# Bounds on Perfect Node Classification: A Convex Graph Clustering Perspective

## TL;DR

This paper introduces a new convex optimization approach for perfect node classification in graphs, leveraging community structure and node-specific data to improve accuracy under milder conditions.

## Contribution

It proposes a novel spectral graph clustering framework that integrates node labels and features, providing theoretical guarantees for perfect community recovery.

## Key findings

- Guarantees perfect community recovery under milder conditions
- Demonstrates synergy between graph structure and node-specific information
- Validates approach with numerical experiments

## Abstract

We present an analysis of the transductive node classification problem, where the underlying graph consists of communities that agree with the node labels and node features. For node classification, we propose a novel optimization problem that incorporates the node-specific information (labels and features) in a spectral graph clustering framework. Studying this problem, we demonstrate a synergy between the graph structure and node-specific information. In particular, we show that suitable node-specific information guarantees the solution of our optimization problem perfectly recovering the communities, under milder conditions than the bounds on graph clustering alone. We present algorithmic solutions to our optimization problem and numerical experiments that confirm such a synergy.