What is GMI?
GMI, also known as Graphic Mutual Information, is a measurement method used to determine the correlation between input graphs and high-level hidden representations. Different from the conventional mutual information computations that take place in vector space, GMI extends the calculation to the graph domain. Measuring mutual information from two aspects of node features and topological structure is essential in the graph domain, and GMI makes that possible.
Benefits
GMI provides several benefits in the area of graph representation learning. One of them is that it is invariant to the isomorphic transformation of input graphs. In many existing graph representation learning algorithms, isomorphic transformation constraints are inevitable. GMI solves this problem.
An isomorphic transformation occurs when the structure of the original graph changes, but it still contains the same nodes and edges.
Another advantage of GMI is that it can be efficiently estimated and maximized by current mutual information estimation methods such as MINE. From this, we can conclude that the use of GMI can improve the efficiency and accuracy of mutual information measurements.
How GMI Works
As previously mentioned, GMI measures mutual information from two different aspects of graphs - node features and topological structure. This means that GMI is calculated based on the similarities between the input graphs and the high-level hidden representations.
The measurement process is carried out in three steps:
Step 1: Representing Graphs
The first step in the measurement process is to represent the graphs. In this case, input graphs are converted into a numerical representation. The numerical representation is then stored in a vector form to make it easier for computation. Both the node features and topological structure are taken into account during this step.
This step is necessary because it is difficult to compare two graphs in their original form. Comparing numerical values is easier for machines and algorithms.
Step 2: Calculating Mutual Information
After representing the graphs, the next step is to calculate the mutual information between them. As mentioned earlier, GMI uses the MINE method to efficiently estimate the mutual information.
The MINE method is a recent development in mutual information estimation, and it has been shown to be an effective method for GMI estimation.
Step 3: Maximizing Mutual Information
After calculating the mutual information, the last step is to maximize it. Maximizing mutual information involves adjusting the hidden representation to optimize the correlation with the input graph.
By optimizing the correlation between the input graph and the hidden representation, GMI ensures that the resulting representation captures both node features and topological structure accurately.
Conclusion
GMI is a powerful tool for graph representation learning that can help solve the problem of isomorphic transformation constraints in existing graph representation learning algorithms. With its ability to measure mutual information from two different aspects of graphs and the use of the efficient MINE method for estimation, GMI is an effective way to improve the efficiency and accuracy of mutual information measurements.
