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Graph Convolutional Neural Networks (GCNN) are becoming a preferred model fordata processing on irregular domains, yet their analysis and principles ofoperation are rarely examined due to the black box nature of NNs. To this end,we revisit the operation of GCNNs and show that their convolution layerseffectively perform matched filtering of input data with the chosen patterns(features). This allows us to provide a unifying account of GCNNs through amatched filter perspective, whereby the nonlinear ReLU and max-pooling layersare also discussed within the matched filtering framework. This is followed bya step-by-step guide on information propagation and learning in GCNNs. It isalso shown that standard CNNs and fully connected NNs can be obtained as aspecial case of GCNNs. A carefully chosen numerical example guides the readerthrough the various steps of GCNN operation and learning both visually andnumerically.

Understanding the Basis of Graph Convolutional Neural Networks via an Intuitive Matched Filtering Approach