", delta=0.01, n_jobs=None): """ Constructor for the WassersteinDistance class. Parameters: - order (int): exponent for Wasserstein, default value is 2., see :func:`gudhi.wasserstein.wasserstein_distance`. - internal_p (int): ground metric on the (upper-half) plane (i.e. norm l_p in R^2), default value is 2 (euclidean norm), see :func:`gudhi.wasserstein.wasserstein_distance`. - mode (str): method for computing Wasserstein distance. Either "pot" or "hera". + order (int): exponent for Wasserstein, default value is 1., see :func:`gudhi.wasserstein.wasserstein_distance`. + internal_p (int): ground metric on the (upper-half) plane (i.e. norm l_p in R^2), default value is `np.inf`, see :func:`gudhi.wasserstein.wasserstein_distance`. + mode (str): method for computing Wasserstein distance. Either "pot" or "hera". Default set to "hera". delta (float): relative error 1+delta. Used only if mode == "hera". + n_jobs (int): number of jobs to use for the computation. See :func:`pairwise_persistence_diagram_distances` for details. """ self.order, self.internal_p, self.mode = order, internal_p, mode - self.metric = "pot_wasserstein" if mode == "pot" else "hera_wasserstein" + if mode == "pot": + self.metric = "pot_wasserstein" + elif mode == "hera": + self.metric = "hera_wasserstein" + else: + raise NameError("Unknown mode. Current available values for mode are 'hera' and 'pot'") self.delta = delta + self.n_jobs = n_jobs def fit(self, X, y=None): """ @@ -368,9 +399,9 @@ class WassersteinDistance(BaseEstimator, TransformerMixin): numpy array of shape (number of diagrams in **diagrams**) x (number of diagrams in X): matrix of pairwise Wasserstein distances. """ if self.metric == "hera_wasserstein": - Xfit = pairwise_persistence_diagram_distances(X, self.diagrams_, metric=self.metric, order=self.order, internal_p=self.internal_p, delta=self.delta) + Xfit = pairwise_persistence_diagram_distances(X, self.diagrams_, metric=self.metric, order=self.order, internal_p=self.internal_p, delta=self.delta, n_jobs=self.n_jobs) else: - Xfit = pairwise_persistence_diagram_distances(X, self.diagrams_, metric=self.metric, order=self.order, internal_p=self.internal_p, matching=False) + Xfit = pairwise_persistence_diagram_distances(X, self.diagrams_, metric=self.metric, order=self.order, internal_p=self.internal_p, matching=False, n_jobs=self.n_jobs) return Xfit def __call__(self, diag1, diag2): diff --git a/src/python/gudhi/representations/preprocessing.py b/src/python/gudhi/representations/preprocessing.py index a8545349..8722e162 100644 --- a/src/python/gudhi/representations/preprocessing.py +++ b/src/python/gudhi/representations/preprocessing.py @@ -1,10 +1,11 @@ # This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. # See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. -# Author(s): Mathieu Carrière +# Author(s): Mathieu Carrière, Vincent Rouvreau # # Copyright (C) 2018-2019 Inria # # Modification(s): +# - 2021/10 Vincent Rouvreau: Add DimensionSelector # - YYYY/MM Author: Description of the modification import numpy as np @@ -75,7 +76,7 @@ class Clamping(BaseEstimator, TransformerMixin): Constructor for the Clamping class. Parameters: - limit (double): clamping value (default np.inf). + limit (float): clamping value (default np.inf). """ self.minimum = minimum self.maximum = maximum @@ -234,7 +235,7 @@ class ProminentPoints(BaseEstimator, TransformerMixin): use (bool): whether to use the class or not (default False). location (string): either "upper" or "lower" (default "upper"). Whether to keep the points that are far away ("upper") or close ("lower") to the diagonal. num_pts (int): cardinality threshold (default 10). If location == "upper", keep the top **num_pts** points that are the farthest away from the diagonal. If location == "lower", keep the top **num_pts** points that are the closest to the diagonal. - threshold (double): distance-to-diagonal threshold (default -1). If location == "upper", keep the points that are at least at a distance **threshold** from the diagonal. If location == "lower", keep the points that are at most at a distance **threshold** from the diagonal. + threshold (float): distance-to-diagonal threshold (default -1). If location == "upper", keep the points that are at least at a distance **threshold** from the diagonal. If location == "lower", keep the points that are at most at a distance **threshold** from the diagonal. """ self.num_pts = num_pts self.threshold = threshold @@ -317,7 +318,7 @@ class DiagramSelector(BaseEstimator, TransformerMixin): Parameters: use (bool): whether to use the class or not (default False). - limit (double): second coordinate value that is the criterion for being an essential point (default numpy.inf). + limit (float): second coordinate value that is the criterion for being an essential point (default numpy.inf). point_type (string): either "finite" or "essential". The type of the points that are going to be extracted. """ self.use, self.limit, self.point_type = use, limit, point_type @@ -363,3 +364,51 @@ class DiagramSelector(BaseEstimator, TransformerMixin): n x 2 numpy array: extracted persistence diagram. """ return