Automatic Determination of the Number of Clusters Using Spectral Algorithms

G. Sanguinetti, J. Laidler, N.D. Lawrence

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We introduce a novel spectral clustering algorithm that allows us to automatically determine the number of clusters in a dataset. The algorithm is based on a theoretical analysis of the spectral properties of block diagonal affinity matrices; in contrast to established methods, we do not normalise the rows of the matrix of eigenvectors, and argue that the non-normalised data contains key information that allows the automatic determination of the number of clusters present. We present several examples of datasets successfully clustered by our algorithm, both artificial and real, obtaining good results even without employing refined feature extraction techniques
Original languageEnglish
Title of host publicationMachine Learning for Signal Processing, 2005 IEEE Workshop on
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages6
ISBN (Print)0-7803-9517-4
Publication statusPublished - 1 Sep 2005


  • eigenvalues and eigenfunctions
  • feature extraction
  • matrix algebra
  • pattern clustering
  • spectral analysis
  • block diagonal affinity matrices
  • dataset clusters
  • eigenvectors
  • nonnormalised data
  • spectral algorithm
  • spectral clustering
  • Algorithm design and analysis
  • Clustering algorithms
  • Computer science
  • Feature extraction
  • Image segmentation
  • Information analysis
  • Iterative algorithms
  • Partitioning algorithms
  • Spectral analysis
  • Speech recognition


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