Recursive Prediction of Graph Signals with Incoming Nodes

TL;DR

This paper introduces a recursive method for updating linear regression coefficients on expanding graphs, enabling efficient predictions with incoming nodes without re-solving the entire regression problem.

Contribution

It proposes a recursive approach for Linear Regression over Graphs that efficiently updates coefficients as the graph grows, avoiding repeated full regressions.

Findings

Approach achieves prediction performance close to full graph knowledge.

Method effectively handles dynamic graph expansion.

Experimental results validate the efficiency and accuracy of the recursive updates.

Abstract

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.