Merge pull request #402 from MathieuCarriere/perslay

perslay

6 files changed, 566 insertions, 23 deletions

diff --git a/src/python/CMakeLists.txt b/src/python/CMakeLists.txt
index 39e2acd4..198d0c65 100644
--- a/src/python/CMakeLists.txt
+++ b/src/python/CMakeLists.txt
@@ -291,8 +291,8 @@ 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 "${CMAKE_CURRENT_BINARY_DIR}/gudhi")    
-    file(COPY "gudhi/tensorflow" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi")
+    file(COPY "gudhi/tensorflow" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi/")
+    file(COPY "gudhi/wasserstein" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi")
     file(COPY "gudhi/point_cloud" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi")
     file(COPY "gudhi/clustering" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi" FILES_MATCHING PATTERN "*.py")
     file(COPY "gudhi/weighted_rips_complex.py" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}/gudhi")
@@ -572,6 +572,11 @@ if(PYTHONINTERP_FOUND)
       add_gudhi_py_test(test_diff)
     endif()
 
+    # Perslay
+    if(TENSORFLOW_FOUND AND SKLEARN_FOUND)
+      add_gudhi_py_test(test_perslay)
+    endif()
+
     # Betti curves
     if(SKLEARN_FOUND AND SCIPY_FOUND)
       add_gudhi_py_test(test_betti_curve_representations)
diff --git a/src/python/doc/installation.rst b/src/python/doc/installation.rst
index 5491542f..7200b2f0 100644
--- a/src/python/doc/installation.rst
+++ b/src/python/doc/installation.rst
@@ -396,11 +396,13 @@ mathematics, science, and engineering.
 TensorFlow
 ----------
 
+:class:`~gudhi.tensorflow.perslay.Perslay` from the :doc:`persistence representations </representations>` module
+requires `TensorFlow <https://www.tensorflow.org/>`_.
 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>`_
+and :doc:`Rips complex </rips_complex_tflow_itf_ref>` modules require `TensorFlow`_
 for incorporating them in neural nets. 
 
-`TensorFlow <https://www.tensorflow.org>`_ is also used in some automatic differentiation tests.
+`TensorFlow`_ is also used in some automatic differentiation tests.
 
 Bug reports and contributions
 *****************************
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:
diff --git a/src/python/doc/representations_sum.inc b/src/python/doc/representations_sum.inc
index 9515f044..f8c31ecf 100644
--- a/src/python/doc/representations_sum.inc
+++ b/src/python/doc/representations_sum.inc
@@ -1,14 +1,16 @@
 .. table::
    :widths: 30 40 30
 
-   +------------------------------------------------------------------+----------------------------------------------------------------+-------------------------------------------------------------------------+
-   | .. figure::                                                      | Vectorizations, distances and kernels that work on persistence | :Author: Mathieu Carrière, Martin Royer, Gard Spreemann, Wojciech Reise |
-   |      img/sklearn-tda.png                                         | diagrams, compatible with scikit-learn.                        |                                                                         |
-   |                                                                  |                                                                | :Since: GUDHI 3.1.0                                                     |
-   |                                                                  |                                                                |                                                                         |
-   |                                                                  |                                                                | :License: MIT                                                           |
-   |                                                                  |                                                                |                                                                         |
-   |                                                                  |                                                                | :Requires: `Scikit-learn <installation.html#scikit-learn>`_             |
-   +------------------------------------------------------------------+----------------------------------------------------------------+-------------------------------------------------------------------------+
-   | * :doc:`representations`                                                                                                                                                                                    |
-   +------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------+
+   +------------------------------------------------------------------+----------------------------------------------------------------+------------------------------------------------------------------------------------------------------------+
+   | .. figure::                                                      | Vectorizations, distances and kernels that work on persistence | :Author: Mathieu Carrière, Martin Royer, Gard Spreemann, Wojciech Reise                                    |
+   |      img/sklearn-tda.png                                         | diagrams, compatible with scikit-learn and tensorflow.         |                                                                                                            |
