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Article
Singular Value Decomposition and Its Visualization
Journal of Computational and Graphical Statistics (2007)
  • Lingsong Zhang, Harvard School of Public Health
  • J. S. Marron, University of North Carolina at Chapel Hill
  • Haipeng Shen, University of North Carolina at Chapel Hill
  • Zhengyuan Zhu, University of North Carolina at Chapel Hill
Abstract
Singular value decomposition (SVD) is a useful tool in functional data analysis (FDA). Compared to principal component analysis (PCA), SVD is more fundamental, because SVD simultaneously provides the PCAs in both row and column spaces. We compare SVD and PCA from the FDA view point, and extend the usual SVD to variations by considering different centerings. A generalized scree plot is proposed to select an appropriate centering in practice. Several useful matrix views of the SVD components are introduced to explore different features in data, including SVD surface plots, image plots, curve movies, and rotation movies. These methods visualize both column and row information of a two-way matrix simultaneously, relate the matrix to relevant curves, show local variations, and highlight interactions between columns and rows. Several toy examples are designed to compare the different variations of SVD, and real data examples are used to illustrate the usefulness of the visualization methods.
Keywords
  • Exploratory data analysis,
  • Functional data analysis,
  • Principal component analysis
Publication Date
2007
DOI
10.1198/106186007X256080
Publisher Statement
This is the Submitted Manuscript of an article published by Taylor & Francis as Zhang, Lingsong, J. S. Marron, Haipeng Shen, and Zhengyuan Zhu. "Singular value decomposition and its visualization." Journal of Computational and Graphical Statistics 16, no. 4 (2007): 833-854. Available online DOI: 10.1198/106186007X256080

Copyright 2007 American Statistical Association, Institute of Mathematical Statistics,
and Interface Foundation of North America
Citation Information
Lingsong Zhang, J. S. Marron, Haipeng Shen and Zhengyuan Zhu. "Singular Value Decomposition and Its Visualization" Journal of Computational and Graphical Statistics Vol. 16 Iss. 4 (2007) p. 833 - 854
Available at: http://works.bepress.com/zhengyuan-zhu/5/