Editorial Type:
Article
Article Type:
Article Commentary

Some Comments on Singular Value Decomposition Analysis

Steve Cherry Department of Mathematical Sciences, Montana State University, Bozeman, Montana

Search for other papers by Steve Cherry in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Jul 1997
DOI:
https://doi.org/10.1175/1520-0442(1997)010<1759:SCOSVD>2.0.CO;2
Page(s):
1759–1761
Restricted access

Abstract

The singular value decomposition analysis (SVD) method is discussed in the context of the simultaneous orthogonal rotation of two matrices. It is demonstrated that the singular vectors are rotated EOFs and the SVD expansion coefficients are rotated sets of principal component expansion coefficients. This way of thinking about SVD aids in the interpretation of results and provides guidance as to when and how to use SVD.

Corresponding author address: Dr. Steve Cherry, Dept. of Mathematical Sciences, Montana State University, Bozeman, MT 59717-0240. E-mail: imsgschemath.montana.edu

Abstract

The singular value decomposition analysis (SVD) method is discussed in the context of the simultaneous orthogonal rotation of two matrices. It is demonstrated that the singular vectors are rotated EOFs and the SVD expansion coefficients are rotated sets of principal component expansion coefficients. This way of thinking about SVD aids in the interpretation of results and provides guidance as to when and how to use SVD.

Corresponding author address: Dr. Steve Cherry, Dept. of Mathematical Sciences, Montana State University, Bozeman, MT 59717-0240. E-mail: imsgschemath.montana.edu

Save
Cover Journal of Climate
Journal of Climate

  • Bretherton, C. S., C. Smith, and J. M. Wallace, 1992: An intercomparison of methods for finding coupled patterns in climate data. J. Climate,5, 541–560.

  • Cherry, S., 1997: Singular value decomposition analysis and canonical correlation analysis. J. Climate,9, 2003–2009.

  • Cliff, N., 1966: Orthogonal rotation to congruence. Psychometrika,31, 33–42.

  • Hsu, H., 1994: Relationship between tropical heating and global circulation: Interannual variability. J. Geophys. Res.,99, 10 473–10 489.

  • Lanzante, J. R., 1984: A rotated eigenanalysis of the correlation between 700-mb heights and sea surface temperatures in the Pacific and Atlantic. Mon. Wea. Rev.,112, 2270–2280.

  • Lau, N., and M. J. Nath, 1994: A modeling study of the relative roles of tropical and extratropical SST anomalies in the variability of the global atmosphere–ocean system. J. Climate,7, 1184–1207.

  • Newman, M., and P. D. Sardeshmukh, 1995: A caveat concerning singular value decomposition. J. Climate,8, 352–360.

  • Prohaska, J., 1976: A technique for analyzing the linear relationships between two meteorological fields. Mon. Wea. Rev.,104, 1345–1353.

  • Tucker, N. J., 1958: An inter-battery method of factor analysis. Psychometrika,23, 111–136.

  • van de Geer, J. P., 1984: Linear relations among k sets of variables. Psychometrika,49, 79–94.

  • Wallace, J. M., C. Smith, and C. S. Bretherton, 1992: Singular value decomposition of wintertime sea surface temperature and 500-mb height anomalies. J. Climate,5, 561–576.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 687 198 5
PDF Downloads 425 98 9