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
12 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 ...
9 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 ...
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-...
  • 35k
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,...
4 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 ...
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

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' (...
3 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 ...
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
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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 ...
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 ...
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 ...
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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 ...
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 ...
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 ...
  • 35k
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 ...
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 ...
  • 1,098
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 ...
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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 ...
  • 741
1 vote

What kind of features does each node have as an input graph to a graph neural network?

Applying GNNs to images can be realized in different ways. If you only substitute a visual ConvNet by a GNN, then the pixel values would be the same as what goes into a ConvNet. The only difference ...
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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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1 vote
Accepted

Is there a graph neural network algorithm that can deal with a different number of input and output nodes?

I suggest you look into link prediction. I have had good luck with the StellarGraph library. They have several algorithms implemented, including GCN. Link prediction is a binary classification problem....
1 vote
Accepted

Graph Convolutional Networks: why are non-parametric filters not localized in space?

Your explanation is correct. Probably, the term non-parametric is not very appropriate. But the meaning of it here, as far as I understand, is the parametrization ...
1 vote
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 ...
1 vote
Accepted

Does the Weisfeiler-Lehman Isomorphism Test end?

Notice that a partition (set of nodes with the same label) can never get combined with another partition during an iteration. If two nodes are in different partitions, they stay in different ...
1 vote
Accepted

How do convolutional layers of basic Graph Convolutional Networks work?

Actually, the given pipeline was used in the old days of Graph Neural Networks. Canonical paper on the subject is Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering. You ...
1 vote

How does a GCN handle new input graphs?

Graph neural networks, of which GCNs are a specific type, are able to handle arbitrary graphs as input. GNNs operate first over "neighborhoods" of nodes to compute individual node ...
1 vote

What is the best resources to learn Graph Convolutional Neural Networks?

There is also the proto-book Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges (2021), written by some of the experts on the topic. The book does not focus only on graphs and graph ...
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1 vote

Are there neural networks that accept graphs or trees as inputs?

There are types of neural networks designed exactly for that purpose. For example, graph convolutional networks (GCN) by Thomas N. Kipf. The input to the network will be a matrix of size $N \times F$, ...
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