What is the difference between graph convolutional networks (GCNs) and traditional CNNs?

Example Answer

A conventional CNN uses the regular grid of an image: its filter sees a fixed arrangement of nearby pixels, and the same weights are reused across locations. A graph convolution instead combines features according to graph connections, so different nodes can have different numbers of neighbors. Locality comes from edges rather than pixel coordinates. For example, two users can be connected even when they have no meaningful physical distance. Both approaches learn local patterns, but their inputs and aggregation rules differ. I would use a CNN for an appropriate grid representation and a GCN when the graph relationships carry useful information for the prediction task.

More Detail

At a fundamental level, the primary distinction between GCNs and traditional CNNs lies in the structure of the data they are designed to process. CNNs are exceptionally well-suited for grid-like data structures, such as images, where the spatial hierarchy allows for the application of convolutional filters to extract features. This process involves sliding these filters across the image, capturing local dependencies, and preserving spatial relationships between pixels. It's this mechanism that enables CNNs to excel in tasks like image recognition and classification.

In contrast, GCNs are tailored to handle graph-structured data, which inherently differs from the grid-like structure processed by CNNs. Graphs consist of nodes (or vertices) and edges, representing complex relationships and interdependencies in the data that are not inherently spatial or sequential. GCNs capitalize on this structure by applying the convolutional principle directly to graphs. This involves aggregating feature information from a node's neighbors, effectively capturing the local neighborhood's structure. Unlike in CNNs, where the convolution operation is defined in a fixed Euclidean space, the convolution in GCNs adapts to the topology of the graph. This flexibility allows GCNs to be applied to a wide range of tasks beyond image analysis, such as node classification, link prediction, and graph classification, where understanding the relationships and patterns within the data is crucial.

Another key difference is in how these networks conceptualize locality and feature extraction. In CNNs, locality is defined by physical proximity within the image. The filters applied during convolution capture patterns based on the arrangement of pixels in their immediate vicinity. However, in GCNs, locality is determined by the graph's connectivity. A node's features are updated based on the features of its adjacent nodes, meaning that the network learns to extract features based on the structure of the graph itself rather than spatial proximity. This distinction underscores the adaptability of GCNs in capturing the essence of relational data.

References

Graph convolutional networks · Localized spectral graph filters