Sublinear Models for Graphs

TL;DR

This paper introduces sublinear models for graphs, providing theoretical insights and empirical validation, demonstrating their effectiveness and properties similar to linear models for feature vectors.

Contribution

It extends linear models to graph data, offering a geometric interpretation, a learning rule, convergence analysis, and VC-dimension bounds.

Findings

Sublinear models exhibit similar properties to linear models on graphs.

Theoretical results include convergence and VC-dimension analysis.

Empirical results validate the models' effectiveness on graph data.

Abstract

This contribution extends linear models for feature vectors to sublinear models for graphs and analyzes their properties. The results are (i) a geometric interpretation of sublinear classifiers, (ii) a generic learning rule based on the principle of empirical risk minimization, (iii) a convergence theorem for the margin perceptron in the sublinearly separable case, and (iv) the VC-dimension of sublinear functions. Empirical results on graph data show that sublinear models on graphs have similar properties as linear models for feature vectors.