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Graph wavelets API documentation

diffusion_wavelets 

diffusion_wavelets(T, n_scales)

Compute diffusion wavelet filter bank.

Computes diffusion wavelets from from input diffusion matrix. Implementation based off the algorithm originally described in Coifman et. al 2006.

Parameters:

Name Type Description Default
T Tensor

Input diffusion matrix computed from adjacency matrix

 required
n_scales int

Number of scales to use in wavelet transform

 required

Returns:

Name Type Description
phi Tensor

wavelet filter bank
Source code in gsxform/wavelets.py 
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def diffusion_wavelets(T: torch.Tensor, n_scales: int) -> torch.Tensor:
    """Compute diffusion wavelet filter bank.

    Computes diffusion wavelets from from input diffusion matrix.
    Implementation based off the algorithm originally described in
    Coifman et. al 2006.

    Parameters
    ----------
    T: torch.Tensor
        Input diffusion matrix computed from adjacency matrix
    n_scales: int
        Number of scales to use in wavelet transform

    Returns
    -------
    phi: torch.Tensor
        wavelet filter bank
    """
    # make n_node x n_node identity matrix
    I_N = torch.eye(T.shape[1], device=T.device)

    # compute zero-eth order (J=0) wavelet filter
    # one half the normalized laplacian operator 1/2(I-D^-1/2WD^-1/2)
    psi = I_N - T

    for jj in range(1, n_scales):
        # compute jth diffusion operator (wavelet kernel)
        T_j = torch.matrix_power(T, 2 ** (jj - 1))
        # compute jth wavelet filter
        psi_j = einsum(T_j, I_N - T_j, "b ni nk, b nk nj -> b ni nj")
        # append wavelets
        psi = torch.cat((psi, psi_j), dim=0)

    psi = rearrange(psi, "(ns b) ni nj -> b ns ni nj", ns=n_scales)

    return psi

tighthann_wavelets 

tighthann_wavelets(W_adj, n_scales, kernel)

Compute spectrum adapted tight Hann wavelets.

Based off the algorithm described in Shuman et. al 2015.

Parameters:

Name Type Description Default
W_adj Tensor

Input batch of adjacency matricies

 required
n_scales int

Number of scales to use in wavelet transform

 required
kernel TightHannKernel

Adaptive kernel used in wavelet transform.

 required

Returns:

Name Type Description
psi Tensor

wavelet filter bank
Source code in gsxform/wavelets.py 
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def tighthann_wavelets(
    W_adj: torch.Tensor, n_scales: int, kernel: TightHannKernel
) -> torch.Tensor:
    """Compute spectrum adapted tight Hann wavelets.

    Based off the algorithm described in Shuman et. al 2015.

    Parameters
    ----------
    W_adj: torch.Tensor
        Input batch of adjacency matricies
    n_scales: int
        Number of scales to use in wavelet transform
    kernel: TightHannKernel
        Adaptive kernel used in wavelet transform.

    Returns
    -------
    psi: torch.Tensor
        wavelet filter bank

    """
    E, V = compute_spectra(W_adj)

    # compute wavelet coeffs
    psi = torch.empty(V.shape[0], 0, V.shape[1], V.shape[2], device=V.device)
    for jj in range(0, n_scales):
        # compute adapted kernel
        adapted_kernel = kernel.get_adapted_kernel(E, jj + 1)

        # compute jth wavelet filter, V diag(kernel) V^H without building the
        # diagonal; the second V is indexed transposed, giving the hermetian
        psi_j = einsum(V, adapted_kernel, V, "b ni nk, b nk, b nj nk -> b ni nj")

        # append wavelets
        psi_j = rearrange(psi_j, "b n m -> b 1 n m")

        psi = torch.cat((psi, psi_j), dim=1)

    return psi