self.fit_transform([diag])[0] + + +# Mermaid sequence diagram - https://mermaid-js.github.io/mermaid-live-editor/ +# sequenceDiagram +# USER->>DimensionSelector: fit_transform(<br/>[[array( Hi(X0) ), array( Hj(X0) ), ...],<br/> [array( Hi(X1) ), array( Hj(X1) ), ...],<br/> ...]) +# DimensionSelector->>thread1: _transform([array( Hi(X0) ), array( Hj(X0) )], ...) +# DimensionSelector->>thread2: _transform([array( Hi(X1) ), array( Hj(X1) )], ...) +# Note right of DimensionSelector: ... +# thread1->>DimensionSelector: array( Hn(X0) ) +# thread2->>DimensionSelector: array( Hn(X1) ) +# Note right of DimensionSelector: ... +# DimensionSelector->>USER: [array( Hn(X0) ), <br/> array( Hn(X1) ), <br/> ...] + +class DimensionSelector(BaseEstimator, TransformerMixin): + """ + This is a class to select persistence diagrams in a specific dimension from its index. + """ + + def __init__(self, index=0): + """ + Constructor for the DimensionSelector class. + + Parameters: + index (int): The returned persistence diagrams dimension index. Default value is `0`. + """ + self.index = index + + def fit(self, X, Y=None): + """ + Nothing to be done, but useful when included in a scikit-learn Pipeline. + """ + return self + + def transform(self, X, Y=None): + """ + Select persistence diagrams from its dimension. + + Parameters: + X (list of list of tuple): List of list of persistence pairs, i.e. + `[[array( Hi(X0) ), array( Hj(X0) ), ...], [array( Hi(X1) ), array( Hj(X1) ), ...], ...]` + + Returns: + list of tuple: + Persistence diagrams in a specific dimension. i.e. if `index` was set to `m` and `Hn` is at index `m` of + the input, it returns `[array( Hn(X0) ), array( Hn(X1), ...]` + """ + + return [persistence[self.index] for persistence in X] diff --git a/src/python/gudhi/representations/vector_methods.py b/src/python/gudhi/representations/vector_methods.py index 46fee086..ce74aee5 100644 --- a/src/python/gudhi/representations/vector_methods.py +++ b/src/python/gudhi/representations/vector_methods.py @@ -1,16 +1,25 @@ # This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT. # See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details. -# Author(s): Mathieu Carrière +# Author(s): Mathieu Carrière, Martin Royer, Gard Spreemann # -# Copyright (C) 2018-2019 Inria +# Copyright (C) 2018-2020 Inria # # Modification(s): -# - YYYY/MM Author: Description of the modification +# - 2020/06 Martin: ATOL integration +# - 2020/12 Gard: A more flexible Betti curve class capable of computing exact curves. +# - 2021/11 Vincent Rouvreau: factorize _automatic_sample_range import numpy as np from sklearn.base import BaseEstimator, TransformerMixin +from sklearn.exceptions import NotFittedError from sklearn.preprocessing import MinMaxScaler, MaxAbsScaler -from sklearn.neighbors import DistanceMetric +from sklearn.metrics import pairwise +try: + # New location since 1.0 + from sklearn.metrics import DistanceMetric +except ImportError: + # Will be removed in 1.3 + from sklearn.neighbors import DistanceMetric from .preprocessing import DiagramScaler, BirthPersistenceTransform @@ -44,10 +53,14 @@ class PersistenceImage(BaseEstimator, TransformerMixin): y (n x 1 array): persistence diagram labels (unused). """ if np.isnan(np.array(self.im_range)).any(): - new_X = BirthPersistenceTransform().fit_transform(X) - pre = DiagramScaler(use=True, scalers=[([0], MinMaxScaler()), ([1], MinMaxScaler())]).fit(new_X,y) - [mx,my],[Mx,My] = [pre.scalers[0][1].data_min_[0], pre.scalers[1][1].data_min_[0]], [pre.scalers[0][1].data_max_[0], pre.scalers[1][1].data_max_[0]] - self.im_range = np.where(np.isnan(np.array(self.im_range)), np.array([mx, Mx, my, My]), np.array(self.im_range)) + try: + new_X = BirthPersistenceTransform().fit_transform(X) + pre = DiagramScaler(use=True, scalers=[([0], MinMaxScaler()), ([1], MinMaxScaler())]).fit(new_X,y) + [mx,my],[Mx,My] = [pre.scalers[0][1].data_min_[0], pre.scalers[1][1].data_min_[0]], [pre.scalers[0][1].data_max_[0], pre.scalers[1][1].data_max_[0]] + self.im_range = np.where(np.isnan(np.array(self.im_range)), np.array([mx, Mx, my, My]), np.array(self.im_range)) + except ValueError: + # Empty persistence diagram case - https://github.com/GUDHI/gudhi-devel/issues/507 + pass return self def transform(self, X): @@ -77,7 +90,7 @@ class PersistenceImage(BaseEstimator, TransformerMixin): Xfit.append(image.flatten()[np.newaxis,:]) - Xfit = np.concatenate(Xfit,0) + Xfit = np.concatenate(Xfit, 0) return Xfit @@ -93,11 +106,57 @@ class PersistenceImage(BaseEstimator, TransformerMixin): """ return self.fit_transform([diag])[0,:] +def _automatic_sample_range(sample_range, X): + """ + Compute and returns sample range from the persistence diagrams if one of the sample_range values is numpy.nan. + + Parameters: + sample_range (a numpy array of 2 float): minimum and maximum of all piecewise-linear function domains, of + the form [x_min, x_max]. + X (list of n x 2 numpy arrays): input persistence diagrams. + y (n x 1 array): persistence diagram labels (unused). + """ + nan_in_range = np.isnan(sample_range) + if nan_in_range.any(): + try: + pre = DiagramScaler(use=True, scalers=[([0], MinMaxScaler()), ([1], MinMaxScaler())]).fit(X) + [mx,my] = [pre.scalers[0][1].data_min_[0], pre.scalers[1][1].data_min_[0]] + [Mx,My] = [pre.scalers[0][1].data_max_[0], pre.scalers[1][1].data_max_[0]] + return np.where(nan_in_range, np.array([mx, My]), sample_range) + except ValueError: + # Empty persistence diagram case - https://github.com/GUDHI/gudhi-devel/issues/507 + pass + return sample_range + + +def _trim_endpoints(x, are_endpoints_nan): + if are_endpoints_nan[0]: + x = x[1:] + if are_endpoints_nan[1]: + x = x[:-1] + return x + + +def _grid_from_sample_range(self, X): + sample_range = np.array(self.sample_range) + self.nan_in_range = np.isnan(sample_range) + self.new_resolution = self.resolution + if not self.keep_endpoints: + self.new_resolution += self.nan_in_range.sum() + self.sample_range_fixed = _automatic_sample_range(sample_range, X) + self.grid_ = np.linspace(self.sample_range_fixed[0], self.sample_range_fixed[1], self.new_resolution) + if not self.keep_endpoints: + self.grid_ = _trim_endpoints(self.grid_, self.nan_in_range) + + class Landscape(BaseEstimator, TransformerMixin): """ This is a class for computing persistence landscapes from a list of persistence diagrams. A persistence landscape is a collection of 1D piecewise-linear functions computed from the rank function associated to the persistence diagram. These piecewise-linear functions are then sampled evenly on a given range and the corresponding vectors of samples are concatenated and returned. See http://jmlr.org/papers/v16/bubenik15a.html for more details. + + Attributes: + grid_ (1d array): The grid on which the landscapes are computed. """ - def __init__(self, num_landscapes=5, resolution=100, sample_range=[np.nan, np.nan]): + def __init__(self, num_landscapes=5, resolution=100, sample_range=[np.nan, np.nan], *, keep_endpoints=False): """ Constructor for the Landscape class. @@ -105,10 +164,10 @@ class Landscape(BaseEstimator, TransformerMixin): num_landscapes (int): number of piecewise-linear functions to output (default 5). resolution (int): number of sample for all piecewise-linear functions (default 100). sample_range ([double, double]): minimum and maximum of all piecewise-linear function domains, of the form [x_min, x_max] (default [numpy.nan, numpy.nan]). It is the interval on which samples will be drawn evenly. If one of the values is numpy.nan, it can be computed from the persistence diagrams with the fit() method. + keep_endpoints (bool): when computing `sample_range`, use the exact extremities (where the value is always 0). This is mostly useful for plotting, the default is to use a slightly smaller range. """ self.num_landscapes, self.resolution, self.sample_range = num_landscapes, resolution, sample_range - self.nan_in_range = np.isnan(np.array(self.sample_range)) - self.new_resolution = self.resolution + self.nan_in_range.sum() + self.keep_endpoints = keep_endpoints def fit(self, X, y=None): """ @@ -118,10 +177,7 @@ class Landscape(BaseEstimator, TransformerMixin): X (list of n x 2 numpy arrays): input persistence diagrams. y (n x 1 array): persistence diagram labels (unused). """ - if self.nan_in_range.any(): - pre = DiagramScaler(use=True, scalers=[([0], MinMaxScaler()), ([1], MinMaxScaler())]).fit(X,y) - [mx,my],[Mx,My] = [pre.scalers[0][1].data_min_[0], pre.scalers[1][1].data_min_[0]], [pre.scalers[0][1].data_max_[0], pre.scalers[1][1].data_max_[0]] - self.sample_range = np.where(self.nan_in_range, np.array([mx, My]), np.array(self.sample_range)) + _grid_from_sample_range(self, X) return self def transform(self, X): @@ -134,53 +190,26 @@ class Landscape(BaseEstimator, TransformerMixin): Returns: numpy array with shape (number of diagrams) x (number of samples = **num_landscapes** x **resolution**): output persistence landscapes. """ - num_diag, Xfit = len(X), [] - x_values = np.linspace(self.sample_range[0], self.sample_range[1], self.new_resolution) - step_x = x_values[1] - x_values[0] - - for i in range(num_diag): - - diagram, num_pts_in_diag = X[i], X[i].shape[0] - ls = np.zeros([self.num_landscapes, self.new_resolution]) + Xfit = [] + x_values = self.grid_ + for diag in X: + midpoints, heights = (diag[:, 0] + diag[:, 1]) / 2., (diag[:, 1] - diag[:, 0]) / 2. + tent_functions = np.maximum(heights[None, :] - np.abs(x_values[:, None] - midpoints[None, :]), 0) + n_points = diag.shape[0] + # Complete the array with zeros to get the right number of landscapes + if self.num_landscapes > n_points: + tent_functions = np.concatenate( + [tent_functions, np.zeros((tent_functions.shape[0], self.num_landscapes-n_points))], + axis=1 + ) + tent_functions.partition(tent_functions.shape[1]-self.num_landscapes, axis=1) + landscapes = np.sort(tent_functions[:, -self.num_landscapes:], axis=1)[:, ::-1].T - events = [] - for j in range(self.new_resolution): - events.append([]) + landscapes = np.sqrt(2) * np.ravel(landscapes) + Xfit.append(landscapes) - for j in range(num_pts_in_diag): - [px,py] = diagram[j,:2] - min_idx = np.clip(np.ceil((px - self.sample_range[0]) / step_x).astype(int), 0, self.new_resolution) - mid_idx = np.clip(np.ceil((0.5*(py+px) - self.sample_range[0]) / step_x).astype(int), 0, self.new_resolution) - max_idx = np.clip(np.ceil((py - self.sample_range[0]) / step_x).astype(int), 0, self.new_resolution) - - if min_idx < self.new_resolution and max_idx > 0: - - landscape_value = self.sample_range[0] + min_idx * step_x - px - for k in range(min_idx, mid_idx): - events[k].append(landscape_value) - landscape_value += step_x - - landscape_value = py - self.sample_range[0] - mid_idx * step_x - for k in range(mid_idx, max_idx): - events[k].append(landscape_value) - landscape_value -= step_x - - for j in range(self.new_resolution): - events[j].sort(reverse=True) - for k in range( min(self.num_landscapes, len(events[j])) ): - ls[k,j] = events[j][k] - - if self.nan_in_range[0]: - ls = ls[:,1:] - if self.nan_in_range[1]: - ls = ls[:,:-1] - ls = np.sqrt(2)*np.reshape(ls,[1,-1]) - Xfit.append(ls) - - Xfit = np.concatenate(Xfit,0) - - return Xfit + return np.stack(Xfit, axis=0) def __call__(self, diag): """ @@ -192,13 +221,16 @@ class Landscape(BaseEstimator, TransformerMixin): Returns: numpy array with shape (number of samples = **num_landscapes** x **resolution**): output persistence landscape. """ - return self.fit_transform([diag])[0,:] + return self.fit_transform([diag])[0, :] class Silhouette(BaseEstimator, TransformerMixin): """ This is a class for computing persistence silhouettes from a list of persistence diagrams. A persistence silhouette is computed by taking a weighted average of the collection of 1D piecewise-linear functions given by the persistence landscapes, and then by evenly sampling this average on a given range. Finally, the corresponding vector of samples is returned. See https://arxiv.org/abs/1312.0308 for more details. + + Attributes: + grid_ (1d array): The grid on which the silhouette is computed. """ - def __init__(self, weight=lambda x: 1, resolution=100, sample_range=[np.nan, np.nan]): + def __init__(self, weight=lambda x: 1, resolution=100, sample_range=[np.nan, np.nan], *, keep_endpoints=False): """ Constructor for the Silhouette class. @@ -206,8 +238,10 @@ class Silhouette(BaseEstimator, TransformerMixin): weight (function): weight function for the persistence diagram points (default constant function, ie lambda x: 1). This function must be defined on 2D points, ie on lists or numpy arrays of the form [p_x,p_y]. resolution (int): number of samples for the weighted average (default 100). sample_range ([double, double]): minimum and maximum for the weighted average domain, of the form [x_min, x_max] (default [numpy.nan, numpy.nan]). It is the interval on which samples will be drawn evenly. If one of the values is numpy.nan, it can be computed from the persistence diagrams with the fit() method. + keep_endpoints (bool): when computing `sample_range`, use the exact extremities (where the value is always 0). This is mostly useful for plotting, the default is to use a slightly smaller range. """ self.weight, self.resolution, self.sample_range = weight, resolution, sample_range + self.keep_endpoints = keep_endpoints def fit(self, X, y=None): """ @@ -217,10 +251,7 @@ class Silhouette(BaseEstimator, TransformerMixin): X (list of n x 2 numpy arrays): input persistence diagrams. y (n x 1 array): persistence diagram labels (unused). """ - if np.isnan(np.array(self.sample_range)).any(): - pre = DiagramScaler(use=True, scalers=[([0], MinMaxScaler()), ([1], MinMaxScaler())]).fit(X,y) - [mx,my],[Mx,My] = [pre.scalers[0][1].data_min_[0], pre.scalers[1][1].data_min_[0]], [pre.scalers[0][1].data_max_[0], pre.scalers[1][1].data_max_[0]] - self.sample_range = np.where(np.isnan(np.array(self.sample_range)), np.array([mx, My]), np.array(self.sample_range)) + _grid_from_sample_range(self, X) return self def transform(self, X): @@ -233,44 +264,19 @@ class Silhouette(BaseEstimator, TransformerMixin): Returns: numpy array with shape (number of diagrams) x (**resolution**): output persistence silhouettes. """ - num_diag, Xfit = len(X), [] - x_values = np.linspace(self.sample_range[0], self.sample_range[1], self.resolution) - step_x = x_values[1] - x_values[0] - - for i in range(num_diag): - - diagram, num_pts_in_diag = X[i], X[i].shape[0] + Xfit = [] + x_values = self.grid_ - sh, weights = np.zeros(self.resolution), np.zeros(num_pts_in_diag) - for j in range(num_pts_in_diag): - weights[j] = self.weight(diagram[j,:]) + for diag in X: + midpoints, heights = (diag[:, 0] + diag[:, 1]) / 2., (diag[:, 1] - diag[:, 0]) / 2. + weights = np.array([self.weight(pt) for pt in diag]) total_weight = np.sum(weights) - for j in range(num_pts_in_diag): - - [px,py] = diagram[j,:2] - weight = weights[j] / total_weight - min_idx = np.clip(np.ceil((px - self.sample_range[0]) / step_x).astype(int), 0, self.resolution) - mid_idx = np.clip(np.ceil((0.5*(py+px) - self.sample_range[0]) / step_x).astype(int), 0, self.resolution) - max_idx = np.clip(np.ceil((py - self.sample_range[0]) / step_x).astype(int), 0, self.resolution) - - if min_idx < self.resolution and max_idx > 0: + tent_functions = np.maximum(heights[None, :] - np.abs(x_values[:, None] - midpoints[None, :]), 0) + silhouette = np.sum(weights[None, :] / total_weight * tent_functions, axis=1) + Xfit.append(silhouette * np.sqrt(2)) - silhouette_value = self.sample_range[0] + min_idx * step_x - px - for k in range(min_idx, mid_idx): - sh[k] += weight * silhouette_value - silhouette_value += step_x - - silhouette_value = py - self.sample_range[0] - mid_idx * step_x - for k in range(mid_idx, max_idx): - sh[k] += weight * silhouette_value - silhouette_value -= step_x - - Xfit.append(np.reshape(np.sqrt(2) * sh, [1,-1])) - - Xfit = np.concatenate(Xfit, 0) - - return Xfit + return np.stack(Xfit, axis=0) def __call__(self, diag): """ @@ -284,83 +290,174 @@ class Silhouette(BaseEstimator, TransformerMixin): """ return self.fit_transform([diag])[0,:] + class BettiCurve(BaseEstimator, TransformerMixin): """ - This is a class for computing Betti curves from a list of persistence diagrams. A Betti curve is a 1D piecewise-constant function obtained from the rank function. It is sampled evenly on a given range and the vector of samples is returned. See https://www.researchgate.net/publication/316604237_Time_Series_Classification_via_Topological_Data_Analysis for more details. + Compute Betti curves from persistence diagrams. There are several modes of operation: with a given resolution (with or without a sample_range), with a predefined grid, and with none of the previous. With a predefined grid, the class computes the Betti numbers at those grid points. Without a predefined grid, if the resolution is set to None, it can be fit to a list of persistence diagrams and produce a grid that consists of (at least) the filtration values at which at least one of those persistence diagrams changes Betti numbers, and then compute the Betti numbers at those grid points. In the latter mode, the exact Betti curve is computed for the entire real line. Otherwise, if the resolution is given, the Betti curve is obtained by sampling evenly using either the given sample_range or based on the persistence diagrams. + + Examples + -------- + If pd is a persistence diagram and xs is a nonempty grid of finite values such that xs[0] >= pd.min(), then the results of: + + >>> bc = BettiCurve(predefined_grid=xs) # doctest: +SKIP + >>> result = bc(pd) # doctest: +SKIP + + and + + >>> from scipy.interpolate import interp1d # doctest: +SKIP + >>> bc = BettiCurve(resolution=None, predefined_grid=None) # doctest: +SKIP + >>> bettis = bc.fit_transform([pd]) # doctest: +SKIP + >>> interp = interp1d(bc.grid_, bettis[0, :], kind="previous", fill_value="extrapolate") # doctest: +SKIP + >>> result = np.array(interp(xs), dtype=int) # doctest: +SKIP + + are the same. + + Attributes + ---------- + grid_ : 1d array + The grid on which the Betti numbers are computed. If predefined_grid was specified, `grid_` will always be that grid, independently of data. If not and resolution is None, the grid is fitted to capture all filtration values at which the Betti numbers change. """ - def __init__(self, resolution=100, sample_range=[np.nan, np.nan]): + + def __init__(self, resolution=100, sample_range=[np.nan, np.nan], predefined_grid=None, *, keep_endpoints=False): """ Constructor for the BettiCurve class. Parameters: - resolution (int): number of sample for the piecewise-constant function (default 100). + resolution (int): number of samples for the piecewise-constant function (default 100), or None for the exact curve. sample_range ([double, double]): minimum and maximum of the piecewise-constant function domain, of the form [x_min, x_max] (default [numpy.nan, numpy.nan]). It is the interval on which samples will be drawn evenly. If one of the values is numpy.nan, it can be computed from the persistence diagrams with the fit() method. + predefined_grid (1d array or None, default=None): Predefined filtration grid points at which to compute the Betti curves. Must be strictly ordered. Infinities are ok. If None (default), and resolution is given, the grid will be uniform from x_min to x_max in 'resolution' steps, otherwise a grid will be computed that captures all changes in Betti numbers in the provided data. + keep_endpoints (bool): when computing `sample_range` (fixed `resolution`, no `predefined_grid`), use the exact extremities. This is mostly useful for plotting, the default is to use a slightly smaller range. """ - self.resolution, self.sample_range = resolution, sample_range - def fit(self, X, y=None): + if (predefined_grid is not None) and (not isinstance(predefined_grid, np.ndarray)): + raise ValueError("Expected predefined_grid as array or None.") + + self.predefined_grid = predefined_grid + self.resolution = resolution + self.sample_range = sample_range + self.keep_endpoints = keep_endpoints + + def is_fitted(self): + return hasattr(self, "grid_") + + def fit(self, X, y = None): """ - Fit the BettiCurve class on a list of persistence diagrams: if any of the values in **sample_range** is numpy.nan, replace it with the corresponding value computed on the given list of persistence diagrams. + Fit the BettiCurve class on a list of persistence diagrams: if any of the values in **sample_range** is numpy.nan, replace it with the corresponding value computed on the given list of persistence diagrams. When no predefined grid is provided and resolution set to None, compute a filtration grid that captures