diff options
Diffstat (limited to 'src/python')
25 files changed, 543 insertions, 37 deletions
diff --git a/src/python/CMakeLists.txt b/src/python/CMakeLists.txt index 99e8b57c..10dcd161 100644 --- a/src/python/CMakeLists.txt +++ b/src/python/CMakeLists.txt @@ -229,7 +229,7 @@ if(PYTHONINTERP_FOUND) # Other .py files file(COPY "gudhi/persistence_graphical_tools.py" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi") file(COPY "gudhi/representations" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi/") - file(COPY "gudhi/wasserstein.py" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi") + file(COPY "gudhi/wasserstein" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi") file(COPY "gudhi/point_cloud" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi") add_custom_command( @@ -402,6 +402,7 @@ if(PYTHONINTERP_FOUND) # Wasserstein if(OT_FOUND AND PYBIND11_FOUND) add_gudhi_py_test(test_wasserstein_distance) + add_gudhi_py_test(test_wasserstein_barycenter) endif() # Representations diff --git a/src/python/doc/alpha_complex_user.rst b/src/python/doc/alpha_complex_user.rst index 60319e84..265a82d2 100644 --- a/src/python/doc/alpha_complex_user.rst +++ b/src/python/doc/alpha_complex_user.rst @@ -204,8 +204,8 @@ the program output is: [3, 6] -> 30.25 CGAL citations -============== +-------------- .. bibliography:: ../../biblio/how_to_cite_cgal.bib - :filter: docnames + :filter: docname in docnames :style: unsrt diff --git a/src/python/doc/bottleneck_distance_user.rst b/src/python/doc/bottleneck_distance_user.rst index 9435c7f1..206fcb63 100644 --- a/src/python/doc/bottleneck_distance_user.rst +++ b/src/python/doc/bottleneck_distance_user.rst @@ -65,3 +65,10 @@ The output is: Bottleneck distance approximation = 0.81 Bottleneck distance value = 0.75 + +Bibliography +------------ + +.. bibliography:: ../../biblio/bibliography.bib + :filter: docname in docnames + :style: unsrt diff --git a/src/python/doc/cubical_complex_user.rst b/src/python/doc/cubical_complex_user.rst index 93ca6b24..e8c94bf6 100644 --- a/src/python/doc/cubical_complex_user.rst +++ b/src/python/doc/cubical_complex_user.rst @@ -160,8 +160,8 @@ Examples. End user programs are available in python/example/ folder. Bibliography -============ +------------ .. bibliography:: ../../biblio/bibliography.bib - :filter: docnames + :filter: docname in docnames :style: unsrt diff --git a/src/python/doc/img/barycenter.png b/src/python/doc/img/barycenter.png Binary files differnew file mode 100644 index 00000000..cad6af70 --- /dev/null +++ b/src/python/doc/img/barycenter.png diff --git a/src/python/doc/index.rst b/src/python/doc/index.rst index 3387a64f..c153cdfc 100644 --- a/src/python/doc/index.rst +++ b/src/python/doc/index.rst @@ -71,6 +71,7 @@ Wasserstein distance .. include:: wasserstein_distance_sum.inc + Persistence representations =========================== @@ -90,5 +91,5 @@ Bibliography ************ .. bibliography:: ../../biblio/bibliography.bib - :filter: docnames + :filter: docname in docnames :style: unsrt diff --git a/src/python/doc/installation.rst b/src/python/doc/installation.rst index d459145b..48425d5e 100644 --- a/src/python/doc/installation.rst +++ b/src/python/doc/installation.rst @@ -175,8 +175,8 @@ Documentation To build the documentation, `sphinx-doc <http://www.sphinx-doc.org>`_ and `sphinxcontrib-bibtex <https://sphinxcontrib-bibtex.readthedocs.io>`_ are required. As the documentation is auto-tested, `CGAL`_, `Eigen`_, -`Matplotlib`_, `NumPy`_ and `SciPy`_ are also mandatory to build