19
votes
What is geometric deep learning?
To complete the first answer that is rather graph oriented, I will write a little about deep learning on manifolds, which is quite general in terms of GDL thanks to the nature of manifolds.
Note ...
- 301
16
votes
Accepted
What is non-Euclidean data?
I presume this question was prompted by the paper Geometric deep learning:
going beyond Euclidean data (2017). If we look at its abstract:
Many scientific fields study data with an underlying ...
- 1,031
10
votes
What is non-Euclidean data?
Non-Euclidian geometry can be generally boiled down to the phrase
the shortest path between 2 points isn't necessarily a straight line.
Or, put in a way that lends itself very much to machine ...
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8
votes
Accepted
What is geometric deep learning?
The article Geometric deep learning: going beyond Euclidean data (by Michael M. Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, Pierre Vandergheynst) provides an overview of this relatively new sub-...
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6
votes
Accepted
What is a filter in the context of graph convolutional networks?
Short answer
Check out the paper of Shuman et al. [1], it provides some background on Graph Signal Processing, including answers to your questions in sections II.C and III.A
Long Answer
Question 1
Yes,...
6
votes
What is the difference between graph convolution in the spatial vs spectral domain?
Spectral Convolution
In a spectral graph convolution, we perform an Eigen decomposition of the Laplacian Matrix of the graph. This Eigen decomposition helps us in understanding the underlying ...
4
votes
Is there an open-source implementation for graph convolution networks for weighted graphs?
You can use Pytorch_Geometric library for your projects. Its supports weighted GCNs. It is a rapidly evolving open-source library with easy to use syntax. It is mentioned in the landing page of ...
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3
votes
How does the K-dimensional WL test work?
I never used a k-WL in practice, but I did apply weisfeiler-lehman for my graph tasks.
As you can know, the WL provides the coloring by interactive procedure that's assign each node a 'color' (...
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3
votes
Accepted
How do graph neural networks adapt to different number of nodes and connections of different graphs?
The essence of the reason, why this approach works for graphs with a different number of nodes is the locality and node order permutation invariance.
The typical form of the layer-wise signal ...
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3
votes
Accepted
How are GCN doing semi-supervised learning?
In the introduction, the authors write
We consider the problem of classifying nodes (such as documents) in a graph (such as a citation network), where labels are only available for a small subset of ...
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3
votes
Accepted
What is the best resources to learn Graph Convolutional Neural Networks?
I believe Graph Representation Learning book by William L. Hamilton is a great resource to start
- 366
3
votes
Machine learning with graph as input and output
You can flatten the graph into a matrix and then train it like a normal neural network input. Perhaps an adjacency graph or maybe simply a series of linear equations representing the nodes and convert ...
- 31
3
votes
Accepted
Using GraphSAGE model for multigraph datasets
My question is if GraphSAGE is suitable for this kind of data?
To my knowledge, GraphSAGE is designed for very large graphs with highly connected nodes (like social networks). The neighborhood ...
- 1,748
3
votes
Accepted
Node classification with random labels for GNNs
The Cora dataset is unbalanced (s. here). It's graph consists of 2708 nodes and the label distribution (for labels 1 to 7) is 818, 426, 418, 351, 298, 217, 180, i.e....
- 1,748
2
votes
What is a graph neural network?
Graph Neural Networks
The term Graph Neural Network, in its broadest sense, refers to any Neural Network designed to take graph structured data as its input:
To cover a broader range of methods, this ...
- 1,031
2
votes
What is the difference between graph convolution in the spatial vs spectral domain?
After I read multiple explanations from different sources I think I found the main difference between the two methods. Implementation wise the only difference is the matrix that you're multiplying the ...
- 1,148
2
votes
Are there neural networks that accept graphs or trees as inputs?
Yes, there are numerous, coming under the umbrella term Graph Neural Networks (GNN).
The most common input structures accepted by these techniques are the adjacency matrix of the graph (optionally ...
- 1,031
2
votes
Accepted
Understanding the node information score in the paper "Hierarchical Graph Pooling with Structure Learning"
Here, $H$ is a $n * d$ matrix where $n$ is the number of total nodes in the graph and $d$ is the dimension of embedding of each node.
Using the notation in the question, the basic GNN formulation ...
- 310
2
votes
Accepted
What are some conferences for publishing papers on graph convolutional networks?
Based on past publications, here are some journals and conferences where you can possibly publish or present a research paper on geometric deep learning or graph neural networks
Neural Information ...
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2
votes
Accepted
Is there an open-source implementation for graph convolution networks for weighted graphs?
A Comprehensive Survey on Graph Neural Networks (2019) presents a list of ConvGNN's. All of the following accept weighted graphs, and three accept those with edge weights as well:
And below is a ...
- 1,031
2
votes
How Graph Convolutional Neural Networks forward propagate?
I think the picture you're presenting is mostly for educational purposes and that's why they are excluding the node itself from it's neighbors and using two distinct networks (most of the papers I've ...
- 1,148
2
votes
Are Graph Neural Networks generalizations of Convolutional Neural Networks?
Excuse my lack of rigor. Although I believe this could be rigorously proven for certain definitions of GNN, the term is still too loose for me to honestly claim one way or another on this. Hopefully ...
- 125
2
votes
What is the best GNN for a NMT task?
I will start by saying that I do not have any experience with Graph2Seq networks or GGNN, but I have some knowledge about GNN in general and the other three architectures.
Firstly, it is essential to ...
- 31
2
votes
Accepted
Why don't we use diffusion for non-graph CNNs?
Just for completeness, here is one simple formalization of a diffusion GCN (Gasteiger et al.):
$\text{D-GCN}(X) = \sum_{k=1}^K A^k X W_k$
You have a diffusion factor $k \in [1 .. K]$ and you apply ...
- 1,748
2
votes
Accepted
Relevance of Weisfeiler–Lehman Graph Isomorphism Test limitation for Graph Neural Networks
Firstly, as already stated in the Wikipedia quote: Observing that a type of GNN is as expressive as the Weisfeiler–Lehman (WL) Test, means in practice that two graphs $\mathcal{G}_1$ and $\mathcal{G}...
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2
votes
Why is the output of my graph neural network not permutation equivariant?
It seems that the graph filter layer in your GNN takes information from the immediate neighbors for every node and applies a ReLU nonlinearity. However, the architecture you've shown does not ...
2
votes
How can I improve this toy Graph Neural Network Generative Language model
First of all, I would like to encourage you to keep trying new things, it sounds super fun! There are a few things I would like you to clarify about Graph Neural Networks (GNNs) and Graph ...
- 598
2
votes
Accepted
Why is there a shared matrix W in graph attention networks instead of the query-key-value trio like in regular transformers?
To my understanding, there isn't any theoretical reason why the query, key and values weights are absent.
I feel that the difference may lie in the way the additive attention is calculated vs the dot-...
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2
votes
How to pass batch of Graphs in GATv2Conv?
For efficiency reasons, it is the standard for graph learning libraries to use the format [n_batches x num_nodes, node_feature_dim], instead of having batches in an ...
- 1,748
1
vote
Accepted
Is "node embedding" in GNN analogous to "hidden layer" of FFN?
Embeddings are vectors. Layers are functions.
So, node embeddings (e.g. produced by TransE) are analogous to word embeddings or code embeddings, i.e. they are vector (and lower-dimensional) ...
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