<abstract xmlns="http://www.w3.org/1999/xhtml">
<p>Our previous experiments demonstrated that subsets of 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 of subsets yield clusters close to clustering of the entire dataset. Our approach differs from other research streams in that we rely on the entire set (spectrum) of eigenvalues, whereas the other researchers concentrate on few eigenvectors related to lowest eigenvalues. Such eigenvectors are considered in the literature as of low reliability.</p>
</abstract>

Our previous experiments demonstrated that subsets of 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 of subsets yield clusters close to clustering of the entire dataset. Our approach differs from other research streams in that we rely on the entire set (spectrum) of eigenvalues, whereas the other researchers concentrate on few eigenvectors related to lowest eigenvalues. Such eigenvectors are considered in the literature as of low reliability.

Eigenvalue-Based Incremental Spectral Clustering

Journal of Artificial Intelligence and Soft Computing Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Eigenvalue-Based Incremental Spectral Clustering"}

Our previous experiments demonstrated that subsets of collections of (short) documents (with several hundred entries) share a common, normalized in some way,...

Eigenvalue-Based Incremental Spectral Clustering

Published Online: Mar 19, 2024

Page range: 157 - 169

Received: Sep 01, 2023

Accepted: Feb 07, 2024

DOI: https://doi.org/10.2478/jaiscr-2024-0009

Keywords
text mining, artificial intelligence, machine learning, graph spectral clustering, incremental clustering, combinatorial Laplacian, eigenvalue spectrum analysis

© 2024 Mieczysław A. Kłopotek et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Eigenvalue-Based Incremental Spectral Clustering

Published Online: Mar 19, 2024

Page range: 157 - 169

Received: Sep 01, 2023

Accepted: Feb 07, 2024

DOI: https://doi.org/10.2478/jaiscr-2024-0009

Keywordstext mining, artificial intelligence, machine learning, graph spectral clustering, incremental clustering, combinatorial Laplacian, eigenvalue spectrum analysis

© 2024 Mieczysław A. Kłopotek et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
text mining, artificial intelligence, machine learning, graph spectral clustering, incremental clustering, combinatorial Laplacian, eigenvalue spectrum analysis