Encyclopedia of Database Systems

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

Singular Value Decomposition

  • Yanchun Zhang
  • Guandong Xu
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_538

Synonyms

Latent semantic indexing; Principle component analysis; SVD transformation

Definition

The SVD definition of a matrix is illustrated as follows [ 1]: For a real matrix A = [ a ij] m × n, without loss of generality, suppose mn and there exists SVD of A (shown in Fig. 1):
$$ A=U\left(\begin{array}{l}{\Sigma}_1\\ {}0\end{array}\right){V}^T={U}_{m\times m}{\sum}_{m\times n}{V}_{n\times n}^T $$
This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Datta B. Numerical linear algebra and application. Pacific Grove: Brooks/Cole Publishing Company; 1995.zbMATHGoogle Scholar
  2. 2.
    Hofmann T. Latent semantic models for collaborative filtering. ACM Trans Inf Syst. 2004;22(1):89–115.CrossRefGoogle Scholar
  3. 3.
    Zhang Y, Yu JX, Hou J. Web communities: analysis and construction. Berlin: Springer; 2006.Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Victoria UniversityMelbourneAustralia
  2. 2.University of Technology SydneySydneyAustralia

Section editors and affiliations

  • Xiaofang Zhou
    • 1
  1. 1.School of Inf. Tech. & Elec. Eng.Univ. of QueenslandBrisbaneAustralia