diff options
Diffstat (limited to 'src/python/doc')
| -rw-r--r-- | src/python/doc/alpha_complex_user.rst | 8 | ||||
| -rw-r--r-- | src/python/doc/bottleneck_distance_user.rst | 1 | ||||
| -rw-r--r-- | src/python/doc/cubical_complex_user.rst | 7 | ||||
| -rw-r--r-- | src/python/doc/img/barycenter.png | bin | 0 -> 12433 bytes | |||
| -rw-r--r-- | src/python/doc/index.rst | 8 | ||||
| -rw-r--r-- | src/python/doc/installation.rst | 36 | ||||
| -rw-r--r-- | src/python/doc/persistent_cohomology_user.rst | 7 | ||||
| -rw-r--r-- | src/python/doc/simplex_tree_ref.rst | 1 | ||||
| -rw-r--r-- | src/python/doc/tangential_complex_user.rst | 8 | ||||
| -rw-r--r-- | src/python/doc/wasserstein_distance_sum.inc | 10 | ||||
| -rw-r--r-- | src/python/doc/wasserstein_distance_user.rst | 96 | ||||
| -rw-r--r-- | src/python/doc/witness_complex_user.rst | 7 | ||||
| -rw-r--r-- | src/python/doc/zbibliography.rst | 10 |
13 files changed, 138 insertions, 61 deletions
diff --git a/src/python/doc/alpha_complex_user.rst b/src/python/doc/alpha_complex_user.rst index 60319e84..a3b35c10 100644 --- a/src/python/doc/alpha_complex_user.rst +++ b/src/python/doc/alpha_complex_user.rst @@ -10,7 +10,7 @@ Definition .. include:: alpha_complex_sum.inc `AlphaComplex` is constructing a :doc:`SimplexTree <simplex_tree_ref>` using -`Delaunay Triangulation <http://doc.cgal.org/latest/Triangulation/index.html#Chapter_Triangulations>`_ +`Delaunay Triangulation <http://doc.cgal.org/latest/Triangulation/index.html#Chapter_Triangulations>`_ :cite:`cgal:hdj-t-19b` from `CGAL <http://www.cgal.org/>`_ (the Computational Geometry Algorithms Library :cite:`cgal:eb-19b`). @@ -203,9 +203,3 @@ the program output is: [4, 5, 6] -> 22.74 [3, 6] -> 30.25 -CGAL citations -============== - -.. bibliography:: ../../biblio/how_to_cite_cgal.bib - :filter: docnames - :style: unsrt diff --git a/src/python/doc/bottleneck_distance_user.rst b/src/python/doc/bottleneck_distance_user.rst index 9435c7f1..89da89d3 100644 --- a/src/python/doc/bottleneck_distance_user.rst +++ b/src/python/doc/bottleneck_distance_user.rst @@ -65,3 +65,4 @@ The output is: Bottleneck distance approximation = 0.81 Bottleneck distance value = 0.75 + diff --git a/src/python/doc/cubical_complex_user.rst b/src/python/doc/cubical_complex_user.rst index 93ca6b24..e4733653 100644 --- a/src/python/doc/cubical_complex_user.rst +++ b/src/python/doc/cubical_complex_user.rst @@ -158,10 +158,3 @@ Examples. --------- End user programs are available in python/example/ folder. - -Bibliography -============ - -.. bibliography:: ../../biblio/bibliography.bib - :filter: 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..13e51047 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 =========================== @@ -85,10 +86,3 @@ Point cloud utilities ********************* .. include:: point_cloud_sum.inc - -Bibliography -************ - -.. bibliography:: ../../biblio/bibliography.bib - :filter: docnames - :style: unsrt diff --git a/src/python/doc/installation.rst b/src/python/doc/installation.rst index d459145b..09a843d5 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 @@ -211,6 +211,14 @@ The following examples requires CGAL version ≥ 4.11.0: * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>` +EagerPy +======= + +Some Python functions can handle automatic differentiation (possibly only when +a flag `enable_autodiff=True` is used). In order to reduce code duplication, we +use `EagerPy <https://eagerpy.jonasrauber.de/>`_ which wraps arrays from +PyTorch, TensorFlow and JAX in a common interface. + Eigen ===== @@ -229,6 +237,13 @@ The following examples require `Eigen <http://eigen.tuxfamily.org/>`_ version ≠* :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>` +Hnswlib +======= + +:class:`~gudhi.point_cloud.knn.KNearestNeighbors` can