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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 ...


7

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

Generally speaking a graph CNN is applied to data represented by graphs, not images. a graph is a collection of nodes and edges connecting them. an image is a 2D or 3D matrix, in which each element denotes a pixel in space If your data are just images, or something similar (e.g. some fMRI data), you usually cannot benefit from graph CNN compared with ...


3

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 structure of the graph with which we can identify clusters/sub-groups of this graph. This is done in the Fourier space. An analogy is PCA where we understand the spread ...


3

I'm seeing recent trend of combining RNN/CNN with GNN(graph neural networks) so that both time dependency and topology are captured. I would suggest you to start by looking at DCRNN (Yaguang Li et al.), it's a strong baseline that everyone uses nowadays. Other good resources: Graph wavenet for deep spatial-temporal graph modeling (Zonghan Wu et al.) Spatio-...


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 ...


2

Bioinformatics is an area that Graph Convolutional Neural Network is useful. Consider protein networks, or gene-gene networks. Surely, the biological networks can be represented as a graph. Now, you should see how GCN is useful for bioinformatics.


2

There are some problems that involve graphs and manifolds (sometimes collectively called non-Euclidean data), such as molecule design and generation, drug repositioning, social networks analysis, brain imaging, fake news detection, recommender systems, neutrino detection, computer vision and graphics and shape (e.g. hand or face) completion or generation (...


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

You can take a look at traffic data for example if you follow link1, link2 you can find 3 publicly available traffic datasets which are already preprocessed. You cold also look at air quality datasets offered by the government link3


2

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 signal with (Laplacian/adjacency matrix). But by using the Laplacian, you're encoding the graph structure (in-out degree of each node) which dictates how a ...


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

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

It's perfectly reasonable to apply 'traditional' Deep Learning approaches to try and learn an adjacency matrix (a matrix is just a vector of vectors, which can be flattened into a single output vector) but you might need a lot of training data as N gets larger. Your outputs could certainly have the form of an adjacency matrix, as you describe. Whether it's ...


2

The simplest way I could come with is to pad with 0 each feature which is not present. You said that you're going to add too much noise to the network, but I don't see the problem (please correct me if I'm wrong). For example we have two nodes, the first one has only 2 features with the 3rd one missing and the second node has all features X=[[1,2,0], [3,4,5]]...


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:


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

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

The first place I would have directed you would be Sklearn and pydiffmap. I found this paper specifically about the problem you are doing using python the reference a package called megaman It seems like an active Github . I suggest not just looking at manifold learning papers but leaning towards a search toward non linear embedding or non linear ...


1

Low order/low level information refers to the most granular level of information. This is the most informative in terms of volume of information, but it can often be difficult to conceptualise for humans. High order/high level information refers to abstractions of the low level information to more intuitive but less easy to describe technically concepts. ...


1

The authors of your cited paper use the term graph-based semi-supervised learning (G-SSL) to refer to semi-supervised learning techniques which take graph structured data as their input. Given their main example, the MNIST dataset, is not graph structured, they detail a method for converting the raw Euclidean data $X$ into said form (represented by its ...


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

In the paper Neural Message Passing for Quantum Chemistry (2017), the authors (from Google, Google Brain and Google DeepMind) introduce a framework called message passing neural network (MPNN), which generalizes previously proposed geometric deep learning models. In section 2 of the paper, they describe this MPNN framework and they state that edge features ...


1

Both study properties of a network. The literature under respective titles seems to focus on certain topics. Network analysis seems to focus on understanding the structure of a network. Centrality , modularity, assortativity etc are metrics used to study properties of networks. Key areas of research are for egs community detection, centrality measures, ...


1

Network analysis does not necessarily use deep learning techniques, while geometric deep learning (GDL) on graphs uses only deep learning techniques (that is, you train a neural network using gradient descent or other optimization methods). You can do some network analysis using GDL.


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 ...


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