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Spectral Clustering

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  • First Online:
Encyclopedia of Database Systems

  • 27 Accesses

Synonyms

Graph-based clustering

Definition

Let X be a set X = {x1, x2,…,xN} of N data points. An m-clustering of X, is defined as the partition of X into m sets (clusters), C1,…,Cm, so that the following three conditions are met:

  • Ci ≠ Ø, i = 1,…,m

  • ∪i=1m  Ci = X

  • Ci ∩ Cj = Ø, i ≠ j, i, j = 1,…,m

In addition, the data points contained in a cluster Ci are “more similar” to each other and “less similar” to the points of the other clusters. The terms “similar” and “dissimilar” depend very much on the types of clusters the user expects to recover from X. A clustering defined as above is known as hard clustering, to distinguish it from the fuzzy clustering case.

Historical Background

The essence of clustering is to “reveal” the organization of patterns into “sensible” groups. It has been used as a critical analysis tool in a vast range of disciplines, such as medicine, social sciences, engineering, computer science, machine learning, bioinformatics, data mining and information retrieval. The...

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Author information

Authors and Affiliations

  1. University of Athens, Athens, Greece

    Sergios Theodoridis

  2. Institute for Space Applications and Remote Sensing, Athens, Greece

    Konstantinos Koutroumbas

Authors
  1. Sergios Theodoridis
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  2. Konstantinos Koutroumbas
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Corresponding author

Correspondence to Sergios Theodoridis .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology College of Computing, Atlanta, GA, USA

    Ling Liu

  2. University of Waterloo School of Computer Science, Waterloo, ON, Canada

    M. Tamer Özsu

Section Editor information

  1. Department of Computer Science and Engineering, The University of California at Riverside, Bourns College of Engineering, Riverside, CA, USA

    Dimitrios Gunopulos

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Theodoridis, S., Koutroumbas, K. (2018). Spectral Clustering. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_606

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