use the Python package +`Hnswlib <https://github.com/nmslib/hnswlib>`_ as a backend if explicitly +requested, to speed-up queries. + Matplotlib ========== @@ -251,6 +266,13 @@ The following examples require the `Matplotlib <http://matplotlib.org>`_: * :download:`euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_strong_witness_complex_diagram_persistence_from_off_file_example.py>` * :download:`euclidean_witness_complex_diagram_persistence_from_off_file_example.py <../example/euclidean_witness_complex_diagram_persistence_from_off_file_example.py>` +PyKeOps +======= + +:class:`~gudhi.point_cloud.knn.KNearestNeighbors` can use the Python package +`PyKeOps <https://www.kernel-operations.io/keops/python/>`_ as a backend if +explicitly requested, to speed-up queries using a GPU. + Python Optimal Transport ======================== @@ -258,6 +280,12 @@ The :doc:`Wasserstein distance </wasserstein_distance_user>` module requires `POT <https://pot.readthedocs.io/>`_, a library that provides several solvers for optimization problems related to Optimal Transport. +PyTorch +======= + +`PyTorch <https://pytorch.org/>`_ is currently only used as a dependency of +`PyKeOps`_, and in some tests. + Scikit-learn ============ diff --git a/src/python/doc/persistent_cohomology_user.rst b/src/python/doc/persistent_cohomology_user.rst index 5f931b3a..4d743aac 100644 --- a/src/python/doc/persistent_cohomology_user.rst +++ b/src/python/doc/persistent_cohomology_user.rst @@ -111,10 +111,3 @@ We provide several example files: run these examples with -h for details on thei * :download:`rips_complex_diagram_persistence_from_distance_matrix_file_example.py <../example/rips_complex_diagram_persistence_from_distance_matrix_file_example.py>` * :download:`random_cubical_complex_persistence_example.py <../example/random_cubical_complex_persistence_example.py>` * :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 - :style: unsrt diff --git a/src/python/doc/simplex_tree_ref.rst b/src/python/doc/simplex_tree_ref.rst index 9eb8c199..46b2c1e5 100644 --- a/src/python/doc/simplex_tree_ref.rst +++ b/src/python/doc/simplex_tree_ref.rst @@ -8,7 +8,6 @@ Simplex tree reference manual .. autoclass:: gudhi.SimplexTree :members: - :undoc-members: :show-inheritance: .. automethod:: gudhi.SimplexTree.__init__ diff --git a/src/python/doc/tangential_complex_user.rst b/src/python/doc/tangential_complex_user.rst index 852cf5b6..3d45473b 100644 --- a/src/python/doc/tangential_complex_user.rst +++ b/src/python/doc/tangential_complex_user.rst @@ -194,11 +194,3 @@ The output is: Tangential contains 4 vertices. Inconsistencies has been fixed. - - -Bibliography -============ - -.. bibliography:: ../../biblio/bibliography.bib - :filter: 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..c443bab5 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 +84,83 @@ 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 ]] diff --git a/src/python/doc/witness_complex_user.rst b/src/python/doc/witness_complex_user.rst index 7087fa98..08dcd288 100644 --- a/src/python/doc/witness_complex_user.rst +++ b/src/python/doc/witness_complex_user.rst @@ -126,10 +126,3 @@ Example2: Computing persistence using strong relaxed witness complex Here is an example of constructing a strong witness complex filtration and computing persistence on it: * :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 - :style: unsrt diff --git a/src/python/doc/zbibliography.rst b/src/python/doc/zbibliography.rst new file mode 100644 index 00000000..e23fcf25 --- /dev/null +++ b/src/python/doc/zbibliography.rst @@ -0,0 +1,10 @@ +:orphan: + +.. To get rid of WARNING: document isn't included in any toctree + +Bibliography +------------ + +.. bibliography:: ../../biblio/bibliography.bib + :style: plain + |
