Encyclopedia of Database Systems

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

Principal Component Analysis

  • Heng Tao Shen
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_540

Synonyms

PCA

Definition

Principal components analysis (PCA) is a linear technique used to reduce a high-dimensional dataset to a lower dimensional representations for analysis and indexing. For a dataset P in D-dimensional space with its principal component set Φ, given a point p∈P, its projection on the lower d-dimensional subspace can be defined as: p. Φd, where Φd represents the matrix containing 1st to dth largest principal components in Φ and d < D.

Key Points

PCA finds a low-dimensional embedding of the data points that best preserves their variance as measured in the high-dimensional input space [1, 2, 3]. It identifies the directions that best preserve the associated variances of the data points while minimize “least-squares” (Euclidean) error measured by analyzing data covariance matrix. The first principal component is the eigenvector corresponding to the largest eigenvalue of the dataset’s co-variance matrix, the second component corresponds to the eigenvector with the...

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Recommended Reading

  1. 1.
    Jolliffe IT. Principal component analysis. 2nd ed. New-York: Springer; 2002.zbMATHGoogle Scholar
  2. 2.
    Huang Z, Shen HT, Shao J, Rüger SM, Zhou X. Locality condensation: a new dimensionality reduction method for image retrieval. In: Proceedings of the 16th ACM International Conference on Multimedia; 2008. p. 219–28.Google Scholar
  3. 3.
    Shen HT, Zhou X, Zhou A. An adaptive and dynamic dimensionality reduction method for high-dimensional indexing. VLDB J. 2007;16(2):219–34.CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.School of Information Technology and Electrical EngineeringThe University of QueenslandBrisbaneAustralia
  2. 2.University of Electronic Science and Technology of ChinaChengduSichuanChina

Section editors and affiliations

  • Xiaofang Zhou
    • 1
  1. 1.School of Information Technology and Electrical EngineeringUniversity of QueenslandBrisbaneAustralia