# Vertex Classification on Weighted Networks

## TL;DR

This paper introduces a new vertex classification method for weighted networks by extending the stochastic block model with edge weight distributions, demonstrating improved accuracy through spectral embedding techniques.

## Contribution

It develops a novel classification approach for weighted networks by integrating edge weight distributions into the stochastic block model and spectral embedding methods.

## Key findings

- Proposed classifiers outperform traditional methods in weighted network classification.
- Effectiveness demonstrated through comparison with quadratic discriminant analysis.
- Methods perform well even when edge weights do not encode class information.

## Abstract

This paper proposes a discrimination technique for vertices in a weighted network. We assume that the edge weights and adjacencies in the network are conditionally independent and that both sources of information encode class membership information. In particular, we introduce a edge weight distribution matrix to the standard K-Block Stochastic Block Model to model weighted networks. This allows us to develop simple yet powerful extensions of classification techniques using the spectral embedding of the unweighted adjacency matrix. We consider two assumptions on the edge weight distributions and propose classification procedures in both settings. We show the effectiveness of the proposed classifiers by comparing them to quadratic discriminant analysis following the spectral embedding of a transformed weighted network. Moreover, we discuss and show how the methods perform when the edge weights do not encode class membership information.