Standard Polynomial

standard_poly(A, poly_degree=3)

Computes Standard Polynomial function. Current implementation complexity is $O(N^2)$.

Inputs:

• A : 2D Tensor, graph adjacency matrix or (normalized) Laplacian.
• poly_degree: Integer, polynomial degree (default=1).

Outputs:

• 3D Tensor, containing standard polynomial powers of graph adjacency matrix or Laplacian.

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Chebyshev Polynomial

chebyshev_poly(A, poly_degree=3)

Computes Chebyshev Polynomial function. Current implementation complexity is $O(N^2)$.

Inputs:

• A : 2D Tensor, graph adjacency matrix or (normalized) Laplacian.
• poly_degree: Integer, polynomial degree (default=1).

Outputs:

• 3D Tensor, containing chebyshev polynomial powers of graph adjacency matrix or Laplacian.

References: Defferrard, Michaël, Xavier Bresson, and Pierre Vandergheynst. "Convolutional neural networks on graphs with fast localized spectral filtering." In Advances in Neural Information Processing Systems, pp. 3844-3852. 2016.

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Random Walk Polynomial

chebyshev_poly(A, poly_degree=3)

Computes Random Walk Polynomial function. Current implementation complexity is $O(N^2)$.

Inputs:

• A : 2D Tensor, graph adjacency matrix or (normalized) Laplacian.
• poly_degree: Integer, polynomial degree (default=1).

Outputs:

• 3D Tensor, containing chebyshev polynomial powers of graph adjacency matrix or Laplacian.

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Cayley Polynomial

cayley_poly(A, poly_degree=3)

Computes Cayley Polynomial function. Current implementation complexity is $O(N^3)$.

Inputs:

• A : 2D Tensor, graph adjacency matrix or (normalized) Laplacian.
• poly_degree: Integer, polynomial degree (default=1).

Outputs:

• 3D Tensor, containing cayley polynomial powers of graph adjacency matrix or Laplacian.

References: Levie, Ron, Federico Monti, Xavier Bresson, and Michael M. Bronstein. "Cayleynets: Graph convolutional neural networks with complex rational spectral filters." arXiv preprint arXiv:1705.07664 (2017).

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Combine Polynomial

combine_poly(A, B, poly_degree=3)

Computes combination of polynomial function.

Inputs:

• A : 2D Tensor, graph adjacency or (normalized) Laplacian or cayley matrix.
• B : 2D Tensor, graph adjacency matrix or (normalized) Laplacian or cayley matrix.
• poly_degree: Integer, polynomial degree (default=1).

Outputs:

• 3D Tensor, containing combine polynomial powers of graph adjacency or Laplacian or cayley matrix.