diff options
Diffstat (limited to 'src/python/gudhi')
-rw-r--r-- | src/python/gudhi/simplex_tree.pxd | 2 | ||||
-rw-r--r-- | src/python/gudhi/simplex_tree.pyx | 51 | ||||
-rw-r--r-- | src/python/gudhi/wasserstein/__init__.py | 1 | ||||
-rw-r--r-- | src/python/gudhi/wasserstein/barycenter.py | 159 | ||||
-rw-r--r-- | src/python/gudhi/wasserstein/wasserstein.py (renamed from src/python/gudhi/wasserstein.py) | 15 |
5 files changed, 221 insertions, 7 deletions
diff --git a/src/python/gudhi/simplex_tree.pxd b/src/python/gudhi/simplex_tree.pxd index 82f155de..595f22bb 100644 --- a/src/python/gudhi/simplex_tree.pxd +++ b/src/python/gudhi/simplex_tree.pxd @@ -57,6 +57,8 @@ cdef extern from "Simplex_tree_interface.h" namespace "Gudhi": void remove_maximal_simplex(vector[int] simplex) bool prune_above_filtration(double filtration) bool make_filtration_non_decreasing() + void compute_extended_filtration() + vector[vector[pair[int, pair[double, double]]]] compute_extended_persistence_subdiagrams(vector[pair[int, pair[double, double]]] dgm, double min_persistence) # Iterators over Simplex tree pair[vector[int], double] get_simplex_and_filtration(Simplex_tree_simplex_handle f_simplex) Simplex_tree_simplices_iterator get_simplices_iterator_begin() diff --git a/src/python/gudhi/simplex_tree.pyx b/src/python/gudhi/simplex_tree.pyx index c01cc905..cc3753e1 100644 --- a/src/python/gudhi/simplex_tree.pyx +++ b/src/python/gudhi/simplex_tree.pyx @@ -396,6 +396,57 @@ cdef class SimplexTree: """ return self.get_ptr().make_filtration_non_decreasing() + def extend_filtration(self): + """ Extend filtration for computing extended persistence. This function only uses the + filtration values at the 0-dimensional simplices, and computes the extended persistence + diagram induced by the lower-star filtration computed with these values. + + .. note:: + + Note that after calling this function, the filtration + values are actually modified within the Simplex_tree. + The function :func:`extended_persistence()<gudhi.SimplexTree.extended_persistence>` + retrieves the original values. + + .. note:: + + Note that this code creates an extra vertex internally, so you should make sure that + the Simplex_tree does not contain a vertex with the largest possible value (i.e., 4294967295). + """ + return self.get_ptr().compute_extended_filtration() + + def extended_persistence(self, homology_coeff_field=11, min_persistence=0): + """This function retrieves good values for extended persistence, and separate the diagrams + into the Ordinary, Relative, Extended+ and Extended- subdiagrams. + + :param homology_coeff_field: The homology coefficient field. Must be a + prime number. Default value is 11. + :type homology_coeff_field: int. + :param min_persistence: The minimum persistence value (i.e., the absolute value of the difference between the persistence diagram point coordinates) to take into + account (strictly greater than min_persistence). Default value is + 0.0. + Sets min_persistence to -1.0 to see all values. + :type min_persistence: float. + :returns: A list of four persistence diagrams in the format described in :func:`persistence()<gudhi.SimplexTree.persistence>`. The first one is Ordinary, the second one is Relative, the third one is Extended+ and the fourth one is Extended-. See https://link.springer.com/article/10.1007/s10208-008-9027-z and/or section 2.2 in https://link.springer.com/article/10.1007/s10208-017-9370-z for a description of these subtypes. + + .. note:: + + This function should be called only if :func:`extend_filtration()<gudhi.SimplexTree.extend_filtration>` has been called first! + + .. note:: + + The coordinates of the persistence diagram points might be a little different than the + original filtration values due to the internal transformation (scaling to [-2,-1]) that is + performed on these values during the computation of extended persistence. + """ + cdef vector[pair[int, pair[double, double]]] persistence_result + if self.pcohptr != NULL: + del self.pcohptr + self.pcohptr = new Simplex_tree_persistence_interface(self.get_ptr(), False) + persistence_result = self.pcohptr.get_persistence(homology_coeff_field, -1.) + return self.get_ptr().compute_extended_persistence_subdiagrams(persistence_result, min_persistence) + + def persistence(self, homology_coeff_field=11, min_persistence=0, persistence_dim_max = False): """This function returns the persistence