Graph neural network: Difference between revisions

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:<math>\mathbf{X}' = (\mathbf{X} \odot \text{sigmoid}(\mathbf{y}))_{\mathbf{i}}</math>
 
:<math>\mathbf{A}' = \mathbf{A}_{\mathbf{i}, \mathbf{Ii}}</math>
 
Where <math>\mathbf{X}</math> is the matrix of node features, <math>\mathbf{A}</math> is the graph adjacency matrix, <math>\odot</math> denotes element-wise [[matrix multiplication]], and <math>\mathbf{p}</math> is a learnable [[Projection (mathematics)|projection]] vector. The projection vector <math>\mathbf{p}</math> computes a scalar projection value for each graph node. The nodes with the top-k highest projection scores are retained in the new adjacency matrix <math>\mathbf{A}'</math>. The <math>\text{sigmoid}(\cdot)</math> operation makes the projection vector <math>\mathbf{p}</math> trainable by [[backpropagation]], which otherwise would produce discrete outputs.<ref name=gao2019 />