diff options
Diffstat (limited to 'src/python')
| -rw-r--r-- | src/python/CMakeLists.txt | 9 | ||||
| -rw-r--r-- | src/python/doc/cubical_complex_sum.inc | 25 | ||||
| -rw-r--r-- | src/python/doc/cubical_complex_tflow_itf_ref.rst | 40 | ||||
| -rw-r--r-- | src/python/doc/differentiation_sum.inc | 12 | ||||
| -rw-r--r-- | src/python/doc/installation.rst | 6 | ||||
| -rw-r--r-- | src/python/doc/ls_simplex_tree_tflow_itf_ref.rst | 53 | ||||
| -rw-r--r-- | src/python/doc/rips_complex_sum.inc | 5 | ||||
| -rw-r--r-- | src/python/doc/rips_complex_tflow_itf_ref.rst | 48 | ||||
| -rw-r--r-- | src/python/doc/simplex_tree_sum.inc | 23 | ||||
| -rw-r--r-- | src/python/gudhi/tensorflow/__init__.py | 5 | ||||
| -rw-r--r-- | src/python/gudhi/tensorflow/cubical_layer.py | 80 | ||||
| -rw-r--r-- | src/python/gudhi/tensorflow/lower_star_simplex_tree_layer.py | 84 | ||||
| -rw-r--r-- | src/python/gudhi/tensorflow/rips_layer.py | 91 | ||||
| -rw-r--r-- | src/python/test/test_diff.py | 78 |
14 files changed, 535 insertions, 24 deletions
diff --git a/src/python/CMakeLists.txt b/src/python/CMakeLists.txt index 54221151..2c682437 100644 --- a/src/python/CMakeLists.txt +++ b/src/python/CMakeLists.txt @@ -70,6 +70,7 @@ if(PYTHONINTERP_FOUND) set(GUDHI_PYTHON_MODULES "${GUDHI_PYTHON_MODULES}'euclidean_strong_witness_complex', ") # Modules that should not be auto-imported in __init__.py set(GUDHI_PYTHON_MODULES_EXTRA "${GUDHI_PYTHON_MODULES_EXTRA}'representations', ") + set(GUDHI_PYTHON_MODULES_EXTRA "${GUDHI_PYTHON_MODULES_EXTRA}'tensorflow', ") set(GUDHI_PYTHON_MODULES_EXTRA "${GUDHI_PYTHON_MODULES_EXTRA}'wasserstein', ") set(GUDHI_PYTHON_MODULES_EXTRA "${GUDHI_PYTHON_MODULES_EXTRA}'point_cloud', ") set(GUDHI_PYTHON_MODULES_EXTRA "${GUDHI_PYTHON_MODULES_EXTRA}'weighted_rips_complex', ") @@ -289,7 +290,8 @@ 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" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi") + file(COPY "gudhi/wasserstein" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi") + file(COPY "gudhi/tensorflow" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi") file(COPY "gudhi/point_cloud" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi") file(COPY "gudhi/clustering" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi" FILES_MATCHING PATTERN "*.py") file(COPY "gudhi/weighted_rips_complex.py" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi") @@ -562,6 +564,11 @@ if(PYTHONINTERP_FOUND) add_gudhi_py_test(test_representations) endif() + # Differentiation + if(TENSORFLOW_FOUND) + add_gudhi_py_test(test_diff) + endif() + # Betti curves if(SKLEARN_FOUND AND SCIPY_FOUND) add_gudhi_py_test(test_betti_curve_representations) diff --git a/src/python/doc/cubical_complex_sum.inc b/src/python/doc/cubical_complex_sum.inc index 87db184d..90ec9fc2 100644 --- a/src/python/doc/cubical_complex_sum.inc +++ b/src/python/doc/cubical_complex_sum.inc @@ -1,14 +1,17 @@ .. table:: :widths: 30 40 30 - +--------------------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------+ - | .. figure:: | The cubical complex represents a grid as a cell complex with | :Author: Pawel Dlotko | - | ../../doc/Bitmap_cubical_complex/Cubical_complex_representation.png | cells of all dimensions. | | - | :alt: Cubical complex representation | | :Since: GUDHI 2.0.0 | - | :figclass: align-center | | | - | | | :License: MIT | - | | | | - +--------------------------------------------------------------------------+----------------------------------------------------------------------+-----------------------------+ - | * :doc:`cubical_complex_user` | * :doc:`cubical_complex_ref` | - | | * :doc:`periodic_cubical_complex_ref` | - +--------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------+ + +--------------------------------------------------------------------------+----------------------------------------------------------------------+---------------------------------------------------------+ + | .. figure:: | The cubical complex represents a grid as a cell complex with | :Author: Pawel Dlotko | + | ../../doc/Bitmap_cubical_complex/Cubical_complex_representation.png | cells of all dimensions. | | + | :alt: Cubical complex representation | | :Since: GUDHI 2.0.0 | + | :figclass: align-center | | | + | | | :License: MIT | + | | | | + +--------------------------------------------------------------------------+----------------------------------------------------------------------+---------------------------------------------------------+ + | * :doc:`cubical_complex_user` | * :doc:`cubical_complex_ref` | + | | * :doc:`periodic_cubical_complex_ref` | + +--------------------------------------------------------------------------+----------------------------------------------------------------------+---------------------------------------------------------+ + | | * :doc:`cubical_complex_tflow_itf_ref` | :requires: `TensorFlow <installation.html#tensorflow>`_ | + | | | | + +--------------------------------------------------------------------------+----------------------------------------------------------------------+---------------------------------------------------------+ diff --git a/src/python/doc/cubical_complex_tflow_itf_ref.rst b/src/python/doc/cubical_complex_tflow_itf_ref.rst new file mode 100644 index 00000000..18b97adf --- /dev/null +++ b/src/python/doc/cubical_complex_tflow_itf_ref.rst @@ -0,0 +1,40 @@ +:orphan: + +.. To get rid of WARNING: document isn't included in any toctree + +TensorFlow layer for cubical persistence +######################################## + +.. include:: differentiation_sum.inc + +Example of gradient computed from cubical persistence +----------------------------------------------------- + +.. testcode:: + + from gudhi.tensorflow import CubicalLayer + import tensorflow as tf + + X = tf.Variable([[0.,2.,2.],[2.,2.,2.],[2.,2.,1.]], dtype=tf.float32, trainable=True) + cl = CubicalLayer(dimensions=[0]) + + with tf.GradientTape() as tape: + dgm = cl.call(X)[0][0] + loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0]))) + + grads = tape.gradient(loss, [X]) + print(grads[0].numpy()) + +.. testoutput:: + + [[ 0. 0. 0. ] + [ 0. 0.5 0. ] + [ 0. 0. -0.5]] + +Documentation for CubicalLayer +------------------------------ + +.. autoclass:: gudhi.tensorflow.CubicalLayer + :members: + :special-members: __init__ + :show-inheritance: diff --git a/src/python/doc/differentiation_sum.inc b/src/python/doc/differentiation_sum.inc new file mode 100644 index 00000000..3aec33df --- /dev/null +++ b/src/python/doc/differentiation_sum.inc @@ -0,0 +1,12 @@ +.. list-table:: + :widths: 40 30 30 + :header-rows: 0 + + * - :Since: GUDHI 3.5.0 + - :License: MIT + - :Requires: `TensorFlow <installation.html#tensorflow>`_ + +We provide TensorFlow 2 models that can handle automatic differentiation for the computation of persistence diagrams from complexes available in the Gudhi library. +This includes simplex trees, cubical complexes and Vietoris-Rips complexes. Detailed example on how to use these layers in practice are available +in the following `notebook <https://github.com/GUDHI/TDA-tutorial/blob/master/Tuto-GUDHI-optimization.ipynb>`_. Note that even if TensorFlow GPU is enabled, all +internal computations using Gudhi will be done on CPU. diff --git a/src/python/doc/installation.rst b/src/python/doc/installation.rst index cff84691..dd476054 100644 --- a/src/python/doc/installation.rst +++ b/src/python/doc/installation.rst @@ -396,7 +396,11 @@ mathematics, science, and engineering. TensorFlow ---------- -`TensorFlow <https://www.tensorflow.org>`_ is currently only used in some automatic differentiation tests. +The :doc:`cubical complex </cubical_complex_tflow_itf_ref>`, :doc:`simplex tree </ls_simplex_tree_tflow_itf_ref>` +and :doc:`Rips complex </rips_complex_tflow_itf_ref>` modules require `TensorFlow <https://www.tensorflow.org>`_ +for incorporating them in neural nets. + +`TensorFlow <https://www.tensorflow.org>`_ is also used in some automatic differentiation tests. Bug reports and contributions ***************************** diff --git a/src/python/doc/ls_simplex_tree_tflow_itf_ref.rst b/src/python/doc/ls_simplex_tree_tflow_itf_ref.rst new file mode 100644 index 00000000..b8518cdb --- /dev/null +++ b/src/python/doc/ls_simplex_tree_tflow_itf_ref.rst @@ -0,0 +1,53 @@ +:orphan: + +.. To get rid of WARNING: document isn't included in any toctree + +TensorFlow layer for lower-star persistence on simplex trees +############################################################ + +.. include:: differentiation_sum.inc + +Example of gradient computed from lower-star filtration of a simplex tree +------------------------------------------------------------------------- + +.. testcode:: + + from gudhi.tensorflow import LowerStarSimplexTreeLayer + import tensorflow as tf + import gudhi as gd + + st = gd.SimplexTree() + st.insert([0, 1]) + st.insert([1, 2]) + st.insert([2, 3]) + st.insert([3, 4]) + st.insert([4, 5]) + st.insert([5, 6]) + st.insert([6, 7]) + st.insert([7, 8]) + st.insert([8, 9]) + st.insert([9, 10]) + + F = tf.Variable([6.,4.,3.,4.,5.,4.,3.,2.,3.,4.,5.], dtype=tf.float32, trainable=True) + sl = LowerStarSimplexTreeLayer(simplextree=st, dimensions=[0]) + + with tf.GradientTape() as tape: + dgm = sl.call(F)[0][0] + loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0]))) + + grads = tape.gradient(loss, [F]) + print(grads[0].indices.numpy()) + print(grads[0].values.numpy()) + +.. testoutput:: + + [2 4] + [-1. 1.] + +Documentation for LowerStarSimplexTreeLayer +------------------------------------------- + +.. autoclass:: gudhi.tensorflow.LowerStarSimplexTreeLayer + :members: + :special-members: __init__ + :show-inheritance: diff --git a/src/python/doc/rips_complex_sum.inc b/src/python/doc/rips_complex_sum.inc index 2cb24990..6931ebee 100644 --- a/src/python/doc/rips_complex_sum.inc +++ b/src/python/doc/rips_complex_sum.inc @@ -11,4 +11,7 @@ | | | | +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------------------+ | * :doc:`rips_complex_user` | * :doc:`rips_complex_ref` | - +----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------+ + +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------------------+ + | | * :doc:`rips_complex_tflow_itf_ref` | :requires: `TensorFlow <installation.html#tensorflow>`_ | + | | | | + +----------------------------------------------------------------+------------------------------------------------------------------------+----------------------------------------------------------------------------------+ diff --git a/src/python/doc/rips_complex_tflow_itf_ref.rst b/src/python/doc/rips_complex_tflow_itf_ref.rst new file mode 100644 index 00000000..6c65c562 --- /dev/null +++ b/src/python/doc/rips_complex_tflow_itf_ref.rst @@ -0,0 +1,48 @@ +:orphan: + +.. To get rid of WARNING: document isn't included in any toctree + +TensorFlow layer for Vietoris-Rips persistence +############################################## + +.. include:: differentiation_sum.inc + +Example of gradient computed from Vietoris-Rips persistence +----------------------------------------------------------- + +.. testsetup:: + + import numpy + numpy.set_printoptions(precision=4) + +.. testcode:: + + from gudhi.tensorflow import RipsLayer + import tensorflow as tf + + X = tf.Variable([[1.,1.],[2.,2.]], dtype=tf.float32, trainable=True) + rl = RipsLayer(maximum_edge_length=2., dimensions=[0]) + + with tf.GradientTape() as tape: + dgm = rl.call(X)[0][0] + loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0]))) + + grads = tape.gradient(loss, [X]) + print(grads[0].numpy()) + +.. testcleanup:: + + numpy.set_printoptions(precision=8) + +.. testoutput:: + + [[-0.5 -0.5] + [ 0.5 0.5]] + +Documentation for RipsLayer +--------------------------- + +.. autoclass:: gudhi.tensorflow.RipsLayer + :members: + :special-members: __init__ + :show-inheritance: diff --git a/src/python/doc/simplex_tree_sum.inc b/src/python/doc/simplex_tree_sum.inc index a8858f16..3ad1292c 100644 --- a/src/python/doc/simplex_tree_sum.inc +++ b/src/python/doc/simplex_tree_sum.inc @@ -1,13 +1,16 @@ .. table:: :widths: 30 40 30 - +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------+ - | .. figure:: | The simplex tree is an efficient and flexible data structure for | :Author: Clément Maria | - | ../../doc/Simplex_tree/Simplex_tree_representation.png | representing general (filtered) simplicial complexes. | | - | :alt: Simplex tree representation | | :Since: GUDHI 2.0.0 | - | :figclass: align-center | The data structure is described in | | - | | :cite:`boissonnatmariasimplextreealgorithmica` | :License: MIT | - | | | | - +----------------------------------------------------------------+------------------------------------------------------------------------+-----------------------------+ - | * :doc:`simplex_tree_user` | * :doc:`simplex_tree_ref` | - +----------------------------------------------------------------+------------------------------------------------------------------------------------------------------+ + +----------------------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------------------+ + | .. figure:: | The simplex tree is an efficient and flexible data structure for | :Author: Clément Maria | + | ../../doc/Simplex_tree/Simplex_tree_representation.png | representing general (filtered) simplicial complexes. | | + | :alt: Simplex tree representation | | :Since: GUDHI 2.0.0 | + | :figclass: align-center | The data structure is described in | | + | | :cite:`boissonnatmariasimplextreealgorithmica` | :License: MIT | + | | | | + +----------------------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------------------+ + | * :doc:`simplex_tree_user` | * :doc:`simplex_tree_ref` | + +----------------------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------------------+ + | | * :doc:`ls_simplex_tree_tflow_itf_ref` | :requires: `TensorFlow <installation.html#tensorflow>`_ | + | | | | + +----------------------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------------------+ diff --git a/src/python/gudhi/tensorflow/__init__.py b/src/python/gudhi/tensorflow/__init__.py new file mode 100644 index 00000000..1599cf52 --- /dev/null +++ b/src/python/gudhi/tensorflow/__init__.py @@ -0,0 +1,5 @@ +from .cubical_layer import CubicalLayer +from .lower_star_simplex_tree_layer import LowerStarSimplexTreeLayer +from .rips_layer import RipsLayer + +__all__ = ["LowerStarSimplexTreeLayer", "RipsLayer", "CubicalLayer"] diff --git a/src/python/gudhi/tensorflow/cubical_layer.py b/src/python/gudhi/tensorflow/cubical_layer.py new file mode 100644 index 00000000..e8674d7b --- /dev/null +++ b/src/python/gudhi/tensorflow/cubical_layer.py @@ -0,0 +1,80 @@ +import numpy as np +import tensorflow as tf +from ..cubical_complex import