+   |                                                                  |                                                                | :Since: GUDHI 3.1.0                                                                                        |
+   |                                                                  |                                                                |                                                                                                            |
+   |                                                                  |                                                                | :License: MIT                                                                                              |
+   |                                                                  |                                                                |                                                                                                            |
+   |                                                                  |                                                                | :Requires: `Scikit-learn <installation.html#scikit-learn>`_, `TensorFlow <installation.html#tensorflow>`_  |
+   |                                                                  |                                                                |                                                                                                            |
+   +------------------------------------------------------------------+----------------------------------------------------------------+------------------------------------------------------------------------------------------------------------+
+   | * :doc:`representations`                                                                                                                                                                                                                       |
+   +------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
+
diff --git a/src/python/gudhi/tensorflow/perslay.py b/src/python/gudhi/tensorflow/perslay.py
new file mode 100644
index 00000000..9976c5f3
--- /dev/null
+++ b/src/python/gudhi/tensorflow/perslay.py
@@ -0,0 +1,284 @@
+# 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):       Mathieu Carrière
+#
+# Copyright (C) 2021 Inria
+#
+# Modification(s):
+#   - YYYY/MM Author: Description of the modification
+
+import tensorflow as tf
+import math
+
+class GridPerslayWeight(tf.keras.layers.Layer):
+    """
+    This is a class for computing a differentiable weight function for persistence diagram points. This function is defined from an array that contains its values on a 2D grid.
+    """
+    def __init__(self, grid, grid_bnds, **kwargs):
+        """
+        Constructor for the GridPerslayWeight class.
+  
+        Parameters:
+            grid (n x n numpy array): grid of values.
+            grid_bnds (2 x 2 numpy array): boundaries of the grid, of the form [[min_x, max_x], [min_y, max_y]].
+        """
+        super().__init__(dynamic=True, **kwargs)
+        self.grid = tf.Variable(initial_value=grid, trainable=True)
+        self.grid_bnds = grid_bnds
+    
+    def build(self, input_shape):
+        return self
+
+    def call(self, diagrams):
+        """
+        Apply GridPerslayWeight on a ragged tensor containing a list of persistence diagrams.
+
+        Parameters:
+            diagrams (n x None x 2): ragged tensor containing n persistence diagrams. The second dimension is ragged since persistence diagrams can have different numbers of points.
+
+        Returns:
+            weight (n x None): ragged tensor containing the weights of the points in the n persistence diagrams. The second dimension is ragged since persistence diagrams can have different numbers of points.
+        """
+        grid_shape = self.grid.shape
+        indices = []
+        for dim in range(2):
+            [m,M] = self.grid_bnds[dim]
+            coords = tf.expand_dims(diagrams[:,:,dim],-1)
+            ids = grid_shape[dim]*(coords-m)/(M-m)
+            indices.append(tf.cast(ids, tf.int32))
+        weight = tf.gather_nd(params=self.grid, indices=tf.concat(indices, axis=2))
+        return weight
+    
+class GaussianMixturePerslayWeight(tf.keras.layers.Layer):
+    """
+    This is a class for computing a differentiable weight function for persistence diagram points. This function is defined from a mixture of Gaussian functions.
+    """
+    def __init__(self, gaussians, **kwargs):
+        """
+        Constructor for the GridPerslayWeight class.
+  
+        Parameters:
+            gaussians (4 x n numpy array): parameters of the n Gaussian functions, of the form transpose([[mu_x^1, mu_y^1, sigma_x^1, sigma_y^1], ..., [mu_x^n, mu_y^n, sigma_x^n, sigma_y^n]]). 
+        """
+        super().__init__(dynamic=True, **kwargs)
+        self.W = tf.Variable(initial_value=gaussians, trainable=True)
+
+    def build(self, input_shape):
+        return self
+        
+    def call(self, diagrams):
+        """
+        Apply GaussianMixturePerslayWeight on a ragged tensor containing a list of persistence diagrams.