of the simplicial complex. diff --git a/src/python/gudhi/wasserstein/__init__.py b/src/python/gudhi/wasserstein/__init__.py new file mode 100644 index 00000000..ed225ba4 --- /dev/null +++ b/src/python/gudhi/wasserstein/__init__.py @@ -0,0 +1 @@ +from .wasserstein import wasserstein_distance diff --git a/src/python/gudhi/wasserstein/barycenter.py b/src/python/gudhi/wasserstein/barycenter.py new file mode 100644 index 00000000..de7aea81 --- /dev/null +++ b/src/python/gudhi/wasserstein/barycenter.py @@ -0,0 +1,159 @@ +# 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): Theo Lacombe +# +# Copyright (C) 2019 Inria +# +# Modification(s): +# - YYYY/MM Author: Description of the modification + + +import ot +import numpy as np +import scipy.spatial.distance as sc + +from gudhi.wasserstein import wasserstein_distance + + +def _mean(x, m): + ''' + :param x: a list of 2D-points, off diagonal, x_0... x_{k-1} + :param m: total amount of points taken into account, + that is we have (m-k) copies of diagonal + :returns: the weighted mean of x with (m-k) copies of the diagonal + ''' + k = len(x) + if k > 0: + w = np.mean(x, axis=0) + w_delta = (w[0] + w[1]) / 2 * np.ones(2) + return (k * w + (m-k) * w_delta) / m + else: + return np.array([0, 0]) + + +def lagrangian_barycenter(pdiagset, init=None, verbose=False): + ''' + :param pdiagset: a list of ``numpy.array`` of shape `(n x 2)` + (`n` can variate), encoding a set of + persistence diagrams with only finite coordinates. + :param init: The initial value for barycenter estimate. + If ``None``, init is made on a random diagram from the dataset. + Otherwise, it can be an ``int`` + (then initialization is made on ``pdiagset[init]``) + or a `(n x 2)` ``numpy.array`` enconding + a persistence diagram with `n` points. + :type init: ``int``, or (n x 2) ``np.array`` + :param verbose: if ``True``, returns additional information about the + barycenter. + :type verbose: boolean + :returns: If not verbose (default), a ``numpy.array`` encoding + the barycenter estimate of pdiagset + (local minimum of the energy function). + If ``pdiagset`` is empty, returns ``None``. + If verbose, returns a couple ``(Y, log)`` + where ``Y`` is the barycenter estimate, + and ``log`` is a ``dict`` that contains additional informations: + + - `"groupings"`, a list of list of pairs ``(i,j)``. + Namely, ``G[k] = [...(i, j)...]``, where ``(i,j)`` indicates + that ``pdiagset[k][i]`` is matched to ``Y[j]`` + if ``i = -1`` or ``j = -1``, it means they + represent the diagonal. + + - `"energy"`, ``float`` representing the Frechet energy value obtained. + It is the mean of squared distances of observations to the output. + + - `"nb_iter"`, ``int`` number of iterations performed before convergence of the algorithm. + ''' + X = pdiagset # to shorten notations, not a copy + m = len(X) # number of diagrams we are averaging + if m == 0: + print("Warning: computing barycenter of empty diag set. Returns None") + return None + + # store the number of off-diagonal point for each of the X_i + nb_off_diag = np.array([len(X_i) for X_i in X]) + # Initialisation of barycenter + if init is None: + i0 = np.random.randint(m) # Index of first state for the barycenter + Y = X[i0].copy() + else: + if type(init)==int: + Y = X[init].copy() + else: + Y = init.copy() + + nb_iter = 0 + + converged = False # stoping criterion + while not converged: + nb_iter += 1 + K = len(Y) # current nb of points in Y (some might be on diagonal) + G = np.full((K, m), -1, dtype=int) # will store for each j, the (index) + # point matched in each other diagram + #(might be the diagonal). + # that is G[j, i] = k <=> y_j is matched to + # x_k in the diagram i-th diagram X[i] + updated_points = np.zeros((K, 2)) # will store the new positions of + # the points of Y. + # If points disappear, there thrown + # on [0,0] by default. + new_created_points = [] # will store potential new points. + + # Step 1 : compute optimal matching (Y, X_i) for each X_i + # and create new points in Y if needed + for i in range(m): + _, indices = wasserstein_distance(Y, X[i], matching=True, order=2., internal_p=2.) + for y_j, x_i_j in indices: + if y_j >= 0: # we matched an off diagonal point to x_i_j... + if x_i_j >= 0: # ...which is also an off-diagonal point. + G[y_j, i] = x_i_j + else: # ...which is a diagonal point + G[y_j, i] = -1 # -1 stands for the diagonal (mask) + else: # We matched a diagonal