About the edge embedding

[Abraham12580]

As the paper writes, the edge values are either continuous or discrete. But how are the edge values transfered into edge embeddings? what does the edge embedding look like? I dont see this clearly in the paper. Hoping for the authors kindly reply.

[Abraham12580]

[maxiaoba]

The initial edge embedding is the known attribute values from the data matrix, it is updated by equation 3 in section 3.3 in the paper.

[Abraham12580]

Thanks for your reply. I have seen your words in your papar. I'm sorry that I haven't express myself very well. Actually it is the form of edge embedding that puzzles me. In other words, is the edge embedding a real number from data matrix or a vector transformed from data matrix? From Figure 1 in the paper, I think the edge embedding of the edge O1-F1 is a real number, which is 0.3. But I think real number cannot deliver the complex information between sample nodes and feature nodes. If the edge embedding is a vector, I don't kown how it is transformed from a single real number, like 0.3. 

------------------ 原始邮件 ------------------ 发件人: "maxiaoba/GRAPE" <[email protected]>; 发送时间: 2021年2月19日(星期五) 上午7:33 收件人: "maxiaoba/GRAPE"<[email protected]>; 抄送: "兵哥哥"<[email protected]>;"Author"<[email protected]>; 主题: Re: [maxiaoba/GRAPE] About the edge embedding (#5)

The initial edge embedding is the known attribute values from the data matrix, it is updated by equation 3 in section 3.3 in the paper.

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[maxiaoba]

The initial edge embedding is a real number from the data matrix, and this is enough because it contains all we know from the original data matrix. Then at the following layers, it is updated to a vector by equation 3 in section 3.3 in the paper to encode the additional statistical information from message passing.

[Alex-Mathai-98]

Thanks for this great repository ! I had a question regarding equation (3).

@maxiaoba, @dingdaisy, @JiaxuanYou - in equation (3) - I see that you use h_{v}^{l-1} - which is the previous layer embedding of the node (v) that you want to update.

So if I understand correctly, to update Node V we look at the Embedding of Node V and the connecting edge Euv.

In the code, on line 64 of egsage.py, I see this concatenation

m_j = torch.cat((x_j, edge_attr),dim=-1)            
m_j = self.message_activation(self.message_lin(m_j)) 

From what I understand, x_j is the embedding of the neighbouring node (and not the node itself). If this is true, I see a conflict in the equation and in the code.

Can you help me to better understand this ?

I am on a tight deadline - I would really appreciate any help. Thanks so much !

[voladorlu]

@maxiaoba I have a question about the edge embedding. I note the different way to deal with discrete and continuous features. The discrete will be transformed into one-hot vector, while continuous feature will keep its original value. From my understanding, the transformed edge features are not aligned well. The transformed discrete feature is a vector, while the continuous feature is a scalar. However, both node and edge features will be stored in a tensor. Could you please help me on this issue? It'd be better to point out where we can find the piece of code to deal with this problem.