Learning Machines: Foundations of Trainable Pattern-classifying SystemsMcGraw-Hill, 1965 - 137 sivua |
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Sivu 58
... matrix . The first step in its de- velopment is to form a matrix Q ; whose columns are derived from the patterns in X. Subtract from each of the N ; patterns in X ; the sample- mean pattern ( X ) ;; Q ; is then a d X N , matrix whose N ...
... matrix . The first step in its de- velopment is to form a matrix Q ; whose columns are derived from the patterns in X. Subtract from each of the N ; patterns in X ; the sample- mean pattern ( X ) ;; Q ; is then a d X N , matrix whose N ...
Sivu 59
... matrix Σ ; and unknown mean vector . Thus , the d com- ponents of the mean vector are the only unknown parameters of the dis- criminant function . For any known M , X will be normal with mean M and covariance matrix Σ . * That is , p ...
... matrix Σ ; and unknown mean vector . Thus , the d com- ponents of the mean vector are the only unknown parameters of the dis- criminant function . For any known M , X will be normal with mean M and covariance matrix Σ . * That is , p ...
Sivu 131
... matrix and M is the mean vector . From Eq . ( A.6 ) we can write ΣΤΙ = TDDiTt ( A ∙ 11 ) where T is a d x d matrix of the unit eigenvectors of -1 and DD is a d x d diagonal matrix whose entries are the eigenvalues of Σ - 1 . ( It is ...
... matrix and M is the mean vector . From Eq . ( A.6 ) we can write ΣΤΙ = TDDiTt ( A ∙ 11 ) where T is a d x d matrix of the unit eigenvectors of -1 and DD is a d x d diagonal matrix whose entries are the eigenvalues of Σ - 1 . ( It is ...
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 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 |