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Diffstat (limited to 'src/python/doc/representations.rst')
| -rw-r--r-- | src/python/doc/representations.rst | 119 |
1 files changed, 111 insertions, 8 deletions
diff --git a/src/python/doc/representations.rst b/src/python/doc/representations.rst index b0477197..5686974a 100644 --- a/src/python/doc/representations.rst +++ b/src/python/doc/representations.rst @@ -8,10 +8,16 @@ Representations manual .. include:: representations_sum.inc -This module, originally available at https://github.com/MathieuCarriere/sklearn-tda and named sklearn_tda, aims at bridging the gap between persistence diagrams and machine learning, by providing implementations of most of the vector representations for persistence diagrams in the literature, in a scikit-learn format. More specifically, it provides tools, using the scikit-learn standard interface, to compute distances and kernels on persistence diagrams, and to convert these diagrams into vectors in Euclidean space. +This module aims at bridging the gap between persistence diagrams and machine learning, by providing implementations of most of the vector representations for persistence diagrams in the literature, in a scikit-learn format. More specifically, it provides tools, using the scikit-learn standard interface, to compute distances and kernels on persistence diagrams, and to convert these diagrams into vectors in Euclidean space. Moreover, this module also contains `PersLay <http://proceedings.mlr.press/v108/carriere20a.html>`_, which is a general neural network layer for performing deep learning with persistence diagrams, implemented in TensorFlow. A diagram is represented as a numpy array of shape (n,2), as can be obtained from :func:`~gudhi.SimplexTree.persistence_intervals_in_dimension` for instance. Points at infinity are represented as a numpy array of shape (n,1), storing only the birth time. The classes in this module can handle several persistence diagrams at once. In that case, the diagrams are provided as a list of numpy arrays. Note that it is not necessary for the diagrams to have the same number of points, i.e., for the corresponding arrays to have the same number of rows: all classes can handle arrays with different shapes. +This `notebook <https://github.com/GUDHI/TDA-tutorial/blob/master/Tuto-GUDHI-representations.ipynb>`__ explains how to +efficiently combine machine learning and topological data analysis with the +:doc:`representations module<representations>` in a scikit-learn fashion. This `notebook <https://github.com/MathieuCarriere/tda-tutorials/blob/perslay/Tuto-GUDHI-perslay-expe.ipynb>`__ +and `this one <https://github.com/MathieuCarriere/tda-tutorials/blob/perslay/Tuto-GUDHI-perslay-visu.ipynb>`__ explain how to use PersLay. + + Examples -------- @@ -30,8 +36,6 @@ This example computes the first two Landscapes associated to a persistence diagr l=Landscape(num_landscapes=2,resolution=10).fit_transform(diags) print(l) -The output is: - .. testoutput:: [[1.02851895 2.05703791 2.57129739 1.54277843 0.89995409 1.92847304 @@ -45,13 +49,71 @@ Various kernels This small example is also provided :download:`diagram_vectorizations_distances_kernels.py <../example/diagram_vectorizations_distances_kernels.py>` -Machine Learning and Topological Data Analysis -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +PersLay +^^^^^^^ -This `notebook <https://github.com/GUDHI/TDA-tutorial/blob/master/Tuto-GUDHI-representations.ipynb>`_ explains how to -efficiently combine machine learning and topological data analysis with the -:doc:`representations module<representations>`. +.. testsetup:: perslay + + import numpy + numpy.set_printoptions(precision=5) + +.. testcode:: perslay + + import numpy as np + import tensorflow as tf + from sklearn.preprocessing import MinMaxScaler + import gudhi.representations as gdr + import gudhi.tensorflow.perslay as prsl + + diagrams = [np.array([[0.,4.],[1.,2.],[3.,8.],[6.,8.]])] + diagrams = gdr.DiagramScaler(use=True, scalers=[([0,1], MinMaxScaler())]).fit_transform(diagrams) + diagrams = tf.RaggedTensor.from_tensor(tf.constant(diagrams, dtype=tf.float32)) + + rho = tf.identity + phi = prsl.GaussianPerslayPhi((5, 5), ((-.5, 1.5), (-.5, 1.5)), .1) + weight = prsl.PowerPerslayWeight(1.,0.) + perm_op = tf.math.reduce_sum + + perslay = prsl.Perslay(phi=phi, weight=weight, perm_op=perm_op, rho=rho) + vectors = perslay(diagrams) + print(vectors) + +.. testcleanup:: perslay + numpy.set_printoptions(precision=8) + +.. testoutput:: perslay + + tf.Tensor( + [[[[1.72661e-16] + [4.17060e-09] + [1.13369e-08] + [8.57388e-12] + [2.12439e-14]] + + [[4.17151e-09] + [1.00741e-01] + [2.73843e-01] + [3.07242e-02] + [7.61575e-05]] + + [[8.03829e-06] + [1.58027e+00] + [8.29970e-01] + [1.23954e+01] + [3.07241e-02]] + + [[8.02694e-06] + [1.30657e+00] + [9.09230e+00] + [6.16648e-02] + [1.39492e-06]] + + [[9.03313e-13] + [1.49548e-07] + [1.51460e-04] + [1.02051e-06] + [7.80935e-16]]]], shape=(1, 5, 5, 1), dtype=float32) Preprocessing ------------- @@ -80,3 +142,44 @@ Metrics :members: :special-members: :show-inheritance: + +PersLay +------- +.. autoclass:: gudhi.tensorflow.perslay.Perslay + :members: + :special-members: + :show-inheritance: + +Weight functions +^^^^^^^^^^^^^^^^ +.. autoclass:: gudhi.tensorflow.perslay.GaussianMixturePerslayWeight + :members: + :special-members: + :show-inheritance: + +.. autoclass:: gudhi.tensorflow.perslay.GridPerslayWeight + :members: + :special-members: + :show-inheritance: + +.. autoclass:: gudhi.tensorflow.perslay.PowerPerslayWeight + :members: + :special-members: + :show-inheritance: + +Phi functions +^^^^^^^^^^^^^ +.. autoclass:: gudhi.tensorflow.perslay.FlatPerslayPhi + :members: + :special-members: + :show-inheritance: + +.. autoclass:: gudhi.tensorflow.perslay.GaussianPerslayPhi + :members: + :special-members: + :show-inheritance: + +.. autoclass:: gudhi.tensorflow.perslay.TentPerslayPhi + :members: + :special-members: + :show-inheritance: |