all changes in Betti numbers for all the given persistence diagrams. Parameters: - X (list of n x 2 numpy arrays): input persistence diagrams. - y (n x 1 array): persistence diagram labels (unused). + X (list of 2d arrays): Persistence diagrams. + y (None): Ignored. """ - if np.isnan(np.array(self.sample_range)).any(): - pre = DiagramScaler(use=True, scalers=[([0], MinMaxScaler()), ([1], MinMaxScaler())]).fit(X,y) - [mx,my],[Mx,My] = [pre.scalers[0][1].data_min_[0], pre.scalers[1][1].data_min_[0]], [pre.scalers[0][1].data_max_[0], pre.scalers[1][1].data_max_[0]] - self.sample_range = np.where(np.isnan(np.array(self.sample_range)), np.array([mx, My]), np.array(self.sample_range)) + + if self.predefined_grid is None: + if self.resolution is None: # Flexible/exact version + events = np.unique(np.concatenate([pd.flatten() for pd in X] + [[-np.inf]], axis=0)) + self.grid_ = np.array(events) + else: + _grid_from_sample_range(self, X) + else: + self.grid_ = self.predefined_grid # Get the predefined grid from user + return self def transform(self, X): """ - Compute the Betti curve for each persistence diagram individually and concatenate the results. + Compute Betti curves. Parameters: - X (list of n x 2 numpy arrays): input persistence diagrams. - + X (list of 2d arrays): Persistence diagrams. + Returns: - numpy array with shape (number of diagrams) x (**resolution**): output Betti curves. + `len(X).len(self.grid_)` array of ints: Betti numbers of the given persistence diagrams at the grid points given in `self.grid_` """ - num_diag, Xfit = len(X), [] - x_values = np.linspace(self.sample_range[0], self.sample_range[1], self.resolution) - step_x = x_values[1] - x_values[0] - for i in range(num_diag): + if not self.is_fitted(): + raise NotFittedError("Not fitted.") - diagram, num_pts_in_diag = X[i], X[i].shape[0] + if not X: + X = [np.zeros((0, 2))] + + N = len(X) - bc = np.zeros(self.resolution) - for j in range(num_pts_in_diag): - [px,py] = diagram[j,:2] - min_idx = np.clip(np.ceil((px - self.sample_range[0]) / step_x).astype(int), 0, self.resolution) - max_idx = np.clip(np.ceil((py - self.sample_range[0]) / step_x).astype(int), 0, self.resolution) - for k in range(min_idx, max_idx): - bc[k] += 1 + events = np.concatenate([pd.flatten(order="F") for pd in X], axis=0) + sorting = np.argsort(events) + offsets = np.zeros(1 + N, dtype=int) + for i in range(0, N): + offsets[i+1] = offsets[i] + 2*X[i].shape[0] + starts = offsets[0:N] + ends = offsets[1:N + 1] - 1 - Xfit.append(np.reshape(bc,[1,-1])) + bettis = [[0] for i in range(0, N)] - Xfit = np.concatenate(Xfit, 0) + i = 0 + for x in self.grid_: + while i < len(sorting) and events[sorting[i]] <= x: + j = np.searchsorted(ends, sorting[i]) + delta = 1 if sorting[i] - starts[j] < len(X[j]) else -1 + bettis[j][-1] += delta + i += 1 + for k in range(0, N): + bettis[k].append(bettis[k][-1]) - return Xfit + return np.array(bettis, dtype=int)[:, 0:-1] - def __call__(self, diag): + def fit_transform(self, X): + """ + The result is the same as fit(X) followed by transform(X), but potentially faster. """ - Apply BettiCurve on a single persistence diagram and outputs the result. - Parameters: - diag (n x 2 numpy array): input persistence diagram. + if self.predefined_grid is None and self.resolution is None: + if not X: + X = [np.zeros((0, 2))] - Returns: - numpy array with shape (**resolution**): output Betti curve. + N = len(X) + + events = np.concatenate([pd.flatten(order="F") for pd in X], axis=0) + sorting = np.argsort(events) + offsets = np.zeros(1 + N, dtype=int) + for i in range(0, N): + offsets[i+1] = offsets[i] + 2*X[i].shape[0] + starts = offsets[0:N] + ends = offsets[1:N + 1] - 1 + + xs = [-np.inf] + bettis = [[0] for i in range(0, N)] + + for i in sorting: + j = np.searchsorted(ends, i) + delta = 1 if i - starts[j] < len(X[j]) else -1 + if events[i] == xs[-1]: + bettis[j][-1] += delta + else: + xs.append(events[i]) + for k in range(0, j): + bettis[k].append(bettis[k][-1]) + bettis[j].append(bettis[j][-1] + delta) + for k in range(j+1, N): + bettis[k].append(bettis[k][-1]) + + self.grid_ = np.array(xs) + return np.array(bettis, dtype=int) + + else: + return self.fit(X).transform(X) + + def __call__(self, diag): """ - return self.fit_transform([diag])[0,:] + Shorthand for transform on a single persistence diagram. + """ + return self.fit_transform([diag])[0, :] + + class Entropy(BaseEstimator, TransformerMixin): """ This is a class for computing persistence entropy. Persistence entropy is a statistic for persistence diagrams inspired from Shannon entropy. This statistic can also be used to compute a feature vector, called the entropy summary function. See https://arxiv.org/pdf/1803.08304.pdf for more details. Note that a previous implementation was contributed by Manuel Soriano-Trigueros. + + Attributes: + grid_ (1d array): In vector mode, the grid on which the entropy summary function is computed. """ - def __init__(self, mode="scalar", normalized=True, resolution=100, sample_range=[np.nan, np.nan]): + def __init__(self, mode="scalar", normalized=True, resolution=100, sample_range=[np.nan, np.nan], *, keep_endpoints=False): """ Constructor