Recursive Prediction of Graph Signals with Incoming Nodes
This addresses a practical issue for applications with evolving graphs, though it is incremental as it builds on existing Linear Regression over Graphs methods.
The paper tackles the problem of predicting graph signals when graphs expand over time with new nodes, proposing a recursive method to update regression coefficients without solving a new regression problem each time. Experiments show the approach achieves prediction performance close to knowing the entire graph in advance.
Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes get introduced. Keeping this premise in mind, we propose a method to recursively obtain the optimal prediction or regression coefficients for the recently propose Linear Regression over Graphs (LRG), as the graph expands with incoming nodes. This comes as a natural consequence of the structure C(W)= of the regression problem, and obviates the need to solve a new regression problem each time a new node is added. Experiments with real-world graph signals show that our approach results in good prediction performance which tends to be close to that obtained from knowing the entire graph apriori.