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

Graph Convolutional Neural Networks (GCNN) are becoming a preferred model for data processing on irregular domains, yet their analysis and principles of operation 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 layers effectively perform matched filtering of input data with the chosen patterns (features). This allows us to provide a unifying account of GCNNs through a matched filter perspective, whereby the nonlinear ReLU and max-pooling layers are also discussed within the matched filtering framework. This is followed by a step-by-step guide on information propagation and learning in GCNNs. It is also shown that standard CNNs and fully connected NNs can be obtained as a special case of GCNNs. A carefully chosen numerical example guides the reader through the various steps of GCNN operation and learning both visually and numerically.