# Improving Spectral Clustering using the Asymptotic Value of the Normalised Cut

## TL;DR

This paper analyzes the asymptotic behavior of the normalized cut in spectral clustering to improve parameter tuning and automatic cluster number detection, proposing a new algorithm with strong empirical results.

## Contribution

It introduces a theoretical analysis of the normalized cut's asymptotic value and offers practical recommendations and an algorithm to enhance spectral clustering performance.

## Key findings

- Asymptotic normalized cut value derived for large samples
- Proposed algorithm improves cluster detection accuracy
- Empirical results show strong performance gains

## Abstract

Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter, nor for determining automatically the number of clusters to extract. Popular heuristics exist, but corresponding theoretical results are scarce. In this paper we investigate the asymptotic value of the normalised cut for an increasing sample assumed to arise from an underlying probability distribution, and based on this result provide recommendations for improving spectral clustering methodology. A corresponding algorithm is proposed with strong empirical performance.