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Classification into two Multivariate Normal Distributions with Different Covariance Matrices
Open accessAbstract
Linear procedures for classifying an observation as coming from one of two multivariate normal distributions are studied in the case that the two distributions differ both in mean vectors and covariance matrices. We find the class of admissible linear procedures, which is the minimal complete class of linear procedures. It is shown how to construct the linear procedure which minimizes one probability of misclassification given the other and how to obtain the minimax linear procedure; Bayes linear procedures are also discussed.
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The idea of constructing support-vector networks comes from considering general forms of the dot-product in a Hilbert space.
“The idea of constructing support-vector networks comes from considering general forms of the dot-product in a Hilbert space (Anderson & Bahadur, 1966):”
From Support-vector networks (1995) · cites this paper as Anderson & Bahadur, 1966
The Summary and Introduction (p. 1) describe linear classification of two multivariate normal distributions, not the construction of support-vector networks. Searches for support-vector networks, Hilbert spaces, dot products, kernels, and inner products found no passage in our copy addressing the attributed idea. (LLM, conf=0.76)
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Research works printed but not linked: 2
- [1][1] ANDERsoN, T. W. (1958). An Introduction to Multivariate Statistical Analysis. Wiley, New York: -
- [4][4] KuLLBACk, SoLomoN (1959). Information Theory and Statistics. Wiley, New York. -
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Cortes, C., & Vapnik, V. (1995) · Machine Learning · doi:10.1007/bf00994018 · Cited by 59,421
Metadata
- Authors
- Anderson, T. W., & Bahadur, R. R.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1962-06
- Volume
- 33
- Issue
- 2
- Pages
- 420-431
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W1965751196
- Cited by
- 248
- References
- 0
- Citations by year
- 2026: 5 · 2025: 4 · 2024: 5 · 2023: 5 · 2022: 5 · 2021: 3 · 2020: 3 · 2019: 7 · 2018: 1 · 2017: 6 · 2016: 6 · 2015: 7 · 2014: 5 · 2013: 2 · 2012: 3
- FWCI
- 5.57
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Mathematical Statistics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- two-sample problem, unequal covariance matrices, admissibility, complete classes, minimax procedure, misclassification probability, decision theory
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