point to x_i_j... + if x_i_j >= 0: # which is a off-diag point ! + # need to create new point in Y + new_y = _mean(np.array([X[i][x_i_j]]), m) + # Average this point with (m-1) copies of Delta + new_created_points.append(new_y) + + # Step 2 : Update current point position thanks to groupings computed + to_delete = [] + for j in range(K): + matched_points = [X[i][G[j, i]] for i in range(m) if G[j, i] > -1] + new_y_j = _mean(matched_points, m) + if not np.array_equal(new_y_j, np.array([0,0])): + updated_points[j] = new_y_j + else: # this points is no longer of any use. + to_delete.append(j) + # we remove the point to be deleted now. + updated_points = np.delete(updated_points, to_delete, axis=0) + + # we cannot converge if there have been new created points. + if new_created_points: + Y = np.concatenate((updated_points, new_created_points)) + else: + # Step 3 : we check convergence + if np.array_equal(updated_points, Y): + converged = True + Y = updated_points + + + if verbose: + groupings = [] + energy = 0 + log = {} + n_y = len(Y) + for i in range(m): + cost, edges = wasserstein_distance(Y, X[i], matching=True, order=2., internal_p=2.) + groupings.append(edges) + energy += cost + log["groupings"] = groupings + energy = energy/m + log["energy"] = energy + log["nb_iter"] = nb_iter + + return Y, log + else: + return Y + diff --git a/src/python/gudhi/wasserstein.py b/src/python/gudhi/wasserstein/wasserstein.py index 3dd993f9..35315939 100644 --- a/src/python/gudhi/wasserstein.py +++ b/src/python/gudhi/wasserstein/wasserstein.py @@ -9,6 +9,7 @@ import numpy as np import scipy.spatial.distance as sc + try: import ot except ImportError: @@ -29,9 +30,9 @@ def _build_dist_matrix(X, Y, order=2., internal_p=2.): :param Y: (m x 2) numpy.array encoding the second diagram. :param order: exponent for the Wasserstein metric. :param internal_p: Ground metric (i.e. norm L^p). - :returns: (n+1) x (m+1) np.array encoding the cost matrix C. - For 0 <= i < n, 0 <= j < m, C[i,j] encodes the distance between X[i] and Y[j], - while C[i, m] (resp. C[n, j]) encodes the distance (to the p) between X[i] (resp Y[j]) + :returns: (n+1) x (m+1) np.array encoding the cost matrix C. + For 0 <= i < n, 0 <= j < m, C[i,j] encodes the distance between X[i] and Y[j], + while C[i, m] (resp. C[n, j]) encodes the distance (to the p) between X[i] (resp Y[j]) and its orthogonal projection onto the diagonal. note also that C[n, m] = 0 (it costs nothing to move from the diagonal to the diagonal). ''' @@ -58,7 +59,7 @@ def _perstot(X, order, internal_p): :param X: (n x 2) numpy.array (points of a given diagram). :param order: exponent for Wasserstein. Default value is 2. :param internal_p: Ground metric on the (upper-half) plane (i.e. norm L^p in R^2); Default value is 2 (Euclidean norm). - :returns: float, the total persistence of the diagram (that is, its distance to the empty diagram). + :returns: float, the total persistence of the diagram (that is, its distance to the empty diagram). ''' Xdiag = _proj_on_diag(X) return (np.sum(np.linalg.norm(X - Xdiag, ord=internal_p, axis=1)**order))**(1./order) @@ -66,16 +67,16 @@ def _perstot(X, order, internal_p): def wasserstein_distance(X, Y, matching=False, order=2., internal_p=2.): ''' - :param X: (n x 2) numpy.array encoding the (finite points of the) first diagram. Must not contain essential points + :param X: (n x 2) numpy.array encoding the (finite points of the) first diagram. Must not contain essential points (i.e. with infinite coordinate). :param Y: (m x 2) numpy.array encoding the second diagram. :param matching: if True, computes and returns the optimal matching between X and Y, encoded as a (n x 2) np.array [...[i,j]...], meaning the i-th point in X is matched to the j-th point in Y, with the convention (-1) represents the diagonal. :param order: exponent for Wasserstein; Default value is 2. - :param internal_p: Ground metric on the (upper-half) plane (i.e. norm L^p in R^2); + :param internal_p: Ground metric on the (upper-half) plane (i.e. norm L^p in R^2); Default value is 2 (Euclidean norm). - :returns: the Wasserstein distance of order q (1 <= q < infinity) between persistence diagrams with + :returns: the Wasserstein distance of order q (1 <= q < infinity) between persistence diagrams with respect to the internal_p-norm as ground metric. If matching is set to True, also returns the optimal matching between X and Y. ''' |