Learning Machines: Foundations of Trainable Pattern-classifying Systems |
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Sivu 58
i = ; where Ni 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 ( 2 ) : is called the sample covariance matrix of the ith category .
i = ; where Ni 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 ( 2 ) : is called the sample covariance matrix of the ith category .
Sivu 60
By expanding the exponent in Eq . ( 3-46 ) , it is a straightforward matter to identify the mean vector and covariance ... < + x ) ' - + * ( * + :) Kv - * ( + ) ** ( 3:49 ) + N N and the sample mean N ( X ) Σ Σ 60 PARAMETRIC TRAINING METHODS.
By expanding the exponent in Eq . ( 3-46 ) , it is a straightforward matter to identify the mean vector and covariance ... < + x ) ' - + * ( * + :) Kv - * ( + ) ** ( 3:49 ) + N N and the sample mean N ( X ) Σ Σ 60 PARAMETRIC TRAINING METHODS.
Sivu 61
and the sample mean N ( X ) Σ Σ Xi ( 3.50 ) N The optimum a posteriori discriminant function ( after training on the set { X1 , X2 , . . . , Xn } ) is then given by Eq . ( 3:31 ) with M replaced by yn and replaced by 2 + Ky .
and the sample mean N ( X ) Σ Σ Xi ( 3.50 ) N The optimum a posteriori discriminant function ( after training on the set { X1 , X2 , . . . , Xn } ) is then given by Eq . ( 3:31 ) with M replaced by yn and replaced by 2 + Ky .
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Sisältö
I | 1 |
SOME NONPARAMETRIC TRAINING METHODS | 65 |
APPENDIX | 127 |
Tekijänoikeudet | |
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adjusted apply assume bank belonging to category called changes Chapter cluster committee components consider consists contains correction corresponding covariance decision surfaces define denote density depends derivation described discriminant functions discussed distance distribution element equal error-correction estimates example exists expression FIGURE fixed given implemented important initial layered machine linear dichotomies linear machine linearly separable matrix measurements negative normal Note optimum origin parameters partition pattern classifier pattern hyperplane pattern space pattern vector piecewise linear plane points positive presented probability problem proof properties proved PWL machine quadric reduced regions respect response rule sample mean selection separable shown side solution space specific Stanford step Suppose theorem theory threshold training methods training patterns training procedure training sequence training subsets transformation values weight vectors 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 |