+
+        Parameters:
+            diagrams (n x None x 2): ragged tensor containing n persistence diagrams. The second dimension is ragged since persistence diagrams can have different numbers of points.
+
+        Returns:
+            weight (n x None): ragged tensor containing the weights of the points in the n persistence diagrams. The second dimension is ragged since persistence diagrams can have different numbers of points.
+        """
+        means     = tf.expand_dims(tf.expand_dims(self.W[:2,:],0),0)
+        variances = tf.expand_dims(tf.expand_dims(self.W[2:,:],0),0)
+        diagrams  = tf.expand_dims(diagrams, -1)
+        dists     = tf.math.multiply(tf.math.square(diagrams-means), 1/tf.math.square(variances))
+        weight    = tf.math.reduce_sum(tf.math.exp(tf.math.reduce_sum(-dists, axis=2)), axis=2)
+        return weight
+    
+class PowerPerslayWeight(tf.keras.layers.Layer):
+    """
+    This is a class for computing a differentiable weight function for persistence diagram points. This function is defined as a constant multiplied by the distance to the diagonal of the persistence diagram point raised to some power.
+    """
+    def __init__(self, constant, power, **kwargs):
+        """
+        Constructor for the PowerPerslayWeight class.
+  
+        Parameters:
+            constant (float): constant value.
+            power (float): power applied to the distance to the diagonal. 
+        """
+        super().__init__(dynamic=True, **kwargs)
+        self.constant = tf.Variable(initial_value=constant, trainable=True)
+        self.power = power
+        
+    def build(self, input_shape):
+        return self
+    
+    def call(self, diagrams):
+        """
+        Apply PowerPerslayWeight on a ragged tensor containing a list of persistence diagrams.
+
+        Parameters:
+            diagrams (n x None x 2): ragged tensor containing n persistence diagrams. The second dimension is ragged since persistence diagrams can have different numbers of points.
+
+        Returns:
+            weight (n x None): ragged tensor containing the weights of the points in the n persistence diagrams. The second dimension is ragged since persistence diagrams can have different numbers of points.
+        """
+        weight = self.constant * tf.math.pow(tf.math.abs(diagrams[:,:,1]-diagrams[:,:,0]), self.power)
+        return weight
+    
+
+class GaussianPerslayPhi(tf.keras.layers.Layer):
+    """
+    This is a class for computing a transformation function for persistence diagram points. This function turns persistence diagram points into 2D Gaussian functions centered on the points, that are then evaluated on a regular 2D grid.
+    """
+    def __init__(self, image_size, image_bnds, variance, **kwargs):
+        """
+        Constructor for the GaussianPerslayPhi class.
+  
+        Parameters:
+            image_size (int numpy array): number of grid elements on each grid axis, of the form [n_x, n_y].
+            image_bnds (2 x 2 numpy array): boundaries of the grid, of the form [[min_x, max_x], [min_y, max_y]].
+            variance (float): variance of the Gaussian functions. 
+        """
+        super().__init__(dynamic=True, **kwargs)
+        self.image_size = image_size
+        self.image_bnds = image_bnds
+        self.variance   = tf.Variable(initial_value=variance, trainable=True)
+        
+    def build(self, input_shape):
+        return self
+        
+    def call(self, diagrams):
+        """
+        Apply GaussianPerslayPhi on a ragged tensor containing a list of persistence diagrams.
+
+        Parameters:
+            diagrams (n x None x 2): ragged tensor containing n persistence diagrams. The second dimension is ragged since persistence diagrams can have different numbers of points.
+
+        Returns:
+            output (n x None x image_size x image_size x 1): ragged tensor containing the evaluations on the 2D grid of the 2D Gaussian functions corresponding to the persistence diagram points, in the form of a 2D image with 1 channel that can be processed with, e.g., convolutional layers. The second dimension is ragged since persistence diagrams can have different numbers of points.