the -documentation. +`Matplotlib`_, `NumPy`_, `POT`_, `Scikit-learn`_ and `SciPy`_ are +also mandatory to build the documentation. Run the following commands in a terminal: @@ -192,8 +192,8 @@ CGAL ==== Some GUDHI modules (cf. :doc:`modules list </index>`), and few examples -require CGAL, a C++ library that provides easy access to efficient and -reliable geometric algorithms. +require `CGAL <https://www.cgal.org/>`_, a C++ library that provides easy +access to efficient and reliable geometric algorithms. The procedure to install this library diff --git a/src/python/doc/nerve_gic_complex_ref.rst b/src/python/doc/nerve_gic_complex_ref.rst index abde2e8c..6a81b7af 100644 --- a/src/python/doc/nerve_gic_complex_ref.rst +++ b/src/python/doc/nerve_gic_complex_ref.rst @@ -12,3 +12,10 @@ Cover complexes reference manual :show-inheritance: .. automethod:: gudhi.CoverComplex.__init__ + +Bibliography +------------ + +.. bibliography:: ../../biblio/bibliography.bib + :filter: docname in docnames + :style: unsrt diff --git a/src/python/doc/nerve_gic_complex_user.rst b/src/python/doc/nerve_gic_complex_user.rst index 9101f45d..f709ce91 100644 --- a/src/python/doc/nerve_gic_complex_user.rst +++ b/src/python/doc/nerve_gic_complex_user.rst @@ -313,3 +313,10 @@ the program outputs again SC.dot which gives the following visualization after u :alt: Visualization with neato Visualization with neato + +Bibliography +------------ + +.. bibliography:: ../../biblio/bibliography.bib + :filter: docname in docnames + :style: unsrt diff --git a/src/python/doc/persistent_cohomology_user.rst b/src/python/doc/persistent_cohomology_user.rst index 5f931b3a..506fa3a7 100644 --- a/src/python/doc/persistent_cohomology_user.rst +++ b/src/python/doc/persistent_cohomology_user.rst @@ -113,8 +113,8 @@ We provide several example files: run these examples with -h for details on thei * :download:`tangential_complex_plain_homology_from_off_file_example.py <../example/tangential_complex_plain_homology_from_off_file_example.py>` Bibliography -============ +------------ .. bibliography:: ../../biblio/bibliography.bib - :filter: docnames + :filter: docname in docnames :style: unsrt diff --git a/src/python/doc/rips_complex_user.rst b/src/python/doc/rips_complex_user.rst index 8efb12e6..c4bbcfb6 100644 --- a/src/python/doc/rips_complex_user.rst +++ b/src/python/doc/rips_complex_user.rst @@ -347,3 +347,10 @@ until dimension 1 - one skeleton graph in other words), the output is: points in the persistence diagram will be under the diagonal, and bottleneck distance and persistence graphical tool will not work properly, this is a known issue. + +Bibliography +------------ + +.. bibliography:: ../../biblio/bibliography.bib + :filter: docname in docnames + :style: unsrt diff --git a/src/python/doc/simplex_tree_user.rst b/src/python/doc/simplex_tree_user.rst index 3df7617f..1b272c35 100644 --- a/src/python/doc/simplex_tree_user.rst +++ b/src/python/doc/simplex_tree_user.rst @@ -66,3 +66,10 @@ The output is: ([1, 2], 4.0) ([1], 0.0) ([2], 4.0) + +Bibliography +------------ + +.. bibliography:: ../../biblio/bibliography.bib + :filter: docname in docnames + :style: unsrt diff --git a/src/python/doc/tangential_complex_user.rst b/src/python/doc/tangential_complex_user.rst index 852cf5b6..cf8199cc 100644 --- a/src/python/doc/tangential_complex_user.rst +++ b/src/python/doc/tangential_complex_user.rst @@ -197,8 +197,8 @@ The output is: Bibliography -============ +------------ .. bibliography:: ../../biblio/bibliography.bib - :filter: docnames + :filter: docname in docnames :style: unsrt diff --git a/src/python/doc/wasserstein_distance_sum.inc b/src/python/doc/wasserstein_distance_sum.inc index 0ff22035..f9308e5e 100644 --- a/src/python/doc/wasserstein_distance_sum.inc +++ b/src/python/doc/wasserstein_distance_sum.inc @@ -3,11 +3,11 @@ +-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------------------------------------------------+ | .. figure:: | The q-Wasserstein distance measures the similarity between two | :Author: Theo Lacombe | - | ../../doc/Bottleneck_distance/perturb_pd.png | persistence diagrams. It's the minimum value c that can be achieved | | - | :figclass: align-center | by a perfect matching between the points of the two diagrams (+ all | :Since: GUDHI 3.1.0 | - | | diagonal points), where the value of a matching is defined as the | | - | Wasserstein distance is the q-th root of the sum of the | q-th root of the sum of all edge lengths to the power q. Edge lengths| :License: MIT | - | edge lengths to the power q. | are measured in norm p, for :math:`1 \leq p \leq \infty`. | | + | ../../doc/Bottleneck_distance/perturb_pd.png | persistence diagrams using the sum of all edges lengths (instead of | | + | :figclass: align-center | the maximum). It allows to define sophisticated objects such as | :Since: GUDHI 3.1.0 | + | | barycenters of a family of persistence diagrams. | | + | | | :License: MIT | + | | | | | | | :Requires: Python Optimal Transport (POT) :math:`\geq` 0.5.1 | +-----------------------------------------------------------------+----------------------------------------------------------------------+------------------------------------------------------------------+ | * :doc:`wasserstein_distance_user` | | diff --git a/src/python/doc/wasserstein_distance_user.rst b/src/python/doc/wasserstein_distance_user.rst index a9b21fa5..c24da74d 100644 --- a/src/python/doc/wasserstein_distance_user.rst +++ b/src/python/doc/wasserstein_distance_user.rst @@ -9,10 +9,16 @@ Definition .. include:: wasserstein_distance_sum.inc -Functions ---------- -This implementation uses the Python Optimal Transport library and is based on -ideas from "Large Scale Computation of Means and Cluster for Persistence +The q-Wasserstein distance is defined as the minimal value achieved +by a perfect matching between the points of the two diagrams (+ all +diagonal points), where the value of a matching is defined as the +q-th root of the sum of all edge lengths to the power q. Edge lengths +are measured in norm p, for :math:`1 \leq p \leq \infty`. + +Distance Functions +------------------ +This first implementation uses the Python Optimal Transport library and is based +on ideas from "Large Scale Computation of Means and Cluster for Persistence Diagrams via Optimal Transport" :cite:`10.5555/3327546.3327645`. .. autofunction:: gudhi.wasserstein.wasserstein_distance @@ -26,7 +32,7 @@ Morozov, and Arnur Nigmetov. .. autofunction:: gudhi.hera.wasserstein_distance Basic example -------------- +************* This example computes the 1-Wasserstein distance from 2 persistence diagrams with Euclidean ground metric. Note that persistence diagrams must be submitted as (n x 2) numpy arrays and must not contain inf values. @@ -48,9 +54,9 @@ The output is: Wasserstein distance value = 1.45 -We can also have access to the optimal matching by letting `matching=True`. +We can also have access to the optimal matching by letting `matching=True`. It is encoded as a list of indices (i,j), meaning that the i-th point in X -is mapped to