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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 that the description of GDL through the explanation of what are DL on graphs and manifolds, in opposition to DL on euclidean domains, comes from the 2017 paper ...


9

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 learning, things that are similar to each other are not necessarily close if one uses Euclidean distance as a metric (aka the triangle inequality doesn't hold). You ...


8

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-field of deep learning. It answers all the questions asked above (and more). If you are familiar with deep learning, graphs, linear algebra and calculus, you ...


7

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 structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional ...


3

I believe Graph Representation Learning book by William L. Hamilton is a great resource to start


3

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 survey considers GNNs as all deep learning approaches for graph data. A Comprehensive Survey on Graph Neural Networks, Wu et al (2019) However the ...


3

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 it into matrix form.


2

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 series of open source implementations of many of the above:


2

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 accompanied by its node feature matrix and/or edge feature matrix, if the graph has such information). A Comprehensive Survey on Graph Neural Networks, Wu et al (...


2

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 without self loop is: $\text{D}^{-1}\text{A}\text{H}$. If you study this equation closer then you will find that the $i^{th}$ row of $\text{A}\text{H}$ generates ...


2

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 Processing Systems (NIPS) International Conference on Learning Representations (ICLR) Conference on Computer Vision and Pattern Recognition (CVPR) International ...


2

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 read they are using the same network for the neighbors and for the center node). But you are right the two networks needs to have the same input and output ...


2

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 the following thoughts will be helpful anyway. I prefer the term Message Passing Networks as a generalization of many things people like to call GNN. In a ...


1

Notice that a partition (set of nodes with the same label) can never get combined with another partition during an iteration. They can only be split up or stay the same. Therefore, the number of partitions increases with every iteration (except for the last one which signals the end). There can't be more partitions than nodes, therefore the algorithm ...


1

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' (basically some kind of label reflecting the node neighborhood). Counting colors allows to compare two graphs on isomorphism, but it's not that important here, the key ...


1

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. Given two nodes, $v_i$ and $v_j$, does there exist a link between them? Using a library like StellarGraph will also produce node embeddings while performing ...


1

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 representations and then optionally apply a pooling function to reduce these to a single graph-level representation that can be used in classification. This means that ...


1

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 Pytorch. It is the most starred Pytorch github repo for geometric deep learning. Creating a GCN model which can process graphs with weights is as simple as: import ...


1

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 $N \times F$, where $N$ is the number of nodes and $F$ the number of features (for each node). You then can multiply the feature matrix with the adjacency matrix (each node ...


1

It's hard to say because Euclidean space is defined with respect to some kind of metric, so without any clearer exposition on the nature of the data/problem, the phrase itself may or may not be clear. A metric $d: A \times A \rightarrow \mathbb{R}$ is a function that defines distance between any two points in the space with respect to axioms that 1. two ...


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