CubicalComplex + +###################### +# Cubical filtration # +###################### + +# The parameters of the model are the pixel values. + +def _Cubical(Xflat, Xdim, dimensions): + # Parameters: Xflat (flattened image), + # Xdim (shape of non-flattened image) + # dimensions (homology dimensions) + + # Compute the persistence pairs with Gudhi + # We reverse the dimensions because CubicalComplex uses Fortran ordering + cc = CubicalComplex(dimensions=Xdim[::-1], top_dimensional_cells=Xflat) + cc.compute_persistence() + + # Retrieve and ouput image indices/pixels corresponding to positive and negative simplices + cof_pp = cc.cofaces_of_persistence_pairs() + + L_cofs = [] + for dim in dimensions: + + try: + cof = cof_pp[0][dim] + except IndexError: + cof = np.array([]) + + L_cofs.append(np.array(cof, dtype=np.int32)) + + return L_cofs + +class CubicalLayer(tf.keras.layers.Layer): + """ + TensorFlow layer for computing the persistent homology of a cubical complex + """ + def __init__(self, dimensions, min_persistence=None, **kwargs): + """ + Constructor for the CubicalLayer class + + Parameters: + dimensions (List[int]): homology dimensions + min_persistence (List[float]): minimum distance-to-diagonal of the points in the output persistence diagrams (default None, in which case 0. is used for all dimensions) + """ + super().__init__(dynamic=True, **kwargs) + self.dimensions = dimensions + self.min_persistence = min_persistence if min_persistence != None else [0.] * len(self.dimensions) + assert len(self.min_persistence) == len(self.dimensions) + + def call(self, X): + """ + Compute persistence diagram associated to a cubical complex filtered by some pixel values + + Parameters: + X (TensorFlow variable): pixel values of the cubical complex + + Returns: + dgms (list of tuple of TensorFlow variables): list of cubical persistence diagrams. The length of this list is the same than that of dimensions, i.e., there is one persistence diagram per homology dimension provided in the input list dimensions. Moreover, the finite and essential parts of the persistence diagrams are provided separately: each element of this list is a tuple of size two that contains the finite and essential parts of the corresponding persistence diagram, of shapes [num_finite_points, 2] and [num_essential_points, 1] respectively. Note that the essential part is always empty in cubical persistence diagrams, except in homology dimension zero, where the essential part always contains a single point, with abscissa equal to the smallest value in the complex, and infinite ordinate + """ + # Compute pixels associated to positive and negative simplices + # Don't compute gradient for this operation + Xflat = tf.reshape(X, [-1]) + Xdim, Xflat_numpy = X.shape, Xflat.numpy() + indices_list = _Cubical(Xflat_numpy, Xdim, self.dimensions) + index_essential = np.argmin(Xflat_numpy) # index of minimum pixel value for essential persistence diagram + # Get persistence diagram by simply picking the corresponding entries in the image + self.dgms = [] + for idx_dim, dimension in enumerate(self.dimensions): + finite_dgm = tf.reshape(tf.gather(Xflat, indices_list[idx_dim]), [-1,2]) + essential_dgm = tf.reshape(tf.gather(Xflat, index_essential), [-1,1]) if dimension == 0 else tf.zeros([0, 1]) + min_pers = self.min_persistence[idx_dim] + if min_pers >= 0: + persistent_indices = tf.where(tf.math.abs(finite_dgm[:,1]-finite_dgm[:,0]) > min_pers) + self.dgms.append((tf.reshape(tf.gather(finite_dgm, indices=persistent_indices), [-1,2]), essential_dgm)) + else: + self.dgms.append((finite_dgm, essential_dgm)) + return self.dgms diff --git a/src/python/gudhi/tensorflow/lower_star_simplex_tree_layer.py