the j-th point in Y. +is mapped to the j-th point in Y. An index of -1 represents the diagonal. .. testcode:: @@ -78,9 +84,90 @@ An index of -1 represents the diagonal. The output is: .. testoutput:: - + Wasserstein distance value = 2.15 point 0 in dgm1 is matched to point 0 in dgm2 point 1 in dgm1 is matched to point 2 in dgm2 point 2 in dgm1 is matched to the diagonal point 1 in dgm2 is matched to the diagonal + +Barycenters +----------- + +A Frechet mean (or barycenter) is a generalization of the arithmetic +mean in a non linear space such as the one of persistence diagrams. +Given a set of persistence diagrams :math:`\mu_1 \dots \mu_n`, it is +defined as a minimizer of the variance functional, that is of +:math:`\mu \mapsto \sum_{i=1}^n d_2(\mu,\mu_i)^2`. +where :math:`d_2` denotes the Wasserstein-2 distance between +persistence diagrams. +It is known to exist and is generically unique. However, an exact +computation is in general untractable. Current implementation +available is based on (Turner et al., 2014), +:cite:`turner2014frechet` +and uses an EM-scheme to +provide a local minimum of the variance functional (somewhat similar +to the Lloyd algorithm to estimate a solution to the k-means +problem). The local minimum returned depends on the initialization of +the barycenter. +The combinatorial structure of the algorithm limits its +performances on large scale problems (thousands of diagrams and of points +per diagram). + +.. figure:: + ./img/barycenter.png + :figclass: align-center + + Illustration of Frechet mean between persistence + diagrams. + + +.. autofunction:: gudhi.wasserstein.barycenter.lagrangian_barycenter + +Basic example +************* + +This example estimates the Frechet mean (aka Wasserstein barycenter) between +four persistence diagrams. +It is initialized on the 4th diagram. +As the algorithm is not convex, its output depends on the initialization and +is only a local minimum of the objective function. +Initialization can be either given as an integer (in which case the i-th +diagram of the list is used as initial estimate) or as a diagram. +If None, it will randomly select one of the diagrams of the list +as initial estimate. +Note that persistence diagrams must be submitted as +(n x 2) numpy arrays and must not contain inf values. + + +.. testcode:: + + from gudhi.wasserstein.barycenter import lagrangian_barycenter + import numpy as np + + dg1 = np.array([[0.2, 0.5]]) + dg2 = np.array([[0.2, 0.7]]) + dg3 = np.array([[0.3, 0.6], [0.7, 0.8], [0.2, 0.3]]) + dg4 = np.array([]) + pdiagset = [dg1, dg2, dg3, dg4] + bary = lagrangian_barycenter(pdiagset=pdiagset,init=3) + + message = "Wasserstein barycenter estimated:" + print(message) + print(bary) + +The output is: + +.. testoutput:: + + Wasserstein barycenter estimated: + [[0.27916667 0.55416667] + [0.7375 0.7625 ] + [0.2375 0.2625 ]] + +Bibliography +------------ + +.. bibliography:: ../../biblio/bibliography.bib + :filter: docname in docnames + :style: unsrt diff --git a/src/python/doc/witness_complex_user.rst b/src/python/doc/witness_complex_user.rst index 7087fa98..799f5444 100644 --- a/src/python/doc/witness_complex_user.rst +++ b/src/python/doc/witness_complex_user.rst @@ -128,8 +128,8 @@ Here is an example of constructing a strong witness complex filtration and compu * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` Bibliography -============ +------------ .. bibliography:: ../../biblio/bibliography.bib - :filter: docnames + :filter: docname in docnames :style: unsrt 