The returned H of torchnmf.nmf.NMFD() seems wrong

[ZhimaoLin]

I have a matrix $V$ whose dimension is $513 \times 15$. I want to find 15 $W_t$ matrices and an $H$ matrix such that

This the equation 4 from the NMFD paper.

I understand that I need to add an extra dimension to the $V$ matrix for PyTorch. So, after I made the dimension of my $V$ torch.Size([1, 513, 15]), I called net = torchnmf.nmf.NMFD(V_tensor.shape, rank=2, T=15) and net.fit(V_tensor). (Note: V_tensor is the tensor version of my V)

However, the function torchnmf.nmf.NMFD() only returns an H whose dimension is only $1 \times 2 \times 1$. I think the dimension of H should be $1 \times 2 \times 15$.

It seems that in your reconstruct(H, W) function of the NMFD class you calculate the 1d convolution between H and W.

return F.conv1d(H, W.flip(2), padding=pad_size)

In my opinion, this reconstruct is not the same as equation 4 of the original paper. If you expand the summation of equation 4, you can find the non-first column of $W_0 H$ (i.e. W_0H[:, 1:]) has a contribution to the estimated $\hat{V}$. The non-first-two column of $W_1 H$ (i.e. W_1H[:, 2:]) has a contribution to the estimated $\hat{V}$. Therefore, the returned H should not be padded with 0's left and right during the reconstruct function.

Please let me know if I misunderstood it, or if it is actually a bug. I am trying to use your torchnmf.nmf.NMFD() to do some audio analysis. I am very happy to have further discussions with you.

Thank you!

[yoyolicoris]

Hi @ZhimaoLin, good question!
You're right. It's not the same as in the paper. It's just a different interpretation of how convolution works.

In the original definition of convolution, given two sequences with lengths A and B respectively, their convolution results in a sequence with a length of A + B - 1. So in here you can see I actually make H with a size of M - T + 1 and implement the original convolution inside the reconstruct function.
A temporary workaround would be padding extra T - 1 zeros on the right side of your V before passing it to the constructor so you can have H in the size you want.

I plan to add padding options for users to choose which types of convolution they want—probably going to follow the format from scipy where you have three options, full, valid, and same. The current implementation is full, while your requested behaviour is same. For valid the length of H would be M + T - 1. Let me know whether it works for you or if you have other suggestions.

Anyway, thanks for bringing up the issue!