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Kirby](https://dl.acm.org/doi/10.1109/34.41390#artseq-00001), [L. Sirovich](https://dl.acm.org/doi/10.1109/34.41390#artseq-00002)[Authors Info & Claims](https://dl.acm.org/doi/10.1109/34.41390#tab-contributors) [IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 12, Issue 1](https://dl.acm.org/toc/itpm/1990/12/1) Pages 103 - 108 <https://doi.org/10.1109/34.41390> Published: 01 January 1990 [Publication History](https://dl.acm.org/doi/10.1109/34.41390#core-history) 331citation0Downloads Metrics [Total Citations331](https://dl.acm.org/doi/10.1109/34.41390#tab-citations "See Citations pane") [Total Downloads0](https://dl.acm.org/doi/10.1109/34.41390#tab-metrics-inner "See Bibliometrics pane") Last 12 Months0 Last 6 weeks0 Get Citation Alerts ## New Citation Alert added\! This alert has been successfully added and will be sent to: You will be notified whenever a record that you have chosen has been cited. To manage your alert preferences, click on the button below. 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This results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix, without increasing the complexity of the calculation. The resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average. ## References \[1\] {1} L. Sirovich, "Turbulence and the dynamics of coherent structures, Part II: Symmetries and transformations," *Quart. Appl. Math.*, vol. XLV, no. 3, pp. 573-582, 1987. [Crossref](https://doi.org/10.1090/qam/910463) [Google Scholar](https://scholar.google.com/scholar_lookup?doi=10.1090%2Fqam%2F910463) \[2\] {2} S. Watanabe, "Karhunen-Loève expansion and factor analysis theoretical remarks and applications." in *Proc. 4th Prugue Conf. Inform. Theory*. 1965. 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[Read More](https://dl.acm.org/doi/10.5555/795662.796259 "Read More") ## Comments Please enable JavaScript to view the[comments powered by Disqus.](https://disqus.com/?ref_noscript) ## Information & Contributors ### Information #### Published In  IEEE Transactions on Pattern Analysis and Machine Intelligence Volume 12, Issue 1 January 1990 112 pages ISSN:0162-8828 - **Editor:** - [Steven L. Tanimoto](https://dl.acm.org/profile/81100450825 "Steven L. Tanimoto") Univ. of Washington, Seattle [Issue’s Table of Contents](https://dl.acm.org/toc/itpm/1990/12/1) Copyright © Copyright © 1990 IEEE. All Rights Reserved. #### Publisher IEEE Computer Society United States #### Publication History **Published**: 01 January 1990 #### Author Tags 1. [Karhunen-Loeve expansion](https://dl.acm.org/keyword/Karhunen-Loeve+expansion?expand=all) 2. [Karhunen-Loeve procedure](https://dl.acm.org/keyword/Karhunen-Loeve+procedure?expand=all) 3. [covariance matrix](https://dl.acm.org/keyword/covariance+matrix?expand=all) 4. [eigenfunctions](https://dl.acm.org/keyword/eigenfunctions?expand=all) 5. [eigenvalues and eigenfunctions](https://dl.acm.org/keyword/eigenvalues+and+eigenfunctions?expand=all) 6. [human faces](https://dl.acm.org/keyword/human+faces?expand=all) 7. [matrix algebra](https://dl.acm.org/keyword/matrix+algebra?expand=all) 8. [mirror images](https://dl.acm.org/keyword/mirror+images?expand=all) 9. [natural symmetries](https://dl.acm.org/keyword/natural+symmetries?expand=all) 10. 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