+            output_shape (int numpy array): shape of the output tensor.
+        """
+        diagrams_d = tf.concat([diagrams[:,:,0:1], diagrams[:,:,1:2]-diagrams[:,:,0:1]], axis=2)
+        step = [(self.image_bnds[i][1]-self.image_bnds[i][0])/self.image_size[i] for i in range(2)]
+        coords = [tf.range(self.image_bnds[i][0], self.image_bnds[i][1], step[i]) for i in range(2)]
+        M = tf.meshgrid(*coords)
+        mu = tf.concat([tf.expand_dims(tens, 0) for tens in M], axis=0)
+        for _ in range(2):
+            diagrams_d = tf.expand_dims(diagrams_d,-1)
+        dists = tf.math.square(diagrams_d-mu) / (2*tf.math.square(self.variance))
+        gauss = tf.math.exp(tf.math.reduce_sum(-dists, axis=2)) / (2*math.pi*tf.math.square(self.variance))
+        output = tf.expand_dims(gauss,-1)
+        output_shape = M[0].shape + tuple([1])
+        return output, output_shape
+     
+class TentPerslayPhi(tf.keras.layers.Layer):
+    """
+    This is a class for computing a transformation function for persistence diagram points. This function turns persistence diagram points into 1D tent functions (linearly increasing on the first half of the bar corresponding to the point from zero to half of the bar length, linearly decreasing on the second half and zero elsewhere) centered on the points, that are then evaluated on a regular 1D grid.
+    """
+    def __init__(self, samples, **kwargs):
+        """
+        Constructor for the GaussianPerslayPhi class.
+  
+        Parameters:
+            samples (float numpy array): grid elements on which to evaluate the tent functions, of the form [x_1, ..., x_n].
+        """
+        super().__init__(dynamic=True, **kwargs)
+        self.samples   = tf.Variable(initial_value=samples, trainable=True)
+        
+    def build(self, input_shape):
+        return self
+        
+    def call(self, diagrams):
+        """
+        Apply TentPerslayPhi on a ragged tensor containing a list of persistence diagrams.
+
+        Parameters:
+            diagrams (n x None x 2): ragged tensor containing n persistence diagrams. The second dimension is ragged since persistence diagrams can have different numbers of points.
+
+        Returns:
+            output (n x None x num_samples): ragged tensor containing the evaluations on the 1D grid of the 1D tent functions corresponding to the persistence diagram points. The second dimension is ragged since persistence diagrams can have different numbers of points.
+            output_shape (int numpy array): shape of the output tensor.
+        """
+        samples_d = tf.expand_dims(tf.expand_dims(self.samples,0),0)
+        xs, ys = diagrams[:,:,0:1], diagrams[:,:,1:2]
+        output = tf.math.maximum(.5*(ys-xs) - tf.math.abs(samples_d-.5*(ys+xs)), tf.constant([0.]))
+        output_shape = self.samples.shape
+        return output, output_shape
+    
+class FlatPerslayPhi(tf.keras.layers.Layer):
+    """
+    This is a class for computing a transformation function for persistence diagram points. This function turns persistence diagram points into 1D constant functions (that evaluate to half of the bar length on the bar corresponding to the point and zero elsewhere), that are then evaluated on a regular 1D grid.
+    """
+    def __init__(self, samples, theta, **kwargs):
+        """
+        Constructor for the FlatPerslayPhi class.
+  
+        Parameters:
+            samples (float numpy array): grid elements on which to evaluate the constant functions, of the form [x_1, ..., x_n].
+            theta (float): sigmoid parameter used to approximate the constant function with a differentiable sigmoid function. The bigger the theta, the closer to a constant function the output will be. 
+        """
+        super().__init__(dynamic=True, **kwargs)
+        self.samples = tf.Variable(initial_value=samples, trainable=True)
+        self.theta   = tf.Variable(initial_value=theta,   trainable=True)
+        
+    def build(self, input_shape):
+        return self
+        
+    def call(self, diagrams):
+        """
+        Apply FlatPerslayPhi on a ragged tensor containing a list of persistence diagrams.