b/src/python/gudhi/tensorflow/lower_star_simplex_tree_layer.py new file mode 100644 index 00000000..a2e48d8a --- /dev/null +++ b/src/python/gudhi/tensorflow/lower_star_simplex_tree_layer.py @@ -0,0 +1,84 @@ +import numpy as np +import tensorflow as tf + +######################################### +# Lower star filtration on simplex tree # +######################################### + +# The parameters of the model are the vertex function values of the simplex tree. + +def _LowerStarSimplexTree(simplextree, filtration, dimensions): + # Parameters: simplextree (simplex tree on which to compute persistence) + # filtration (function values on the vertices of st), + # dimensions (homology dimensions), + + simplextree.reset_filtration(-np.inf, 0) + + # Assign new filtration values + for i in range(simplextree.num_vertices()): + simplextree.assign_filtration([i], filtration[i]) + simplextree.make_filtration_non_decreasing() + + # Compute persistence diagram + simplextree.compute_persistence() + + # Get vertex pairs for optimization. First, get all simplex pairs + pairs = simplextree.lower_star_persistence_generators() + + L_indices = [] + for dimension in dimensions: + + finite_pairs = pairs[0][dimension] if len(pairs[0]) >= dimension+1 else np.empty(shape=[0,2]) + essential_pairs = pairs[1][dimension] if len(pairs[1]) >= dimension+1 else np.empty(shape=[0,1]) + + finite_indices = np.array(finite_pairs.flatten(), dtype=np.int32) + essential_indices = np.array(essential_pairs.flatten(), dtype=np.int32) + + L_indices.append((finite_indices, essential_indices)) + + return L_indices + +class LowerStarSimplexTreeLayer(tf.keras.layers.Layer): + """ + TensorFlow layer for computing lower-star persistence out of a simplex tree + """ + def __init__(self, simplextree, dimensions, min_persistence=None, **kwargs): + """ + Constructor for the LowerStarSimplexTreeLayer class + + Parameters: + simplextree (gudhi.SimplexTree): underlying simplex tree. Its vertices MUST be named with integers from 0 to n = number of vertices. Note that its filtration values are modified in each call of the class. + dimensions (List[int]): homology dimensions + min_persistence (List[float]): minimum distance-to-diagonal of the points in the output persistence diagrams (default None, in which case 0. is used for all dimensions) + """ + super().__init__(dynamic=True, **kwargs) + self.dimensions = dimensions + self.simplextree = simplextree + self.min_persistence = min_persistence if min_persistence != None else [0. for _ in range(len(self.dimensions))] + assert len(self.min_persistence) == len(self.dimensions) + + def call(self, filtration): + """ + Compute lower-star persistence diagram associated to a function defined on the vertices of the simplex tree + + Parameters: + F (TensorFlow variable): filter function values over the vertices of the simplex tree. The ith entry of F corresponds to vertex i in self.simplextree + + Returns: + dgms (list of tuple of TensorFlow variables): list of lower-star persistence diagrams. The length of this list is the same than that of dimensions, i.e., there is one persistence diagram per homology dimension provided in the input list dimensions. Moreover, the finite and essential parts of the persistence diagrams are provided separately: each element of this list is a tuple of size two that contains the finite and essential parts of the corresponding persistence diagram, of shapes [num_finite_points, 2] and [num_essential_points, 1] respectively + """ + # Don't try to compute gradients for the vertex pairs + indices = _LowerStarSimplexTree(self.simplextree, filtration.numpy(), self.dimensions) + # Get persistence diagrams + self.dgms = [] + for idx_dim, dimension in enumerate(self.dimensions): + finite_dgm = tf.reshape(tf.gather(filtration, indices[idx_dim][0]), [-1,2]) + essential_dgm = tf.reshape(tf.gather(filtration, indices[idx_dim][1]), [-1,1]) + min_pers = self.min_persistence[idx_dim] + if min_pers >= 0: + persistent_indices = tf.where(tf.math.abs(finite_dgm[:,1]-finite_dgm[:,0]) > min_pers) + self.dgms.append((tf.reshape(tf.gather(finite_dgm, indices=persistent_indices),[-1,2]), essential_dgm)) + else: + self.dgms.append((finite_dgm, essential_dgm)) + return self.dgms + diff --git a/src/python/gudhi/tensorflow/rips_layer.py b/src/python/gudhi/tensorflow/rips_layer.py new file mode 100644 index 00000000..b5b58ab4 --- /dev/null +++ b/src/python/gudhi/tensorflow/rips_layer.py @@ -0,0 +1,91 @@ +import numpy as np +import tensorflow as tf +from ..rips_complex import RipsComplex + +############################ +# Vietoris-Rips filtration # +############################ + +# The parameters of the model are the point coordinates. + +def _Rips(DX, max_edge, dimensions): + # Parameters: DX (distance matrix), + # max_edge (maximum edge length for Rips filtration), + # dimensions (homology dimensions) + + # Compute the persistence pairs with Gudhi + rc = RipsComplex(distance_matrix=DX, max_edge_length=max_edge) + st = rc.create_simplex_tree(max_dimension=max(dimensions)+1) + st.compute_persistence() + pairs = st.flag_persistence_generators() + + L_indices = [] + for dimension in dimensions: + + if dimension == 0: + finite_pairs = pairs[0] + essential_pairs = pairs[2] + else: + finite_pairs = pairs[1][dimension-1] if len(pairs[1]) >= dimension else np.empty(shape=[0,4]) + essential_pairs = pairs[3][dimension-1] if len(pairs[3]) >= dimension else np.empty(shape=[0,2]) + + finite_indices = np.array(finite_pairs.flatten(), dtype=np.int32) + essential_indices = np.array(essential_pairs.flatten(), dtype=np.int32) + + L_indices.append((finite_indices, essential_indices)) + + return L_indices + +class RipsLayer(tf.keras.layers.Layer): + """ + TensorFlow layer for computing Rips persistence out of a point cloud + """ + def __init__(self, dimensions, maximum_edge_length=np.inf, min_persistence=None, **kwargs): + """ + Constructor for the RipsLayer class + + Parameters: + maximum_edge_length (float): maximum edge length for the Rips complex + dimensions (List[int]): homology dimensions + min_persistence (List[float]): minimum distance-to-diagonal of the points in the output persistence diagrams (default None, in which case 0. is used for all dimensions) + """ + super().__init__(dynamic=True, **kwargs) + self.max_edge = maximum_edge_length + self.dimensions = dimensions + self.min_persistence = min_persistence if min_persistence != None else [0. for _ in range(len(self.dimensions))] + assert len(self.min_persistence) == len(self.dimensions) + + def call(self, X): + """ + Compute Rips persistence diagram associated to a point cloud + + Parameters: + X (TensorFlow variable): point cloud of shape [number of points, number of dimensions] + + Returns: + dgms (list of tuple of TensorFlow variables): list of Rips persistence diagrams. The length of this list is the same than that of dimensions, i.e., there is one persistence diagram per homology dimension provided in the input list dimensions. Moreover, the finite and essential parts of the persistence diagrams are provided separately: each element of this list is a tuple of size two that contains the finite and essential parts of the corresponding persistence diagram, of shapes [num_finite_points, 2] and [num_essential_points, 1] respectively + """ + # Compute distance matrix + DX = tf.norm(tf.expand_dims(X, 1)-tf.expand_dims(X, 