Graph-convolutional neural networks---how to determine feature matrix

Question

I've been recently studying the GCNs---graph-convolutional neural networks. Given a triplet (A,F,C), where A is the network-adjacency matrix, F the network feature matrix and C the matrix of classes, corresponding to each node, GCNs are able to learn a representation of classes.

The original paper (Kipf et al. 2016, https://github.com/tkipf/gcn) uses Cora dataset and some others, where filters are predefined. My question is, how does one define the feature matrix? Where does this come from?

Thank you!

Answer 1

The feature matrix is defined by the features (variables) of the dataset you're using. Each row of your feature matrix corresponds to a node in your graph, with one column per feature. Let's use an example from the paper

Per your Cora dataset example, the paper states they used the "sparse bag-of-words feature vectors for each document" to create their feature matrix. So each individual research paper is a ${1 \text{ x V} }$ vector, where $\text{V}$ is the size of the vocabulary. Each entry in the bag-of-words vector is either $0$ or $1$ to indicate whether or not the word encoded at that index appears in the research paper.

With that in mind, the example GCN matrix triplet $\text{(A,F,C)}$ for the Cora dataset would be:

• $\text{A}$ would be each research paper's citation links to other research papers (undirected links in the paper)
• $\text{F}$ would be each research paper's bag-of-words vector
• $\text{C}$ would be each research paper's class encoding (Cora has 7 mutually exclusive labels)

Hope this helps!