+
+        Parameters:
+            diagrams (n x None x 2): ragged tensor containing n persistence diagrams. The second dimension is ragged since persistence diagrams can have different numbers of points.
+
+        Returns:
+            output (n x None x num_samples): ragged tensor containing the evaluations on the 1D grid of the 1D constant functions corresponding to the persistence diagram points. The second dimension is ragged since persistence diagrams can have different numbers of points.
+            output_shape (int numpy array): shape of the output tensor.
+        """
+        samples_d = tf.expand_dims(tf.expand_dims(self.samples,0),0)
+        xs, ys = diagrams[:,:,0:1], diagrams[:,:,1:2]
+        output = 1./(1.+tf.math.exp(-self.theta*(.5*(ys-xs)-tf.math.abs(samples_d-.5*(ys+xs)))))
+        output_shape = self.samples.shape
+        return output, output_shape
+
+class Perslay(tf.keras.layers.Layer):
+    """
+    This is a TensorFlow layer for vectorizing persistence diagrams in a differentiable way within a neural network. This function implements the PersLay equation, see `the corresponding article <http://proceedings.mlr.press/v108/carriere20a.html>`_.
+    """
+    def __init__(self, weight, phi, perm_op, rho, **kwargs):
+        """
+        Constructor for the Perslay class.
+
+        Parameters:
+            weight (function): weight function for the persistence diagram points. Can be either :class:`~gudhi.tensorflow.perslay.GridPerslayWeight`, :class:`~gudhi.tensorflow.perslay.GaussianMixturePerslayWeight`, :class:`~gudhi.tensorflow.perslay.PowerPerslayWeight`, or a custom TensorFlow function that takes persistence diagrams as argument (represented as an (n x None x 2) ragged tensor, where n is the number of diagrams).
+            phi (function): transformation function for the persistence diagram points. Can be either :class:`~gudhi.tensorflow.perslay.GaussianPerslayPhi`, :class:`~gudhi.tensorflow.perslay.TentPerslayPhi`, :class:`~gudhi.tensorflow.perslay.FlatPerslayPhi`, or a custom TensorFlow class (that can have trainable parameters) with a method `call` that takes persistence diagrams as argument (represented as an (n x None x 2) ragged tensor, where n is the number of diagrams).
+            perm_op (function): permutation invariant function, such as `tf.math.reduce_sum`, `tf.math.reduce_mean`, `tf.math.reduce_max`, `tf.math.reduce_min`, or a custom TensorFlow function that takes two arguments: a tensor and an axis on which to apply the permutation invariant operation. If perm_op is the string "topk" (where k is a number), this function will be computed as `tf.math.top_k` with parameter `int(k)`.
+            rho (function): postprocessing function that is applied after the permutation invariant operation. Can be any TensorFlow layer.
+        """
+        super().__init__(dynamic=True, **kwargs)
+        self.weight  = weight
+        self.phi     = phi
+        self.perm_op = perm_op  
+        self.rho     = rho
+
+    def build(self, input_shape):
+        return self
+
+    def call(self, diagrams):
+        """
+        Apply Perslay on a ragged tensor containing a list of persistence diagrams.
+
+        Parameters:
+            diagrams (n x None x 2): ragged tensor containing n persistence diagrams. The second dimension is ragged since persistence diagrams can have different numbers of points.
+
+        Returns:
+            vector (n x output_shape): tensor containing the vectorizations of the persistence diagrams.
