Learning Machines: Foundations of Trainable Pattern-classifying SystemsMcGraw-Hill, 1965 - 137 sivua |
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Sivu 6
... X in Ri , gi ( X ) > g ; ( X ) for i , j = 1 , . . . , R , ji . That is , in R , the ith discrimi- nant function has the largest value . We also assume that discriminant functions are continuous across the decision surfaces ; then the ...
... X in Ri , gi ( X ) > g ; ( X ) for i , j = 1 , . . . , R , ji . That is , in R , the ith discrimi- nant function has the largest value . We also assume that discriminant functions are continuous across the decision surfaces ; then the ...
Sivu 47
... gi ( X ) = p ( Xi ) p ( i ) for i = 1 , ... , R It will often be convenient to use the alternative expression gi ( X ) = log p ( Xi ) + log p ( i ) for i = 1 , ... . , ( 3.7a ) R ( 3.76 ) which leads to the same decisions since the log ...
... gi ( X ) = p ( Xi ) p ( i ) for i = 1 , ... , R It will often be convenient to use the alternative expression gi ( X ) = log p ( Xi ) + log p ( i ) for i = 1 , ... . , ( 3.7a ) R ( 3.76 ) which leads to the same decisions since the log ...
Sivu 55
... ( X - M1 ) ' Σ ; ̄1 ( X — M1 ) } for i = 9 R ( 3.28 ) We shall also adopt the convention p ( i ) = Pi . In Sec . 3-4 we learned that for a symmetric loss function , the opti- mum classifier uses the discriminant functions given by gi ( X ) ...
... ( X - M1 ) ' Σ ; ̄1 ( X — M1 ) } for i = 9 R ( 3.28 ) We shall also adopt the convention p ( i ) = Pi . In Sec . 3-4 we learned that for a symmetric loss function , the opti- mum classifier uses the discriminant functions given by gi ( X ) ...
Sisältö
TRAINABLE PATTERN CLASSIFIERS | 1 |
SOME NONPARAMETRIC TRAINING METHODS | 65 |
TRAINING THEOREMS | 79 |
Tekijänoikeudet | |
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assume augmented pattern belonging to category Chapter cluster committee machine committee TLUS components correction increment covariance matrix d-dimensional decision surfaces denote diagonal matrix discussed dot products error-correction procedure Euclidean distance example Fix and Hodges function g(X given Hodges method hypersphere image-space implemented initial weight vectors ith bank layer of TLUS layered machine linear dichotomies linear discriminant functions linearly separable loss function mean vector minimum-distance classifier mode-seeking networks nonparametric number of patterns p₁ parameters partition pattern classifier pattern hyperplane pattern space pattern vector patterns belonging perceptron piecewise linear plane point sets positive probability distributions prototype pattern PWL machine quadratic form quadric function rule sample covariance matrix shown in Fig solution weight vectors Stanford subsets X1 subsidiary discriminant functions Suppose terns TLU response training patterns training sequence training set training subsets transformation two-layer machine values W₁ Wa+1 weight point weight space weight-vector sequence X1 and X2 zero
Viitteet tähän teokseen
A Probabilistic Theory of Pattern Recognition Luc Devroye,László Györfi,Gabor Lugosi Rajoitettu esikatselu - 1997 |