morphoclass.layers.perslay module

Implementation of the PersLay layer.

class morphoclass.layers.perslay.GaussianPointTransformer(out_features)

Bases: morphoclass.layers.perslay.PointTransformer

Applies Gaussian point transformation for persistence diagram embedding.

This transformation can be applied to persistence diagrams, and is implemented as described in [1]. Note that points are assumed to lie in a normalized diagram, i.e. coordinates should lie in the interval (0, 1).

Shapes:

  • input: [N, 2]. N is the total number of points in the batch (belonging to different persistence diagrams as specified by point_index), and 2 refers to the 2 coordinates of each point of each persistence diagram i.e. (birth_date, death_date).

  • point_index: [N]. N is the total number of points in the batch.

  • output: [N, Q]. N is the total number of points in the batch, and Q is the desired number of learnable sample points used in the transformation.

Parameters

out_features (int) – Size of each output sample, corresponding to the desired number of sample points.

sample_points

Sample points of the transformation, with shape [2, Q].

Type

tensor

sample_inverse_sigmas

Inverse standard deviations of the transformation, with shape [2, Q] since each of the 2 dimensions may have different sigma.

Type

tensor

Examples

>>> inp = torch.tensor([[0.2, 0.3], [0.1, 0.4], [0.6, 0.3], [0.2, 0.1],        [0.5, 0.2], [0.1, 0.3], [0.6, 0.2]])
>>> point_index = torch.tensor([0, 0, 0, 1, 1, 2, 2])
>>> m = GaussianPointTransformer(out_features=32)
>>> output = m(inp)
>>> print(inp.size())
torch.Size([7, 2])
>>> print(output.size())
torch.Size([7, 32])

References

[1] Carriere, Mathieu, et al. “PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures.” stat 1050 (2019): 17.

extra_repr()

Get a string representation of layer parameters.

forward(input, point_index)

Perform the forward pass.

Parameters

  • input (torch.Tensor) – A batch of input data.

  • point_index (torch.Tensor) – A segmentation map for the samples in the batch.

Returns

The output tensor.

Return type

torch.Tensor

reset_parameters()

Randomly initialize the trainable parameters.

training: bool
class morphoclass.layers.perslay.PersLay(out_features, transformation='gaussian', operation='sum', weights='uniform')

Bases: torch.nn.modules.module.Module

Applies PersLay embedding layer.

This transformation can be applied to persistence diagrams, and is implemented as described in [1]. Note that points are assumed to lie in a normalized diagram, i.e. coordinates should lie in the interval (0, 1).

Shapes:

  • input : [N, 2]. N is the total number of points in the batch (belonging to different persistence diagrams as specified by point_index), and 2 refers to the 2 coordinates of each point of each persistence diagram i.e. (birth_date, death_date).

  • point_index : [N]. N is the total number of points in the batch.

  • output : [D, Q]. D is the number of different persistence diagrams in the batch, and Q is the desired number of learnable sample points used in the transformation.

Parameters

  • out_features (int) – Output size of the produced embedding.

  • transformation (str or nn.Module) – A point transformation, mapping each point of a persistence diagram to a vector. One of ‘gaussian’, ‘pointwise’, or a nn.Module.

  • operation (str) – A permutation invariant operation. One of ‘sum’, ‘mean’, ‘max’.

  • weights (str) – Approach to be used for the weights. One of ‘attention’ (learnable pointwise weights), ‘uniform’ (all weights set to 1), ‘grid’ (learnable weights on a 10x10 grid).

References

[1] Carriere, Mathieu, et al. “PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures.” stat 1050 (2019): 17.

forward(input, point_index)

Perform the forward pass.

Parameters

  • input (torch.Tensor) – A batch of input data.

  • point_index (torch.Tensor) – A segmentation map for the samples in the batch.

Returns

The output tensor.

Return type

torch.Tensor

point_transformer: PointTransformer
reduction: Callable
reset_parameters()

Randomly initialize trainable parameters.

training: bool
class morphoclass.layers.perslay.PointTransformer

Bases: torch.nn.modules.module.Module, abc.ABC

A point transformation for persistence diagram embedding.

abstract extra_repr() → str

Get a string representation of layer parameters.

abstract forward(input: torch.Tensor, point_index: torch.Tensor) → torch.Tensor

Perform the forward pass.

Parameters

  • input (torch.Tensor) – A batch of input data.

  • point_index (torch.Tensor) – A segmentation map for the samples in the batch.

Returns

The output tensor.

Return type

torch.Tensor

training: bool
class morphoclass.layers.perslay.PointwisePointTransformer(out_features, hidden_features=32)

Bases: morphoclass.layers.perslay.PointTransformer

Applies point-wise point transformation for persistence diagram embedding.

Parameters

  • out_features (int) – Size of each output sample, corresponding to the desired number of sample points.

  • hidden_features (int) – The size of the hidden layer.

extra_repr()

Get a string representation of layer parameters.

forward(input, point_index)

Perform the forward pass.

Parameters

  • input (torch.Tensor) – A batch of input data.

  • point_index (torch.Tensor) – A segmentation map for the samples in the batch.

Returns

The output tensor.

Return type

torch.Tensor

training: bool