MTV and MGV: Two Criteria for Nonlinear PCA

  • Tatsuo Otsu
  • Hiroko Matsuo
Conference paper


MTV (Maximizing Total Variance) and MGV (Minimizing Generalized Variance) are popular criteria for PCA with optimal scaling. They are adopted by the SAS-PRINQUAL procedure and OSMOD (Saito and Otsu, 1988). MTV is an intuitive generalization of linear PCA criterion. We will show some properties of nonlinear PCA with these criteria in an application to the data of NLSY79 (Zagorsky, 1997), a large panel survey in the U.S., conducted over twenty years. We will show the following. (1) The effectiveness of PCA with optimal scaling as a tool for large social research data analysis. We can obtain useful results when it complements analyses by regression models. (2) Features of MTV and MGV, especially their abilities and deficiencies in real data analysis.


Canonical Correlation Analysis Hermite Polynomial Category Score Multiple Correspondence Analysis Hadamard Product 
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Copyright information

© The Institute of Statistical Mathematics 2002

Authors and Affiliations

  • Tatsuo Otsu
    • 1
  • Hiroko Matsuo
    • 1
  1. 1.Department of Behavioral ScienceHokkaido UniversitySapporoJapan

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