Learning Machines: Foundations of Trainable Pattern-classifying Systems |
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Sivu 20
Stated another way , a classification of X is linear and the subsets X1 , X2 , linearly separable if and only if linear discriminant functions g1 , 92 , ... , gr exist such that · • 9 XR are gi ( X ) > g ; ( X ) j = 1 ,. , R , ji for ...
Stated another way , a classification of X is linear and the subsets X1 , X2 , linearly separable if and only if linear discriminant functions g1 , 92 , ... , gr exist such that · • 9 XR are gi ( X ) > g ; ( X ) j = 1 ,. , R , ji for ...
Sivu 21
Because the decision regions of a linear machine are convex , it is easy to show that if the subsets X1 , X2 , ... , XR are linearly separable , then each pair of subsets Xi , X ,, i , j = 1 , , R , ij , is also linearly sepa- rable .
Because the decision regions of a linear machine are convex , it is easy to show that if the subsets X1 , X2 , ... , XR are linearly separable , then each pair of subsets Xi , X ,, i , j = 1 , , R , ij , is also linearly sepa- rable .
Sivu 107
When these conditions are met , ( 1 ) and ( 1 ) are guaranteed to be linearly separable , and thus a two - layer machine ... 6.6 A sufficient condition for image - space linear separability Before stating and proving the sufficient ...
When these conditions are met , ( 1 ) and ( 1 ) are guaranteed to be linearly separable , and thus a two - layer machine ... 6.6 A sufficient condition for image - space linear separability Before stating and proving the sufficient ...
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Sisältö
TRAINABLE PATTERN CLASSIFIERS | 1 |
SOME NONPARAMETRIC TRAINING METHODS | 65 |
TRAINING THEOREMS | 79 |
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adjusted apply assume bank called cells changes Chapter cluster column committee machine components consider consists contains correction corresponding covariance decision surfaces define denote density depends described dichotomies discriminant functions discussed distance distributions elements equal error-correction estimates example exist expression FIGURE fixed given implemented important initial layered machine linear machine linearly separable lines majority matrix mean measurements modes negative networks nonparametric normal Note optimum origin parameters partition pattern classifier pattern hyperplane pattern space pattern vector piecewise linear plane points positive presented probability problem properties PWL machine quadric regions respect response rule selection separable sequence side solution space Stanford step subsidiary discriminant Suppose 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 |
| ISBN | 0070465703, 9780070465701 |
| Pituus | 137 sivua |
| Vie sitaatti | BiBTeX EndNote RefMan |