+        """
+        vector, dim = self.phi(diagrams)
+        weight = self.weight(diagrams)
+        for _ in range(len(dim)):
+            weight = tf.expand_dims(weight, -1)
+        vector = tf.math.multiply(vector, weight)
+          
+        permop = self.perm_op
+        if type(permop) == str and permop[:3] == 'top':
+            k = int(permop[3:])
+            vector = vector.to_tensor(default_value=-1e10)
+            vector = tf.math.top_k(tf.transpose(vector, perm=[0, 2, 1]), k=k).values
+            vector = tf.reshape(vector, [-1,k*dim[0]])
+        else:
+            vector = permop(vector, axis=1)
+
+        vector = self.rho(vector)
+            
+        return vector
diff --git a/src/python/test/test_perslay.py b/src/python/test/test_perslay.py
new file mode 100644
index 00000000..06497712
--- /dev/null
+++ b/src/python/test/test_perslay.py
@@ -0,0 +1,147 @@
+import numpy             as np
+import tensorflow        as tf
+from sklearn.preprocessing import MinMaxScaler
+from gudhi.tensorflow.perslay import *
+import gudhi.representations as gdr
+
+def test_gaussian_perslay():
+
+    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 = GaussianPerslayPhi((5, 5), ((-.5, 1.5), (-.5, 1.5)), .1)
+    weight = PowerPerslayWeight(1.,0.)
+    perm_op = tf.math.reduce_sum
+    
+    perslay = Perslay(phi=phi, weight=weight, perm_op=perm_op, rho=rho)
+    vectors = perslay(diagrams)
+
+    print(vectors.shape)
+
+    assert np.linalg.norm(vectors.numpy() - np.array(
+[[[[1.7266072e-16],
+   [4.1706043e-09],
+   [1.1336876e-08],
+   [8.5738821e-12],
+   [2.1243891e-14]],
+
+  [[4.1715076e-09],
+   [1.0074080e-01],
+   [2.7384272e-01],
+   [3.0724244e-02],
+   [7.6157507e-05]],
+
+  [[8.0382870e-06],
+   [1.5802664e+00],
+   [8.2997030e-01],
+   [1.2395413e+01],
+   [3.0724116e-02]],
+
+  [[8.0269419e-06],
+   [1.3065740e+00],
+   [9.0923014e+00],
+   [6.1664842e-02],
+   [1.3949171e-06]],
+
+  [[9.0331329e-13],
+   [1.4954816e-07],
+   [1.5145997e-04],
+   [1.0205092e-06],
+   [7.8093526e-16]]]]) <= 1e-7)
+
+test_gaussian_perslay()
+
+def test_tent_perslay():
+
+    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 = TentPerslayPhi(np.array(np.arange(-1.,2.,.1), dtype=np.float32))
+    weight = PowerPerslayWeight(1.,0.)
+    perm_op = 'top3'
+
+    perslay = Perslay(phi=phi, weight=weight, perm_op=perm_op, rho=rho)
+    vectors = perslay(diagrams)
+
+    assert np.linalg.norm(vectors-np.array([[0.,         0.,         0.,         0.,         0.,         0.,
+                                             0.,         0.,         0.,         0.,         0.,         0.,
+                                             0.,         0.,         0.,         0.,         0.,         0.,
+                                             0.,         0.,         0.,         0.,         0.,         0.,
+                                             0.,         0.,         0.,         0.,         0.,         0.,
+                                             0.,         0.,         0.,         0.09999999, 0.,         0.,
+                                             0.2,        0.05,       0.,         0.19999999, 0.,         0.,
+                                             0.09999999, 0.02500001, 0.,         0.125,      0.,         0.,
+                                             0.22500002, 0.,         0.,         0.3,        0.,         0.,
+                                             0.19999999, 0.05000001, 0.,         0.10000002, 0.10000002, 0.,
+                                             0.,         0.,         0.,         0.,         0.,         0.,
+                                             0.,         0.,         0.,         0.,         0.,         0.,
+                                             0.,         0.,         0.,         0.,         0.,         0.,
+                                             0.,         0.,         0.,         0.,         0.,         0.,
+                                             0.,         0.,         0.,         0.,         0.,         0.        ]])) <= 1e-7
+
+def test_flat_perslay():
+
+    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 = FlatPerslayPhi(np.array(np.arange(-1.,2.,.1), dtype=np.float32), 100.)
