# A parameter-free graph reduction for spectral clustering and SpectralNet

## TL;DR

This paper presents a parameter-free graph reduction technique that enhances spectral clustering and SpectralNet by automatically constructing stable graphs without the need for parameter tuning.

## Contribution

A novel parameter-free graph reduction method that improves spectral clustering and SpectralNet stability across datasets.

## Key findings

- The method produces stable clustering results without parameter tuning.
- It outperforms parameter-dependent methods in stability across various datasets.
- Experiments demonstrate consistent performance where other methods fluctuate.

## Abstract

Graph-based clustering methods like spectral clustering and SpectralNet are very efficient in detecting clusters of non-convex shapes. Unlike the popular $k$-means, graph-based clustering methods do not assume that each cluster has a single mean. However, these methods need a graph where vertices in the same cluster are connected by edges of large weights. To achieve this goal, many studies have proposed graph reduction methods with parameters. Unfortunately, these parameters have to be tuned for every dataset. We introduce a graph reduction method that does not require any parameters. First, the distances from every point $p$ to its neighbors are filtered using an adaptive threshold to only keep neighbors with similar surrounding density. Second, the similarities with close neighbors are computed and only high similarities are kept. The edges that survive these two filtering steps form the constructed graph that was passed to spectral clustering and SpectralNet. The experiments showed that our method provides a stable alternative, where other methods performance fluctuated according to the setting of their parameters.