# An Automated Spectral Clustering for Multi-scale Data

## TL;DR

This paper introduces an automated spectral clustering method that estimates parameters from data itself, enabling effective multi-scale data grouping without prior input, demonstrated on real-world datasets with high accuracy.

## Contribution

It proposes a novel heuristic of iterative eigengap search with global and local scaling to automatically determine clustering parameters from data.

## Key findings

- Achieves over 90% accuracy in real-world multi-scale datasets
- Effectively identifies patterns at different scales without prior parameter input
- Demonstrates robustness on power variation and gene expression data

## Abstract

Spectral clustering algorithms typically require a priori selection of input parameters such as the number of clusters, a scaling parameter for the affinity measure, or ranges of these values for parameter tuning. Despite efforts for automating the process of spectral clustering, the task of grouping data in multi-scale and higher dimensional spaces is yet to be explored. This study presents a spectral clustering heuristic algorithm that obviates the need for an input by estimating the parameters from the data itself. Specifically, it introduces the heuristic of iterative eigengap search with (1) global scaling and (2) local scaling. These approaches estimate the scaling parameter and implement iterative eigengap quantification along a search tree to reveal dissimilarities at different scales of a feature space and identify clusters. The performance of these approaches has been tested on various real-world datasets of power variation with multi-scale nature and gene expression. Our findings show that iterative eigengap search with a PCA-based global scaling scheme can discover different patterns with an accuracy of higher than 90% in most cases without asking for a priori input information.