+    weight = PowerPerslayWeight(1.,0.)
+    perm_op = tf.math.reduce_sum
+    
+    perslay = Perslay(phi=phi, weight=weight, perm_op=perm_op, rho=rho)
+    vectors = perslay(diagrams)
+
+    assert np.linalg.norm(vectors-np.array([[0.0000000e+00, 0.0000000e+00, 1.8048651e-35, 3.9754645e-31, 8.7565101e-27,
+                                             1.9287571e-22, 4.2483860e-18, 9.3576392e-14, 2.0611652e-09, 4.5398087e-05,
+                                             5.0000376e-01, 1.0758128e+00, 1.9933071e+00, 1.0072457e+00, 1.9240967e+00,
+                                             1.4999963e+00, 1.0000458e+00, 1.0066929e+00, 1.9933071e+00, 1.9999092e+00,
+                                             1.0000000e+00, 9.0795562e-05, 4.1222914e-09, 1.8715316e-13, 8.4967405e-18,
+                                             3.8574998e-22, 1.7512956e-26, 7.9508388e-31, 3.6097302e-35, 0.0000000e+00]]) <= 1e-7)
+
+def test_gmix_weight():
+
+    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 = FlatPerslayPhi(np.array(np.arange(-1.,2.,.1), dtype=np.float32), 100.)
+    weight = GaussianMixturePerslayWeight(np.array([[.5],[.5],[5],[5]], dtype=np.float32))
+    perm_op = tf.math.reduce_sum
+
+    perslay = Perslay(phi=phi, weight=weight, perm_op=perm_op, rho=rho)
+    vectors = perslay(diagrams)
+
+    assert np.linalg.norm(vectors-np.array([[0.0000000e+00, 0.0000000e+00, 1.7869064e-35, 3.9359080e-31, 8.6693818e-27,
+                                             1.9095656e-22, 4.2061142e-18, 9.2645292e-14, 2.0406561e-09, 4.4946366e-05,
+                                             4.9502861e-01, 1.0652492e+00, 1.9753191e+00, 9.9723548e-01, 1.9043801e+00,
+                                             1.4844525e+00, 9.8947650e-01, 9.9604094e-01, 1.9703994e+00, 1.9769192e+00,
+                                             9.8850453e-01, 8.9751818e-05, 4.0749040e-09, 1.8500175e-13, 8.3990662e-18,
+                                             3.8131562e-22, 1.7311636e-26, 7.8594399e-31, 3.5682349e-35, 0.0000000e+00]]) <= 1e-7)
+
+def test_grid_weight():
+
+    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 = FlatPerslayPhi(np.array(np.arange(-1.,2.,.1), dtype=np.float32), 100.)
+    weight = GridPerslayWeight(np.array(np.random.uniform(size=[100,100]),dtype=np.float32),((-0.01, 1.01),(-0.01, 1.01)))
+    perm_op = tf.math.reduce_sum
+    
+    perslay = Perslay(phi=phi, weight=weight, perm_op=perm_op, rho=rho)
+    vectors = perslay(diagrams)
+
+    assert np.linalg.norm(vectors-np.array([[0.0000000e+00, 0.0000000e+00, 1.5124093e-37, 3.3314498e-33, 7.3379791e-29,
+                                             1.6163036e-24, 3.5601592e-20, 7.8417273e-16, 1.7272621e-11, 3.8043717e-07,
+                                             4.1902456e-03, 1.7198652e-02, 1.2386327e-01, 9.2694648e-03, 1.9515079e-01,
+                                             2.0629172e-01, 2.0210314e-01, 2.0442720e-01, 5.4709727e-01, 5.4939687e-01,
+                                             2.7471092e-01, 2.4942532e-05, 1.1324385e-09, 5.1413016e-14, 2.3341474e-18,
+                                             1.0596973e-22, 4.8110000e-27, 2.1841823e-31, 9.9163230e-36, 0.0000000e+00]]) <= 1e-7)