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Penalized Discriminant Analysis
Open accessAbstract
Fisher's linear discriminant analysis (LDA) is a popular data-analytic tool for studying the relationship between a set of predictors and a categorical response. In this paper we describe a penalized version of LDA. It is designed for situations in which there are many highly correlated predictors, such as those obtained by discretizing a function, or the grey-scale values of the pixels in a series of images. In cases such as these it is natural, efficient and sometimes essential to impose a spatial smoothness constraint on the coefficients, both for improved prediction performance and interpretability. We cast the classification problem into a regression framework via optimal scoring. Using this, our proposal facilitates the use of any penalized regression technique in the classification setting. The technique is illustrated with examples in speech recognition and handwritten character recognition.
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Cited by
Model Selection and the Principle of Minimum Description Length
Hansen, M. H., & Yu, B. (2001) · Journal of the American Statistical Association · doi:10.1198/016214501753168398 · Cited by 788
Classification Trees With Unbiased Multiway Splits
Kim, H., & Loh, W.-Y. (2001) · Journal of the American Statistical Association · doi:10.1198/016214501753168271 · Cited by 391
Functional Linear Discriminant Analysis for Irregularly Sampled Curves
James, G. M., & Hastie, T. J. (2001) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00297 · Cited by 310
Self-citationBayesian multi-task learning for decoding multi-subject neuroimaging data
Marquand, A. F., Brammer, M., Williams, S. C. R., & Doyle, O. M. (2014) · NeuroImage · doi:10.1016/j.neuroimage.2014.02.008 · Cited by 59
Spedicato, G., Dutang, C., & Petrini, L. (2018) · Variance · doi:10.66573/001c.116043 · Cited by 5
Metadata
- Authors
- Hastie, T., Buja, A., & Tibshirani, R.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1995-02-01
- Volume
- 23
- Issue
- 1
- Pages
- 73-102
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2089322632
- Cited by
- 849
- References
- 0
- FWCI
- 9.54
- Type
- journal article
- Language
- en
- Open access
- bronze
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