# Eigenvalue-based Incremental Spectral Clustering

arXiv: https://arxiv.org/abs/2308.10999 · HTML: https://mlsanity.com/paper/2308.10999/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 18 Aug 2023.

## Builds on (most cited first, 7 of 7)

- [Ultra-Scalable Spectral Clustering and Ensemble Clustering](https://mlsanity.com/paper/1903.01057/) (2019)
- [Divide-and-conquer based Large-Scale Spectral Clustering](https://mlsanity.com/paper/2104.15042/) (2021)
- [Understanding the Generalization Performance of Spectral Clustering Algorithms](https://mlsanity.com/paper/2205.00281/) (2022)
- [Generalized Dirichlet Energy and Graph Laplacians for Clustering Directed and Undirected Graphs](https://mlsanity.com/paper/2203.03221/) (2022)
- [Heterogeneous Data Fusion Considering Spatial Correlations using Graph Convolutional Networks and its Application in Air Quality Prediction](https://mlsanity.com/paper/2105.13125/) (2021)
- [LSEC: Large-scale spectral ensemble clustering](https://mlsanity.com/paper/2106.09852/) (2021)
- [Clustering and classification of low-dimensional data in explicit feature map domain: intraoperative pixel-wise diagnosis of adenocarcinoma of a colon in a liver](https://mlsanity.com/paper/2203.03636/) (2022)

## Abstract (arXiv)

Our previous experiments demonstrated that subsets collections of (short) documents (with several hundred entries) share a common normalized in some way eigenvalue spectrum of combinatorial Laplacian. Based on this insight, we propose a method of incremental spectral clustering. The method consists of the following steps: (1) split the data into manageable subsets, (2) cluster each of the subsets, (3) merge clusters from different subsets based on the eigenvalue spectrum similarity to form clusters of the entire set. This method can be especially useful for clustering methods of complexity strongly increasing with the size of the data sample,like in case of typical spectral clustering. Experiments were performed showing that in fact the clustering and merging the subsets yields clusters close to clustering the entire dataset.