Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Spectral Clustering

  • Sergios Theodoridis
  • Konstantinos Koutroumbas
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_606

Synonyms

Graph-based clustering

Definition

Let X be a set X = { x 1, x 2,…, x N} of N data points. An m- clustering of X, is defined as the partition of X into m sets ( clusters), C 1,…, C m, so that the following three conditions are met:
  • Ci ≠ Ø, i = 1,…,m

  • i=1m  Ci = X

  • CiCj = Ø, ij, 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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of AthensAthensGreece
  2. 2.Institute for Space Applications and Remote SensingAthensGreece

Section editors and affiliations

  • Dimitrios Gunopulos
    • 1
  1. 1.Department of Computer Science and EngineeringThe University of California at Riverside, Bourns College of EngineeringRiversideUSA