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. ''' diff --git a/src/python/include/Simplex_tree_interface.h b/src/python/include/Simplex_tree_interface.h index 4a7062d6..1a18aed6 100644 --- a/src/python/include/Simplex_tree_interface.h +++ b/src/python/include/Simplex_tree_interface.h @@ -37,8 +37,12 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> { using Filtered_simplices = std::vector<Simplex_and_filtration>; using Skeleton_simplex_iterator = typename Base::Skeleton_simplex_iterator; using Complex_simplex_iterator = typename Base::Complex_simplex_iterator; + using Extended_filtration_data = typename Base::Extended_filtration_data; public: + + Extended_filtration_data efd; + bool find_simplex(const Simplex& vh) { return (Base::find(vh) != Base::null_simplex()); } @@ -117,6 +121,42 @@ class Simplex_tree_interface : public Simplex_tree<SimplexTreeOptions> { return cofaces; } + void compute_extended_filtration() { + this->efd = this->extend_filtration(); + this->initialize_filtration(); + return; + } + + std::vector<std::vector<std::pair<int, std::pair<Filtration_value, Filtration_value>>>> compute_extended_persistence_subdiagrams(const std::vector<std::pair<int, std::pair<Filtration_value, Filtration_value>>>& dgm, Filtration_value min_persistence){ + std::vector<std::vector<std::pair<int, std::pair<Filtration_value, Filtration_value>>>> new_dgm(4); + for (unsigned int i = 0; i < dgm.size(); i++){ + std::pair<Filtration_value, Extended_simplex_type> px = this->decode_extended_filtration(dgm[i].second.first, this->efd); + std::pair<Filtration_value, Extended_simplex_type> py = this->decode_extended_filtration(dgm[i].second.second, this->efd); + std::pair<int, std::pair<Filtration_value, Filtration_value>> pd_point = std::make_pair(dgm[i].first, std::make_pair(px.first, py.first)); + if(std::abs(px.first - py.first) > min_persistence){ + //Ordinary + if (px.second == Extended_simplex_type::UP && py.second == Extended_simplex_type::UP){ + new_dgm[0].push_back(pd_point); + } + // Relative + else if (px.second == Extended_simplex_type::DOWN && py.second == Extended_simplex_type::DOWN){ + new_dgm[1].push_back(pd_point); + } + else{ + // Extended+ + if (px.first < py.first){ + new_dgm[2].push_back(pd_point); + } + //Extended- + else{ + new_dgm[3].push_back(pd_point); + } + } + } + } + return new_dgm; + } + void create_persistence(Gudhi::Persistent_cohomology_interface<Base>* pcoh) { Base::initialize_filtration(); pcoh = new Gudhi::Persistent_cohomology_interface<Base>(*this); diff --git a/src/python/test/test_simplex_tree.py b/src/python/test/test_simplex_tree.py index f7848379..70b26e97 100755 --- a/src/python/test/test_simplex_tree.py +++ b/src/python/test/test_simplex_tree.py @@ -9,6 +9,7 @@ """ from gudhi import SimplexTree +import pytest __author__ = "Vincent Rouvreau" __copyright__ = "Copyright (C) 2016 Inria" @@ -250,6 +251,87 @@ def test_make_filtration_non_decreasing(): assert st.filtration([3, 4]) == 2.0 assert st.filtration([4, 5]) == 2.0 +def test_extend_filtration(): + + # Inserted simplex: + # 5 4 + # o o + # / \ / + # o o + # /2\ /3 + # o o + # 1 0 + + st = SimplexTree() + st.insert([0,2]) + st.insert([1,2]) + st.insert([0,3]) + st.insert([2,5]) + st.insert([3,4]) + st.insert([3,5]) + st.assign_filtration([0], 1.) + st.assign_filtration([1], 2.) + st.assign_filtration([2], 3.) + st.assign_filtration([3], 4.) + st.assign_filtration([4], 5.) + st.assign_filtration([5], 6.) + + assert list(st.get_filtration()) == [ + ([0, 2], 0.0), + ([1, 2], 0.0), + ([0, 3], 0.0), + ([3, 