25 years ago . . .

25 years ago . . . for going beyond the traditional unrotated PCA so- In summary, this is a skillfully organized and well- lutions. Two specific algorithms (Varimax and Pro- written text which draws information from half-a- crustes rotations) are discussed in detail. Again, dozen fields and brings it together into a concise because this chapter is intended as an introduction statement on the theory and geophysical uses of prin- cipal components. W e should be indebted to Curtis to the topic of linear transformations, a few nuances are missing and the reader is therefore encouraged to Mobley for bringing it to fruition after Preisendorfer's supplement the material with texts mentioned above untimely death.—Michael B. Richman and with more recent articles (e.g., Richman 1986). Michael B. Richman is a professional scientist with Two such omissions are the lack of discussion of the the Climate and Meteorology Section at the Illinois role of hyperplanes (as contrasted to clusters) and that State Water Survey. of pairwise graphical plots to explain and validate simple structure. The hypothetical example included References (p. 272) is probably not very realistic compared to Cattell, R. B. 1965. Factor analysis: An introduction to essentials. published eigenvector frames for real data (e.g., Rich- Biometrics 21: 190-215, 405-435. man and Lamb 1985, figure 3), which illustrate that Cliff, N., and D. J. Kruss. 1976. Interpretation of canonical anal- ysis: Rotated vs. unrotated solutions. Psychometrika 41: 35-42. the Varimax rotated PCs isolate both variables in hy- Eckart, C. H., and G. Young. 1936. The approximation of one perplanes and clusters. Despite these criticisms, the matrix by another of a lower rank. Psychometrika 1: 211-218. chapter offers several glimpses of techniques that are Gittins, R. 1985. Canonical Analysis: A Review with Applications only now beginning to be used by geophysical sci- in Ecology. New York: Springer-Verlag. entists; for example, Procrustes Target Analysis and Hall, C. E. 1969. Rotation of canonical variates in multivariate analysis of variance. J. Experimental Educ. 38: 31-38. extended applications of rule N with the principle of Harman, H. H. 1976. Modern Factor Analysis, 3rd Ed. Chicago: mimicry. University of Chicago Press. The derivation of CC A jn a PCA framework (chap- Humphreys, L. G. , and D. R. Ilgen. 1969. Note on a criterion for ter 8) facilitates understanding of a particular aspect the number of common factors. Educ. and Psychol. Measur. 29: 571-578. of CCA in applied research. Preisendorfer ties this Lawley, D. N., and A. E. Maxwell. 1971. Factor Analysis as a into SV D of two datasets using the concept of a cor- Statistical Method. London: Butterworths and Co. relation probe which seeks orientations of maximum Mulaik, S. A. 1972. The Foundations of Factor Analysis. New York: correlations between spaces. The section on selec- McGra w Hill. tion rules for CCA contains previously unpublished Mulaik, S. A. 1986. Factor analysis and Psychometrika: Major developments. Psychometrika 51: 23-33. material; hence, it may prove useful to researchers Prohaska, J. T. 1976. A technique for analyzing the linear rela- engaged in using the method. The bibliographic notes tionships between two meteorological fields. Mon. Wea. Rev. reference needed applications, one of which is Pro- 104: 1345-1353. haska's (1976) paper which diagnoses the correlation Reynolds, T., and E. Jackosfsky. 1981. Interpreting canonical anal- structure of two datasets with particular relevance to ysis: The use of orthogonal transformations. Educ. and Psychol. prediction. One interesting topic not covered in this Measur. 41: 661-671. Richman, M. B. 1986. Rotation of principal components. ). Cli- chapter is the extension of CCA by rotating the ca- matology 6: 293-335. nonical variates for increased interpretation (e.g., Hall Richman, M. B., and P. J. Lamb. 1985. Climatic pattern analysis 1969; Cliff and Kruss 1976; Reynolds and Jackosfsky of three- and seven-day summer rainfall in the central United 1981). The reader might augment Preisendorfer's States: Some methodological considerations and a regionaliza- chapter with Seber (1984) if interested in the tradi- tion. J. Clim. Appl. Meteor. 24: 1325-1343. Seber, G. A. F. 1984. Multivariate Observations. New York: John tional statistical development of CCA, and with Git- Wile y and Sons, Inc. tins (1985) or Thompson (1984) for further applied Thompson, B. 1984. Canonical Correlation Analysis. Beverly Hills: issues. Chapter 9 similarly contains unique discus- Sage. 71 pp. • sions of CC A regression, hindcast skill and how this relates to CCA. The last three chapters deal with statistical-dynam- 25 years ago.. . ical models, partitioning eigenvectors, and complex harmonic PCA. Chapter 10 is an impressive exami- The February 1965 Bulletin contained the minutes of the Boston nation of two examples of substituting eigenmodes meeting of the Council on October 3 and 4, 1964. One of the items into models of atmospheric flow. Likewise, chapter reads as follows: 12 contains a wealth of information, which has never 24. The Secretary brought to the attention of the Council the in- been previously assembled, on complex PCA, moti- dictment of Mr. Kenneth T. C. Cheng, Head of the Taiwan Weather Service, for an incorrect typhoon forecast. The Secretary informed the vated by the thought that "w e may reasonably expect Council that by direction of the Executive Committee he had written that on combining the techniques of PCA and har- to the Ambassador from Taiwan deploring the indictment of a mete- monic analysis, something of greater applicability than orologist for an incorrect forecast, pointing out that if forecasters were each will result for certain diagnostic or predictive indicted each time they made an incorrect forecast there could be, within a fairly short period of time, a total lack of forecasters. tasks." http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the American Meteorological Society American Meteorological Society