for the Entropy class. @@ -369,8 +466,10 @@ class Entropy(BaseEstimator, TransformerMixin): normalized (bool): whether to normalize the entropy summary function (default True). Used only if **mode** = "vector". resolution (int): number of sample for the entropy summary function (default 100). Used only if **mode** = "vector". sample_range ([double, double]): minimum and maximum of the entropy summary function domain, of the form [x_min, x_max] (default [numpy.nan, numpy.nan]). It is the interval on which samples will be drawn evenly. If one of the values is numpy.nan, it can be computed from the persistence diagrams with the fit() method. Used only if **mode** = "vector". + keep_endpoints (bool): when computing `sample_range`, use the exact extremities. This is mostly useful for plotting, the default is to use a slightly smaller range. """ self.mode, self.normalized, self.resolution, self.sample_range = mode, normalized, resolution, sample_range + self.keep_endpoints = keep_endpoints def fit(self, X, y=None): """ @@ -380,10 +479,9 @@ class Entropy(BaseEstimator, TransformerMixin): X (list of n x 2 numpy arrays): input persistence diagrams. y (n x 1 array): persistence diagram labels (unused). """ - if np.isnan(np.array(self.sample_range)).any(): - pre = DiagramScaler(use=True, scalers=[([0], MinMaxScaler()), ([1], MinMaxScaler())]).fit(X,y) - [mx,my],[Mx,My] = [pre.scalers[0][1].data_min_[0], pre.scalers[1][1].data_min_[0]], [pre.scalers[0][1].data_max_[0], pre.scalers[1][1].data_max_[0]] - self.sample_range = np.where(np.isnan(np.array(self.sample_range)), np.array([mx, My]), np.array(self.sample_range)) + if self.mode == "vector": + _grid_from_sample_range(self, X) + self.step_ = self.grid_[1] - self.grid_[0] return self def transform(self, X): @@ -397,33 +495,28 @@ class Entropy(BaseEstimator, TransformerMixin): numpy array with shape (number of diagrams) x (1 if **mode** = "scalar" else **resolution**): output entropy. """ num_diag, Xfit = len(X), [] - x_values = np.linspace(self.sample_range[0], self.sample_range[1], self.resolution) - step_x = x_values[1] - x_values[0] new_X = BirthPersistenceTransform().fit_transform(X) for i in range(num_diag): - - orig_diagram, diagram, num_pts_in_diag = X[i], new_X[i], X[i].shape[0] - new_diagram = DiagramScaler(use=True, scalers=[([1], MaxAbsScaler())]).fit_transform([diagram])[0] - + orig_diagram, new_diagram, num_pts_in_diag = X[i], new_X[i], X[i].shape[0] + + p = new_diagram[:,1] + p = p/np.sum(p) if self.mode == "scalar": - ent = - np.sum( np.multiply(new_diagram[:,1], np.log(new_diagram[:,1])) ) + ent = -np.dot(p, np.log(p)) Xfit.append(np.array([[ent]])) - else: ent = np.zeros(self.resolution) for j in range(num_pts_in_diag): [px,py] = orig_diagram[j,:2] - min_idx = np.clip(np.ceil((px - self.sample_range[0]) / step_x).astype(int), 0, self.resolution) - max_idx = np.clip(np.ceil((py - self.sample_range[0]) / step_x).astype(int), 0, self.resolution) - for k in range(min_idx, max_idx): - ent[k] += (-1) * new_diagram[j,1] * np.log(new_diagram[j,1]) - if self.normalized: - ent = ent / np.linalg.norm(ent, ord=1) - Xfit.append(np.reshape(ent,[1,-1])) - - Xfit = np.concatenate(Xfit, 0) - + min_idx = np.clip(np.ceil((px - self.sample_range_fixed[0]) / self.step_).astype(int), 0, self.resolution) + max_idx = np.clip(np.ceil((py - self.sample_range_fixed[0]) / self.step_).astype(int), 0, self.resolution) + ent[min_idx:max_idx]-=p[j]*np.log(p[j]) + if self.normalized: + ent = ent / np.linalg.norm(ent, ord=1) + Xfit.append(np.reshape(ent,[1,-1])) + + Xfit = np.concatenate(Xfit, axis=0) return Xfit def __call__(self, diag): @@ -484,7 +577,13 @@ class TopologicalVector(BaseEstimator, TransformerMixin): diagram, num_pts_in_diag = X[i], X[i].shape[0] pers = 0.5 * (diagram[:,1]-diagram[:,0]) min_pers = np.minimum(pers,np.transpose(pers)) - distances = DistanceMetric.get_metric("chebyshev").pairwise(diagram) + # Works fine with sklearn 1.0, but an ValueError exception is thrown on past versions + try: + distances = DistanceMetric.get_metric("chebyshev").pairwise(diagram) + except ValueError: + # Empty persistence diagram case - https://github.com/GUDHI/gudhi-devel/issues/507 + assert len(diagram) == 0 + distances = np.empty(shape = [0, 0]) vect = np.flip(np.sort(np.triu(np.minimum(distances, min_pers)), axis=None), 0) dim = min(len(vect), thresh) Xfit[i, :dim] = vect[:dim] @@ -574,3 +673,143 @@ class ComplexPolynomial(BaseEstimator, TransformerMixin): numpy array with shape (**threshold**): output complex vector of coefficients. """ return self.fit_transform([diag])[0,:] + +def _lapl_contrast(measure, centers, inertias): + """contrast function for vectorising `measure` in ATOL""" + return np.exp(-pairwise.pairwise_distances(measure, Y=centers) / inertias) + +def _gaus_contrast(measure, centers, inertias): + """contrast function for vectorising `measure` in ATOL""" + return np.exp(-pairwise.pairwise_distances(measure, Y=centers, squared=True) / inertias**2) + +def _indicator_contrast(diags, centers, inertias): + """contrast function for vectorising `measure` in ATOL""" + robe_curve = np.clip(2-pairwise.pairwise_distances(diags, Y=centers)/inertias, 