Learning Machines: Foundations of Trainable Pattern-classifying Systems |
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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 . The ( X ) i and ( 2 ) i are reasonable
...
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 . The ( X ) i and ( 2 ) i are reasonable
...
Sivu 60
By expanding the exponent in Eq . ( 3 : 46 ) , it is a straightforward matter to
identify the mean vector and covariance matrix Ui = K ( K + 2 ) ... 48 ) where UN =
vx = ( x + $ ) * * + ( x + x ) * * Kv = K ( K + * ) * ( 3 : 49 ) and the sample mean s Xi (
3 .
By expanding the exponent in Eq . ( 3 : 46 ) , it is a straightforward matter to
identify the mean vector and covariance matrix Ui = K ( K + 2 ) ... 48 ) where UN =
vx = ( x + $ ) * * + ( x + x ) * * Kv = K ( K + * ) * ( 3 : 49 ) and the sample mean s Xi (
3 .
Sivu 61
and the sample mean s Xi ( 3 . 50 ) 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 un and replaced by ? + Ky . The process of obtaining yn from
the ...
and the sample mean s Xi ( 3 . 50 ) 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 un and replaced by ? + Ky . The process of obtaining yn from
the ...
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Sisältö
Preface vii | 1 |
SOME NONPARAMETRIC TRAINING METHODS | 65 |
TRAINING THEOREMS | 79 |
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 Development 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 networks 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 Stanford step Suppose theorem theory threshold training methods training procedure training sequence training subsets transformation values weight vectors zero