Michaël Defferrard

I'm not aware of a Keras implementation and don't plan doing it. I however have a pyTorch implementation. Let me now if you find a Keras version or if you...

Do also check: * PyTorch Geometric (PyG): [ChebConv in PyTorch](https://pytorch-geometric.readthedocs.io/en/latest/modules/nn.html#torch_geometric.nn.conv.ChebConv). * Deep Graph Library (DGL): ChebConv in [PyTorch](https://docs.dgl.ai/api/python/nn.pytorch.html#chebconv) and [MXNet](https://docs.dgl.ai/api/python/nn.mxnet.html#chebconv).

Here we set the width `sigma` of the Gaussian kernel `similarity = np.exp(-(distance/sigma)**2)` as the mean of the farthest distance (`sigma2 = sigma**2`). That's an heuristic.

The graph of an image is a 2D grid. You can generate a 10x10 grid (with adjacency and Laplacian matrices) with the PyGSP as `graph = pygsp.graphs.Graph2d(10, 10)` [[doc](https://pygsp.readthedocs.io/en/latest/reference/graphs.html#pygsp.graphs.Grid2d)].

Any polynomial (monomials, Chebyshev, Legendre, etc.) of order K has the same representation power and can be used. We used Chebyshev because we had experience with it and thought it...

Mostly for historical reasons. At first we were *designing* filters (e.g., to solve the diffusion of heat, the propagation of waves, and [many others](https://pygsp.readthedocs.io/en/latest/reference/filters.html)). As Chebyshev polynomials are excellent [function...

Yes. It seems that SGD works well enough to find the best polynomial, whatever the basis. That might also be because we use low-order polynomials when learning.

[Stochastic Gradient Descent](https://en.wikipedia.org/wiki/Stochastic_gradient_descent)

Neither spectral nor polynomial convolutions enforce low-pass filters. Polynomial convolutions enforce local filters (the locality is controlled by the order of the polynomials). Local filters can be high-pass (simply think...

All Laplacians are the same as every MNIST image is supported by the same 28x28 grid graph. For learned filters to generalize across different graphs/Laplacians, you make the hypothesis that...