0), axis=2) + # Compute vertices associated to positive and negative simplices + # Don't compute gradient for this operation + indices = _Rips(DX.numpy(), self.max_edge, self.dimensions) + # Get persistence diagrams by simply picking the corresponding entries in the distance matrix + self.dgms = [] + for idx_dim, dimension in enumerate(self.dimensions): + cur_idx = indices[idx_dim] + if dimension > 0: + finite_dgm = tf.reshape(tf.gather_nd(DX, tf.reshape(cur_idx[0], [-1,2])), [-1,2]) + essential_dgm = tf.reshape(tf.gather_nd(DX, tf.reshape(cur_idx[1], [-1,2])), [-1,1]) + else: + reshaped_cur_idx = tf.reshape(cur_idx[0], [-1,3]) + finite_dgm = tf.concat([tf.zeros([reshaped_cur_idx.shape[0],1]), tf.reshape(tf.gather_nd(DX, reshaped_cur_idx[:,1:]), [-1,1])], axis=1) + essential_dgm = tf.zeros([cur_idx[1].shape[0],1]) + min_pers = self.min_persistence[idx_dim] + if min_pers >= 0: + persistent_indices = tf.where(tf.math.abs(finite_dgm[:,1]-finite_dgm[:,0]) > min_pers) + self.dgms.append((tf.reshape(tf.gather(finite_dgm, indices=persistent_indices),[-1,2]), essential_dgm)) + else: + self.dgms.append((finite_dgm, essential_dgm)) + return self.dgms + diff --git a/src/python/test/test_diff.py b/src/python/test/test_diff.py new file mode 100644 index 00000000..e0a4717c --- /dev/null +++ b/src/python/test/test_diff.py @@ -0,0 +1,78 @@ +from gudhi.tensorflow import * +import numpy as np +import tensorflow as tf +import gudhi as gd + +def test_rips_diff(): + + Xinit = np.array([[1.,1.],[2.,2.]], dtype=np.float32) + X = tf.Variable(initial_value=Xinit, trainable=True) + rl = RipsLayer(maximum_edge_length=2., dimensions=[0]) + + with tf.GradientTape() as tape: + dgm = rl.call(X)[0][0] + loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0]))) + grads = tape.gradient(loss, [X]) + assert tf.norm(grads[0]-tf.constant([[-.5,-.5],[.5,.5]]),1) <= 1e-6 + +def test_cubical_diff(): + + Xinit = np.array([[0.,2.,2.],[2.,2.,2.],[2.,2.,1.]], dtype=np.float32) + X = tf.Variable(initial_value=Xinit, trainable=True) + cl = CubicalLayer(dimensions=[0]) + + with tf.GradientTape() as tape: + dgm = cl.call(X)[0][0] + loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0]))) + grads = tape.gradient(loss, [X]) + assert tf.norm(grads[0]-tf.constant([[0.,0.,0.],[0.,.5,0.],[0.,0.,-.5]]),1) <= 1e-6 + +def test_nonsquare_cubical_diff(): + + Xinit = np.array([[-1.,1.,0.],[1.,1.,1.]], dtype=np.float32) + X = tf.Variable(initial_value=Xinit, trainable=True) + cl = CubicalLayer(dimensions=[0]) + + with tf.GradientTape() as tape: + dgm = cl.call(X)[0][0] + loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0]))) + grads = tape.gradient(loss, [X]) + assert tf.norm(grads[0]-tf.constant([[0.,0.5,-0.5],[0.,0.,0.]]),1) <= 1e-6 + +def test_st_diff(): + + st = gd.SimplexTree() + st.insert([0]) + st.insert([1]) + st.insert([2]) + st.insert([3]) + st.insert([4]) + st.insert([5]) + st.insert([6]) + st.insert([7]) + st.insert([8]) + st.insert([9]) + st.insert([10]) + st.insert([0, 1]) + st.insert([1, 2]) + st.insert([2, 3]) + st.insert([3, 4]) + st.insert([4, 5]) + st.insert([5, 6]) + st.insert([6, 7]) + st.insert([7, 8]) + st.insert([8, 9]) + st.insert([9, 10]) + + Finit = np.array([6.,4.,3.,4.,5.,4.,3.,2.,3.,4.,5.], dtype=np.float32) + F = tf.Variable(initial_value=Finit, trainable=True) + sl = LowerStarSimplexTreeLayer(simplextree=st, dimensions=[0]) + + with tf.GradientTape() as tape: + dgm = sl.call(F)[0][0] + loss = tf.math.reduce_sum(tf.square(.5*(dgm[:,1]-dgm[:,0]))) + grads = tape.gradient(loss, [F]) + + assert tf.math.reduce_all(tf.math.equal(grads[0].indices, tf.constant([2,4]))) + assert tf.math.reduce_all(tf.math.equal(grads[0].values, tf.constant([-1.,1.]))) + |