Identifying intervals for hierarchical clustering using the Gershgorin circle theorem

Raghvenclra Mall*, Siamak Mehrkanoon, Johan A. K. Suykens

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


In this paper we present a novel method for unraveling the hierarchical clusters in a given dataset using the Gershgorin circle theorem. The Gershgorin circle theorem provides upper bounds on the eigenvalues of the normalized Laplacian matrix. This can be utilized to determine the ideal range for the number of clusters (k) at different levels of hierarchy in a given dataset. The obtained intervals help to reduce the search space for identifying the ideal value of k at each level. Another advantage is that we don't need to perform the computationally expensive eigen-decomposition step to obtain the eigenvalues and eigenvectors. The intervals provided for k can be considered as input for any spectral clustering method which uses a normalized Laplacian matrix. We show the effectiveness of the method in combination with a spectral clustering method to generate hierarchical clusters for several synthetic and real world datasets. (C) 2015 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalPattern Recognition Letters
Publication statusPublished - 1 Apr 2015
Externally publishedYes


  • Gershgorin circle theorem
  • k clusters
  • Eigengap


Dive into the research topics of 'Identifying intervals for hierarchical clustering using the Gershgorin circle theorem'. Together they form a unique fingerprint.

Cite this