Encyclopedia of Systems Biology

2013 Edition
| Editors: Werner Dubitzky, Olaf Wolkenhauer, Kwang-Hyun Cho, Hiroki Yokota

Principal Component Analysis (PCA)

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-9863-7_1276

Synonyms

Definition

PCA is a statistical tool used to explore complex series of multivariate observations by which we can summarize a great amount of data through recognition of its most relevant information content. PCA behaves as a filtering-compression technique that captures the main trends in the data while revealing their underlying structure (Johnson and Wichner 1998; Brereton 2003; Wall et al. 2003).

Characteristics

Motivation Problem

When in a set of n “objects” (the experimental units) m attributes are measured, a cloud of points would appear when objects are represented in a space where each axis corresponds to one variable. PCA focuses on the “shape” of such cloud, trying to capture the cloud’s dominating directions(the eigenvectors). When these data are projected onto a lower-dimensional subspace, delimited by the eigenvectors of the cloud, a clearer visualization of the relationship...

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References

  1. Brereton R (2003) Data analysis for the laboratory to chemistry plant. Wiley, New York, pp 121–223 (Chap 4)Google Scholar
  2. Johnson RA, Wichner DW (1998) Applied multivariate statistical analysis, 4th edn. Prentice Hall, New Jersey, pp 458–512Google Scholar
  3. Varmuza K, Filzmoser P (2009) Introduction to multivariate statistical analysis in chemometrics. Taylor and Francis Group-CRC Press, Boca Raton, USA, pp 31–78Google Scholar
  4. Wall ME, Rechtsteiner A, Rocha LM (2003) Singular value decomposition and principal component analysis. In: Dubitzky W, Granzow M, Berrar DP (eds) A practical approach to microarray data analysis. Kluwer, Norwell, pp 91–109. LANL LA-UR-02-4001. http://public.lanl.gov/mewall/kluwer2002.html
  5. Wold S (1987) Principal component analysis. Chemometrics and intelligent laboratory systems, 2(1):37–52Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  1. 1.Department of Systems Biology and BioinformaticsInstitute of Computer Sciences, University of RostockRostockGermany
  2. 2.Department of Biochemistry and Molecular BiologyUniversity of La LagunaSan Cristóbal de La Laguna, Islas CanariasSpain