Learning Machines: Foundations of Trainable Pattern-classifying Systems |
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3.9 Some special cases involving identical covariance matrices For the optimum discriminant functions for normal patterns , expansion of Eq . ( 3-31 ) yields gi ( X ) = = -1 / 1⁄2X'Σ ; -1X + X'2 , -1M ; pi 1/2 i - 1⁄2MΣ ; 1M ; + log p ...
3.9 Some special cases involving identical covariance matrices For the optimum discriminant functions for normal patterns , expansion of Eq . ( 3-31 ) yields gi ( X ) = = -1 / 1⁄2X'Σ ; -1X + X'2 , -1M ; pi 1/2 i - 1⁄2MΣ ; 1M ; + log p ...
Sivu 58
i where N is the number of patterns in the training subset X ;; ( X ) ; is called the sample mean ( or center of gravity ) of the ith category , and ( E ) ; is called the sample covariance matrix of the ith category .
i where N is the number of patterns in the training subset X ;; ( X ) ; is called the sample mean ( or center of gravity ) of the ith category , and ( E ) ; is called the sample covariance matrix of the ith category .
Sivu 59
If we assume appropriate probability distributions for the unknown mean vectors and covariance matrices , we can derive a training process which makes optimum use of the set of training patterns . In this section we shall illustrate ...
If we assume appropriate probability distributions for the unknown mean vectors and covariance matrices , we can derive a training process which makes optimum use of the set of training patterns . In this section we shall illustrate ...
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Sisältö
TRAINABLE PATTERN CLASSIFIERS | 1 |
PARAMETRIC TRAINING METHODS | 43 |
SOME NONPARAMETRIC TRAINING METHODS | 65 |
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adjusted apply assume bank called cells changes Chapter classifier cluster column committee machine components consider consists contains correction corresponding covariance decision surfaces define denote density depends described discriminant functions discussed distance distributions elements equal error-correction estimates example exist expression FIGURE fixed given implemented initial layered machine linear machine linearly separable lines majority matrix mean measurements modes negative networks nonparametric normal Note optimum origin parameters partition pattern hyperplane pattern space pattern vector pattern-classifying piecewise linear plane points positive presented probability problem properties PWL machine quadric regions respect response rule selection separable sequence side solution space step subsidiary discriminant Suppose terns theorem theory threshold training methods training patterns training procedure training sequence training subsets transformation values weight vectors X1 and X2 Y₁ zero
Viitteet tähän teokseen
A Probabilistic Theory of Pattern Recognition Luc Devroye,László Györfi,Gabor Lugosi Rajoitettu esikatselu - 1997 |
Kirjaluettelon tiedot
| Otsikko | Learning Machines: Foundations of Trainable Pattern-classifying Systems McGraw-Hill series in systems science |
| Kirjoittaja | Nils J. Nilsson |
| Painos | kuvitettu |
| Kustantaja | McGraw-Hill, 1965 |
| Alkuperäisteoksen sijainti | Wisconsinin yliopisto - Madison |
| Digitoitu | 16. huhtikuu 2008 |
| ISBN | 0070465703, 9780070465701 |
| Pituus | 137 sivua |
| Vie sitaatti | BiBTeX EndNote RefMan |