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Abstract

for going beyond the traditional unrotated PCA so- In summary, this is a skillfully organized and well- lutions. Two specific algorithms (Varimax and Pro- written text which draws information from half-a- crustes rotations) are discussed in detail. Again, dozen fields and brings it together into a concise because this chapter is intended as an introduction statement on the theory and geophysical uses of prin- cipal components. W e should be indebted to Curtis to the topic of linear transformations, a few nuances are missing and the reader is therefore encouraged to Mobley for bringing it to fruition after Preisendorfer's supplement the material with texts mentioned above untimely death.—Michael B. Richman and with more recent articles (e.g., Richman 1986). Michael B. Richman is a professional scientist with Two such omissions are the lack of discussion of the the Climate and Meteorology Section at the Illinois role of hyperplanes (as contrasted to clusters) and that State Water Survey. of pairwise graphical plots to explain and validate simple structure. The hypothetical example included References (p. 272) is probably not very realistic compared to Cattell, R. B. 1965. Factor analysis: An introduction to essentials. published eigenvector frames for real data (e.g., Rich- Biometrics 21: 190-215, 405-435. man and Lamb 1985, figure 3), which illustrate that Cliff, N., and D. J. Kruss. 1976. Interpretation of canonical anal- ysis: Rotated vs. unrotated solutions. Psychometrika 41: 35-42. the Varimax rotated PCs isolate both variables in hy- Eckart, C. H., and G. Young. 1936. The approximation of one perplanes and clusters. Despite these criticisms, the matrix by another of a lower rank. Psychometrika 1: 211-218. chapter offers several glimpses of techniques that are Gittins, R. 1985. Canonical Analysis: A Review with Applications only now beginning to be used by geophysical sci- in Ecology. New York: Springer-Verlag. entists; for example, Procrustes Target Analysis and Hall, C. E. 1969. Rotation of canonical variates in multivariate analysis of variance. J. Experimental Educ. 38: 31-38. extended applications of rule N with the principle of Harman, H. H. 1976. Modern Factor Analysis, 3rd Ed. Chicago: mimicry. University of Chicago Press. The derivation of CC A jn a PCA framework (chap- Humphreys, L. G. , and D. R. Ilgen. 1969. Note on a criterion for ter 8) facilitates understanding of a particular aspect the number of common factors. Educ. and Psychol. Measur. 29: 571-578. of CCA in applied research. Preisendorfer ties this Lawley, D. N., and A. E. Maxwell. 1971. Factor Analysis as a into SV D of two datasets using the concept of a cor- Statistical Method. London: Butterworths and Co. relation probe which seeks orientations of maximum Mulaik, S. A. 1972. The Foundations of Factor Analysis. New York: correlations between spaces. The section on selec- McGra w Hill. tion rules for CCA contains previously unpublished Mulaik, S. A. 1986. Factor analysis and Psychometrika: Major developments. Psychometrika 51: 23-33. material; hence, it may prove useful to researchers Prohaska, J. T. 1976. A technique for analyzing the linear rela- engaged in using the method. The bibliographic notes tionships between two meteorological fields. Mon. Wea. Rev. reference needed applications, one of which is Pro- 104: 1345-1353. haska's (1976) paper which diagnoses the correlation Reynolds, T., and E. Jackosfsky. 1981. Interpreting canonical anal- structure of two datasets with particular relevance to ysis: The use of orthogonal transformations. Educ. and Psychol. prediction. One interesting topic not covered in this Measur. 41: 661-671. Richman, M. B. 1986. Rotation of principal components. ). Cli- chapter is the extension of CCA by rotating the ca- matology 6: 293-335. nonical variates for increased interpretation (e.g., Hall Richman, M. B., and P. J. Lamb. 1985. Climatic pattern analysis 1969; Cliff and Kruss 1976; Reynolds and Jackosfsky of three- and seven-day summer rainfall in the central United 1981). The reader might augment Preisendorfer's States: Some methodological considerations and a regionaliza- chapter with Seber (1984) if interested in the tradi- tion. J. Clim. Appl. Meteor. 24: 1325-1343. Seber, G. A. F. 1984. Multivariate Observations. New York: John tional statistical development of CCA, and with Git- Wile y and Sons, Inc. tins (1985) or Thompson (1984) for further applied Thompson, B. 1984. Canonical Correlation Analysis. Beverly Hills: issues. Chapter 9 similarly contains unique discus- Sage. 71 pp. • sions of CC A regression, hindcast skill and how this relates to CCA. The last three chapters deal with statistical-dynam- 25 years ago.. . ical models, partitioning eigenvectors, and complex harmonic PCA. Chapter 10 is an impressive exami- The February 1965 Bulletin contained the minutes of the Boston nation of two examples of substituting eigenmodes meeting of the Council on October 3 and 4, 1964. One of the items into models of atmospheric flow. Likewise, chapter reads as follows: 12 contains a wealth of information, which has never 24. The Secretary brought to the attention of the Council the in- been previously assembled, on complex PCA, moti- dictment of Mr. Kenneth T. C. Cheng, Head of the Taiwan Weather Service, for an incorrect typhoon forecast. The Secretary informed the vated by the thought that "w e may reasonably expect Council that by direction of the Executive Committee he had written that on combining the techniques of PCA and har- to the Ambassador from Taiwan deploring the indictment of a mete- monic analysis, something of greater applicability than orologist for an incorrect forecast, pointing out that if forecasters were each will result for certain diagnostic or predictive indicted each time they made an incorrect forecast there could be, within a fairly short period of time, a total lack of forecasters. tasks."

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Bulletin of the American Meteorological SocietyAmerican Meteorological Society

Published: Feb 1, 1990

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