1997
DOI: 10.2307/2291455
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Polychotomous Regression

Abstract: An automatic procedure that uses linear splines and their tensor products is proposed for tting a regression model to data involving a polychotomous response variable and one or more predictors. The tted model can be used for multiple classi cation. The automatic tting procedure involves maximum likelihood estimation, stepwise addition, stepwise deletion, and model selection by AIC, cross-validation or an independent test set. A modi ed version of the algorithm has been constructed that is applicable to large … Show more

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Cited by 58 publications
(13 citation statements)
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“…Classification of multi-spectral and multitemporal images with high accuracy is necessary to improve our understanding of many natural and physical processes that shape our earth. Application of multi-response MARS approach (Elith and Leathwick 2007;Kooperberg et al 1997) for satellite image classification and comparing the results with other widely employed parametric and nonparametric methods such as maximum likelihood, support vector machines and artificial neural networks, etc., would be a promising direction to pursue. In multi-response MARS methodology, the models are constructed and pruned in the same manner as in single-response (i.e., regression) MARS approach.…”
Section: Discussionmentioning
confidence: 99%
“…Classification of multi-spectral and multitemporal images with high accuracy is necessary to improve our understanding of many natural and physical processes that shape our earth. Application of multi-response MARS approach (Elith and Leathwick 2007;Kooperberg et al 1997) for satellite image classification and comparing the results with other widely employed parametric and nonparametric methods such as maximum likelihood, support vector machines and artificial neural networks, etc., would be a promising direction to pursue. In multi-response MARS methodology, the models are constructed and pruned in the same manner as in single-response (i.e., regression) MARS approach.…”
Section: Discussionmentioning
confidence: 99%
“…The POLYCLASS algorithm [46], which achieved the smallest mean error rate, has mean error rate of 19.5%. The Lim, Loh and Shih calculated statistical significance of error rates, which showed that a difference between the mean error rates of two algorithms is statistically significant at the 10% level if they differ by more than 5.9%.…”
Section: The Comparison Testmentioning
confidence: 99%
“…These difficulties are usually overcome by augmenting or replacing the input vector with new variables, basis functions, which are transformations of the input variables, and then by using linear models in this new space of derived input features. Methods like sigmoidal feedforward neural networks (Bishop, 1995), projection pursuit learning (Friedman & Stuetzle, 1981), generalized additive models (Hastie & Tibshirani, 1990) and PolyMARS (Kooperberg, Bose, & Stone, 1997), and a hybrid of multivariate adaptive splines (Friedman, 1991;Tian-Shyug et al, 2006), specifically designed to solve classification problems, can be seen as different non-linear basis function models.…”
Section: Introductionmentioning
confidence: 99%