4], 0.0), + ([2, 5], 0.0), + ([3, 5], 0.0), + ([0], 1.0), + ([1], 2.0), + ([2], 3.0), + ([3], 4.0), + ([4], 5.0), + ([5], 6.0) + ] + + st.extend_filtration() + + assert list(st.get_filtration()) == [ + ([6], -3.0), + ([0], -2.0), + ([1], -1.8), + ([2], -1.6), + ([0, 2], -1.6), + ([1, 2], -1.6), + ([3], -1.4), + ([0, 3], -1.4), + ([4], -1.2), + ([3, 4], -1.2), + ([5], -1.0), + ([2, 5], -1.0), + ([3, 5], -1.0), + ([5, 6], 1.0), + ([4, 6], 1.2), + ([3, 6], 1.4), + ([3, 4, 6], 1.4), + ([3, 5, 6], 1.4), + ([2, 6], 1.6), + ([2, 5, 6], 1.6), + ([1, 6], 1.8), + ([1, 2, 6], 1.8), + ([0, 6], 2.0), + ([0, 2, 6], 2.0), + ([0, 3, 6], 2.0) + ] + + dgms = st.extended_persistence(min_persistence=-1.) + + assert dgms[0][0][1][0] == pytest.approx(2.) + assert dgms[0][0][1][1] == pytest.approx(3.) + assert dgms[1][0][1][0] == pytest.approx(5.) + assert dgms[1][0][1][1] == pytest.approx(4.) + assert dgms[2][0][1][0] == pytest.approx(1.) + assert dgms[2][0][1][1] == pytest.approx(6.) + assert dgms[3][0][1][0] == pytest.approx(6.) + assert dgms[3][0][1][1] == pytest.approx(1.) + def test_simplices_iterator(): st = SimplexTree() diff --git a/src/python/test/test_wasserstein_barycenter.py b/src/python/test/test_wasserstein_barycenter.py new file mode 100755 index 00000000..f68c748e --- /dev/null +++ b/src/python/test/test_wasserstein_barycenter.py @@ -0,0 +1,46 @@ +from gudhi.wasserstein.barycenter import lagrangian_barycenter +import numpy as np + +""" 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 +""" + +__author__ = "Theo Lacombe" +__copyright__ = "Copyright (C) 2019 Inria" +__license__ = "MIT" + + +def test_lagrangian_barycenter(): + + dg1 = np.array([[0.2, 0.5]]) + dg2 = np.array([[0.2, 0.7]]) + dg3 = np.array([[0.3, 0.6], [0.7, 0.8], [0.2, 0.3]]) + dg4 = np.array([]) + dg5 = np.array([]) + dg6 = np.array([]) + res = np.array([[0.27916667, 0.55416667], [0.7375, 0.7625], [0.2375, 0.2625]]) + + dg7 = np.array([[0.1, 0.15], [0.1, 0.7], [0.2, 0.22], [0.55, 0.84], [0.11, 0.91], [0.61, 0.75], [0.33, 0.46], [0.12, 0.41], [0.32, 0.48]]) + dg8 = np.array([[0., 4.], [4, 8]]) + + # error crit. + eps = 1e-7 + + + assert np.linalg.norm(lagrangian_barycenter(pdiagset=[dg1, dg2, dg3, dg4],init=3, verbose=False) - res) < eps + assert np.array_equal(lagrangian_barycenter(pdiagset=[dg4, dg5, dg6], verbose=False), np.empty(shape=(0,2))) + assert np.linalg.norm(lagrangian_barycenter(pdiagset=[dg7], verbose=False) - dg7) < eps + Y, log = lagrangian_barycenter(pdiagset=[dg4, dg8], verbose=True) + assert np.linalg.norm(Y - np.array([[1,3], [5, 7]])) < eps + assert np.abs(log["energy"] - 2) < eps + assert np.array_equal(log["groupings"][0] , np.array([[0, -1], [1, -1]])) + assert np.array_equal(log["groupings"][1] , np.array([[0, 0], [1, 1]])) + assert np.linalg.norm(lagrangian_barycenter(pdiagset=[dg8, dg4], init=np.array([[0.2, 0.6], [0.5, 0.7]]), verbose=False) - np.array([[1, 3], [5, 7]])) < eps + assert lagrangian_barycenter(pdiagset = []) is None + diff --git a/src/python/test/test_wasserstein_distance.py b/src/python/test/test_wasserstein_distance.py index 0d70e11a..7e0d0f5f 100755 --- a/src/python/test/test_wasserstein_distance.py +++ b/src/python/test/test_wasserstein_distance.py @@ -70,7 +70,7 @@ def _basic_wasserstein(wasserstein_distance, delta, test_infinity=True, test_mat assert np.array_equal(match , [[0, -1], [1, -1]]) match = wasserstein_distance(diag1, diag2, matching=True, internal_p=2., order=2.)[1] assert np.array_equal(match, [[0, 0], [1, 1], [2, -1]]) - + def hera_wrap(delta): |