# Why can we perform graph convolution using the standard 2d convolution with $1 \times \Gamma$ kernels?

Recently I was reading this paper Skeleton Based Action RecognitionUsing Spatio Temporal Graph Convolution. In this paper, the authors claim (below equation (\ref{9})) that we can perform graph convolution with the following formula

$$\mathbf{f}_{o u t}=\mathbf{\Lambda}^{-\frac{1}{2}}(\mathbf{A}+\mathbf{I}) \mathbf{\Lambda}^{-\frac{1}{2}} \mathbf{f}_{i n} \mathbf{W} \label{9}\tag{9}$$

using the standard 2d convolution with kernels of shape $$1 \times \Gamma$$ (where $$\Gamma$$ is defined under equation 6 of the paper), and then multiplying it with the normalised adjacency matrix

$$\mathbf{\Lambda}^{-\frac{1}{2}}(\mathbf{A}+\mathbf{I}) \mathbf{\Lambda}^{-\frac{1}{2}}$$

For the past few days, I was thinking about his claim but I can't find an answer. Does anyone read this paper and can help me to find it out, please?

• Isn't this a duplicate of ai.stackexchange.com/q/22650/2444? Or are you interested only in the 1d convolution? If yes, maybe read my answer ai.stackexchange.com/a/21824/2444. I talk about 1d convolutions there, but I don't remember anymore the level of detail I used. – nbro Jul 24 at 19:58
• I am interested in (1xD) convolution specifically. But can you please explain your answer? – Swakshar Deb Jul 24 at 20:01
• Have you read my answer: ai.stackexchange.com/a/21824/2444? (Btw, I edited the comment above to include a link to this answer). I don't know if it answers your question because I don't remember what I wrote there, but I think it should give you some intuition behind 1d convolutions, as far as I remember :P – nbro Jul 24 at 20:02
• Yes, I go through the answer you gave previously. I think you are more focused on FCN and segmentation but I am trying to know can 1xD standard convolution and then multiplying it with adjacency matrix is the same as graph convolution in the skeleton based graphs? – Swakshar Deb Jul 24 at 20:07
• It's been a while since I read something about graph NNs, but can you point me exactly to the part of the paper where the author claims that, so that I have some context? – nbro Jul 24 at 20:14