0, 1) + return robe_curve + +def _cloud_weighting(measure): + """automatic uniform weighting with mass 1 for `measure` in ATOL""" + return np.ones(shape=measure.shape[0]) + +def _iidproba_weighting(measure): + """automatic uniform weighting with mass 1/N for `measure` in ATOL""" + return np.ones(shape=measure.shape[0]) / measure.shape[0] + +class Atol(BaseEstimator, TransformerMixin): + """ + This class allows to vectorise measures (e.g. point clouds, persistence diagrams, etc) after a quantisation step. + + ATOL paper: :cite:`royer2019atol` + + Example + -------- + >>> from sklearn.cluster import KMeans + >>> from gudhi.representations.vector_methods import Atol + >>> import numpy as np + >>> a = np.array([[1, 2, 4], [1, 4, 0], [1, 0, 4]]) + >>> b = np.array([[4, 2, 0], [4, 4, 0], [4, 0, 2]]) + >>> c = np.array([[3, 2, -1], [1, 2, -1]]) + >>> atol_vectoriser = Atol(quantiser=KMeans(n_clusters=2, random_state=202006)) + >>> atol_vectoriser.fit(X=[a, b, c]).centers + array([[ 2.6 , 2.8 , -0.4 ], + [ 2. , 0.66666667, 3.33333333]]) + >>> atol_vectoriser(a) + array([0.42375966, 1.18168665]) + >>> atol_vectoriser(c) + array([1.25157463, 0.02062512]) + >>> atol_vectoriser.transform(X=[a, b, c]) + array([[0.42375966, 1.18168665], + [1.06330156, 0.29861028], + [1.25157463, 0.02062512]]) + """ + # Note the example above must be up to date with the one in tests called test_atol_doc + def __init__(self, quantiser, weighting_method="cloud", contrast="gaussian"): + """ + Constructor for the Atol measure vectorisation class. + + Parameters: + quantiser (Object): Object with `fit` (sklearn API consistent) and `cluster_centers` and `n_clusters` + attributes, e.g. sklearn.cluster.KMeans. It will be fitted when the Atol object function `fit` is called. + weighting_method (string): constant generic function for weighting the measure points + choose from {"cloud", "iidproba"} + (default: constant function, i.e. the measure is seen as a point cloud by default). + This will have no impact if weights are provided along with measures all the way: `fit` and `transform`. + contrast (string): constant function for evaluating proximity of a measure with respect to centers + choose from {"gaussian", "laplacian", "indicator"} + (default: gaussian contrast function, see page 3 in the ATOL paper). + """ + self.quantiser = quantiser + self.contrast = { + "gaussian": _gaus_contrast, + "laplacian": _lapl_contrast, + "indicator": _indicator_contrast, + }.get(contrast, _gaus_contrast) + self.weighting_method = { + "cloud" : _cloud_weighting, + "iidproba": _iidproba_weighting, + }.get(weighting_method, _cloud_weighting) + + def fit(self, X, y=None, sample_weight=None): + """ + Calibration step: fit centers to the sample measures and derive inertias between centers. + + Parameters: + X (list N x d numpy arrays): input measures in R^d from which to learn center locations and inertias + (measures can have different N). + y: Ignored, present for API consistency by convention. + sample_weight (list of numpy arrays): weights for each measure point in X, optional. + If None, the object's weighting_method will be used. + + Returns: + self + """ + if not hasattr(self.quantiser, 'fit'): + raise TypeError("quantiser %s has no `fit` attribute." % (self.quantiser)) + if sample_weight is None: + sample_weight = np.concatenate([self.weighting_method(measure) for measure in X]) + + measures_concat = np.concatenate(X) + self.quantiser.fit(X=measures_concat, sample_weight=sample_weight) + self.centers = self.quantiser.cluster_centers_ + # Hack, but some people are unhappy if the order depends on the version of sklearn + self.centers = self.centers[np.lexsort(self.centers.T)] + if self.quantiser.n_clusters == 1: + dist_centers = pairwise.pairwise_distances(measures_concat) + np.fill_diagonal(dist_centers, 0) + self.inertias = np.array([np.max(dist_centers)/2]) + else: + dist_centers = pairwise.pairwise_distances(self.centers) + dist_centers[dist_centers == 0] = np.inf + self.inertias = np.min(dist_centers, axis=0)/2 + return self + + def __call__(self, measure, sample_weight=None): + """ + Apply measure vectorisation on a single measure. + + Parameters: + measure (n x d numpy array): input measure in R^d. + + Returns: + numpy array in R^self.quantiser.n_clusters. + """ + if sample_weight is None: + sample_weight = self.weighting_method(measure) + return np.sum(sample_weight * self.contrast(measure, self.centers, self.inertias.T).T, axis=1) + + def transform(self, X, sample_weight=None): + """ + Apply measure vectorisation on a list of measures. + + Parameters: + X (list N x d numpy arrays): input measures in R^d from which to learn center locations and inertias + (measures can have different N). + sample_weight (list of numpy arrays): weights for each measure point in X, optional. + If None, the object's weighting_method will be used. + + Returns: + numpy array with shape (number of measures) x (self.quantiser.n_clusters). + """ + if sample_weight is None: + sample_weight = [self.weighting_method(measure) for measure in X] + return np.stack([self(measure, sample_weight=weight) for measure, weight in zip(X, sample_weight)]) |