Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Database Systems pp 1100–1106Cite as

Dimension Reduction Techniques for Clustering

  • Reference work entry
  • First Online:

Synonyms

Graph embedding; Subspace selection

Definition

High dimensional datasets is frequently encountered in data mining and statistical learning. Dimension reduction eliminates noisy data dimensions and thus and improves accuracy in classification and clustering, in addition to reduced computational cost. Here the focus is on unsupervised dimension reduction. The wide used technique is principal component analysis which is closely related to K-means cluster. Another popular method is Laplacian embedding which is closely related to spectral clustering.

Historical Background

Principal component analysis (PCA) was introduced by Pearson in 1901 and formalized in 1933 by Hotelling. PCA is the foundation for modern dimension reduction. A large number of linear dimension reduction techniques were developed during 1950–1970s.

Laplacian graph embedding (also called quadratic placement) is developed by Hall [8] in 1971. Spectral graph partitioning [6], is initially studied in 1970s; it is...

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   4,499.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   6,499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Recommended Reading

  1. Alpert CJ, Kahng AB. Recent directions in netlist partitioning: a survey. Integ VLSI J. 1995;19(1):1–81.

    Article  MATH  Google Scholar 

  2. Belkin M, Niyogi P. Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Advances in neural information processing systems 14, 2001.

    Google Scholar 

  3. Chan PK, Schlag M, Zien JY. Spectral k-way ratio-cut partitioning and clustering. IEEE Trans CAD-Integ Circuit Syst. 1994;13(9):1088–96.

    Article  Google Scholar 

  4. Ding C, He X. K-means clustering and principal component analysis. In: Proceedings of the 21st International Conference on Machine Learning; 2004.

    Google Scholar 

  5. Ding C., He X., Zha H., Simon H. Unsupervised learning: self-aggregation in scaled principal component space. In: Principles of Data Mining and Knowledge Discovery, 6th European Conference; 2002, p. 112–24.

    Chapter  Google Scholar 

  6. Fiedler M. Algebraic connectivity of graphs. Czech Math J. 1973;23(2):298–305.

    MathSciNet  MATH  Google Scholar 

  7. Hagen M, Kahng AB. New spectral methods for ratio cut partitioning and clustering. IEEE Trans Comput Aided Desig. 1992;11(9):1074–85.

    Article  Google Scholar 

  8. Hall KM. An R-dimensional quadratic placement algorithm. Manage Sci. 1971;17(3):219–29.

    Article  MATH  Google Scholar 

  9. Ng AY, Jordan MI, Weiss Y. On spectral clustering: analysis and an algorithm. In: Advances in neural information processing systems 14, 2001.

    Google Scholar 

  10. Pothen A, Simon HD, Liou KP. Partitioning sparse matrices with egenvectors of graph. SIAM J Matrix Anal Appl. 1990;11(3):430–52.

    Article  MathSciNet  MATH  Google Scholar 

  11. Shi J, Malik J. Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell. 2000;22(8):888–905.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Texas at Arlington, Arlington, TX, USA

    Chris Ding

Authors
  1. Chris Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chris Ding .

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

Rights and permissions

Reprints and permissions

Copyright information

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

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Ding, C. (2018). Dimension Reduction Techniques for 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_612

Download citation

Publish with us

Policies and ethics

Search

Navigation