Graph Neural Network(GNN) is a type of neural network that can be directly applied to graph-structured data. My previous post gave a brief introduction on GNN. Readers may be directed to this post for more details.

Many research works have shown GNN’s power for understanding graphs, but the way how and why GNN works still remains a mystery for most people. Unlike CNN, where we can extract activation of each layer to visualize the decisions of the network, in GNN it is hard to get a meaningful explanation of what features the network has learnt. Why does GNN determine a node is class A instead of class B? Why does GNN determine a graph is a chemical or molecule? It seems like GNN sees some useful structural information and determines are made upon these observations. But now the problem is, what observations does GNN see?

## What is GNNExplainer?

GNNExplainer is introduced in this paper.

Briefly speaking, it is trying to build a network to learn what a GNN has learnt.

The main principle of GNNExplainer is by reducing redundant information in a graph which does not directly impact the decisions. To explain a graph, we want to know what are the crucial features or structures in the graph that affect the decisions of a neural network. If a feature is important, then the prediction should be altered largely by removing or replacing this feature with something else. On the other hand, if removing or altering a feature does not affect the prediction outcome, the feature is considered not essential and thus should not be included in the explanation for a graph.

## How does it work?

The primary objective for GNNExplainer is to generate a minimal graph that explains the decision for a node or a graph. To achieve this goal, the problem can be defined as finding a subgraph in the computation graph, that minimizes the difference in the prediction scores using the whole computation graph and the minimal graph. In the paper, this process is formulated as maximizing the mutual information(MI) between the minimal graph Gs and the computation graph G:

Besides, there is a secondary objective: the graph needs to be minimal. Though it was also mentioned in the first objective, we need to have a method to formulate this objective as well. The paper addresses it by adding a loss for the number of edges. Therefore, the loss for GNNExplainer is literally the combination of prediction loss and edge size loss.

#graph #graph-neural-networks #graph-theory #pattern-recognition #machine-learning