torchPersLay 0.1.1

A PyTorch implementation of PersLay.

torchPersLay

torchPersLay is a PyTorch implementation of PersLay, a neural network layer for processing persistence diagrams in topological data analysis (TDA). The original PersLay architecture is available in GUDHI, but only in TensorFlow. This project provides a native, modular, and extensible PyTorch version suitable for modern deep-learning pipelines.

Citation

If you use this neural network layer in your research, please cite the original paper:

PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
Mathieu Carrière, Frédéric Chazal, Yuichi Ike, Théo Lacombe, Martin Royer, Yuhei Umeda
Proceedings of the Twenty-Third International Conference on Artificial Intelligence and Statistics (AISTATS),
PMLR 108:2786–2796, 2020.

Installation

You may install it from the Python Package Index using

pip install torchperslay

Example Usage

This example usage is concerned with a simple regression model that uses PersLay as a single hidden layer.

Import Packages

Import necessary packages. Ensure that all packages are installed in your system.

from torchPersLay import *

import gudhi.representations as gdr
import numpy as np
import torch
import torch.nn as nn
import torch.optim as optim
from sklearn.preprocessing import MinMaxScaler

Define PersLay Layers

Choose the PersLay layer that you want. Consult the official PersLay documentation for the possible options.

constant = 1.0
power = 0.0

weight = PowerPerslayWeight(constant=constant, power=power)
rho = nn.Identity()

image_size = (5, 5)
image_bnds = ((-0.5, 1.5), (-0.5, 1.5))
variance = 0.1

phi = GaussianPerslayPhi(
    image_size=image_size,
    image_bnds=image_bnds,
    variance=variance,
)

perm_op = torch.sum

perslay = Perslay(weight=weight, phi=phi, perm_op=perm_op, rho=rho)

Import Data

This is an example data. Import your own data.

diagrams = [
    np.array([[0.0, 4.0], [1.0, 2.0], [3.0, 8.0], [6.0, 8.0]]),
    np.array([[1.0, 3.0], [2.0, 2.5], [4.0, 7.0], [7.0, 7.5]]),
]

scaler = gdr.DiagramScaler(use=True, scalers=[([0, 1], MinMaxScaler())])
diagrams = scaler.fit_transform(diagrams)
diagrams = torch.from_numpy(np.array(diagrams, dtype=np.float32))

y = torch.tensor([[1.0], [3.0]])

Define Model

This is the creation of the model. This is a simple example. You may add other layers as usual and/or use known architectures to concatenate feature vectors.

class PersLayRegressor(nn.Module):
    def __init__(self, perslay, image_size=(5, 5)):
        super().__init__()
        self.perslay = perslay
        feature_dim = image_size[0] * image_size[1]

        self.regressor = nn.Sequential(
            nn.Linear(feature_dim, 32),
            nn.ReLU(),
            nn.Linear(32, 1)
        )

    def forward(self, diagrams):
        x = self.perslay(diagrams)       # [B, 5, 5, 1]
        x = x.view(x.shape[0], -1)       # [B, 25]
        return self.regressor(x)

model = PersLayRegressor(perslay)

criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=1e-3)

Train Model

This is the model training for PyTorch models.

for epoch in range(100):
    optimizer.zero_grad()
    preds = model(diagrams)
    loss = criterion(preds, y)
    loss.backward()
    optimizer.step()

    if (epoch + 1) % 20 == 0:
        print(f"Epoch {epoch + 1}, Loss = {loss.item():.6f}")

(Optional) Inspect Learned Parameters

You may optionally see the learned parameters.

for name, param in perslay.named_parameters():
    print(name, param.data)