Essential Math for AI

Chapter 9. Graph Models

Now this is something we all want to learn.

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Graphs, diagrams, and networks are all around us: cities and roadmaps, airports and connecting flights, electrical networks, the power grid, the World Wide Web, molecular networks, biological networks such as our nervous system, social networks, terrorist organization networks, schematic representations of mathematical models, artificial neural networks, and many, many others. They are easily recognizable, with distinct nodes representing some entities that we care for, which are then connected by directed or undirected edges indicating the presence of some relationship between the connected nodes.

Data that has a natural graph structure is better understood by a mechanism that exploits and preserves that structure, building functions that operate directly on graphs (however they are mathematically represented), as opposed to feeding graph data into machine learning models that artificially reshape it before analyzing it. This inevitably leads to loss of valuable information. This is the same reason convolutional neural networks are successful with image data, recurrent neural networks are successful with sequential data, and so on.

Graph-based models are very attractive for data scientists and engineers. Graph structures offer a flexibility that is not afforded in spaces with a fixed underlying coordinate system, such as in Euclidean spaces or in relational databases, where the data along with its features ...