Abstract
I propose a modification of exploratory projection pursuit which trades accuracy for interpretability in the resulting description. Interpretability, a generalization of parsimony, is based on the ideas of rotation in factor analysis and of entropy. It is defined as the simplicity of the coefficients which specify the description’s projections. A weighted optimization approach similar to roughness penalty curve-fitting is used to search for a more understandable description, with interpretability replacing smoothness. A real data example is presented. The method retains the nonlinear versatility of projection pursuit but has more intuitive appeal.
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References
Asimov, D. (1985). “The Grand Tour: A tool for viewing multidimensional data,” SIAM Journal of Scientific and Statistical Computing 6, 128–143.
Bellman, R. E. (1961). Adaptive Control Processes, Princeton University Press, Princeton.
Donoho, D. L. and Johnstone, I. M. (1989). “Projection-based approximation and a duality with kernel methods,” Annals of Statistics 17, 58–106.
Friedman, J. H. (1987). “Exploratory projection pursuit,” Journal of the American Statistical Association 82, 249–266.
Friedman, J. H. and Tukey, J. W. (1974). “A projection pursuit algorithm for exploratory data analysis,” IEEE Transactions on Computers C-23, 881–889.
Friedman, J. H. and Stuetzle, W. (1981). “Projection pursuit regression,” Journal of the American Statistical Association 76, 817–823.
Hall, P. (1987). “On polynomial-based projection indices for exploratory projection pursuit,” Annals of Statistics 17, 589–605.
Harman, H. H. (1976). Modern Factor Analysis, The University of Chicago Press, Chicago.
Huber, P. (1985). “Projection pursuit (with discussion),” Annals of Statistics 13, 435–525.
Jones, M. C. and Sibson, R. (1987). “What is projection pursuit? (with discussion),” Journal of the Royal Statistical Society, Series A 150, 1–36.
Mallows, C. L. (1973). “Some comments on Cp,” Technometrics 15, 661–676.
Marshall, A. W. and Olkin, I. (1979). Inequalities: Theory of Majorization and Its Applications, Academic Press, New York.
McDonald, J. A. (1982). “Interactive graphics for data analysis,” Ph.D. Dissertation, Department of Statistics, Stanford University.
Miller, R. P. (1985). Discussion of “Projection pursuit,” Annals of Statistics 17, 510–513.
Morton, S. C. (1989). “Interpretable projection pursuit,” Ph.D. Dissertation, Department of Statistics, Stanford University.
Rényi, A. (1961). “On measures of entropy and information,” in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, ed. J. Neyman, 547–561, University of California Press, Berkeley.
Silverman, B. W. (1984). “Penalized maximum likelihood estimation,” in Encyclopedia of Statistical Sciences, eds. S. Kotz and N. L. Johnson, Wiley, New York, 664–667.
Sun, J. (1989). “P-values in projection pursuit,” Ph.D. Dissertation, Department of Statistics, Stanford University.
Thurstone, L. L. (1935). The Vectors of the Mind, The University of Chicago Press, Chicago.
Tukey, J. W. (1961). “Discussion, emphasizing the connection between analysis of variance and spectrum analysis,” Technometrics 3, 201–202.
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© 1992 Springer-Verlag New York, Inc.
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Morton, S.C. (1992). Interpretable Exploratory Projection Pursuit. In: Page, C., LePage, R. (eds) Computing Science and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2856-1_79
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DOI: https://doi.org/10.1007/978-1-4612-2856-1_79
Publisher Name: Springer, New York, NY
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