Learning Machines: Foundations of Trainable Pattern-classifying Systems |
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Sivu 18
An equivalent classification is obtained by comparing the squared distances ( X –
P : / ? , i = 1 , . . . , R . Squaring both sides of Eq . ( 2 . ... 4 ) The minimum -
distance classification can be effected by comparing the expressions X · Pi – 12P
; .
An equivalent classification is obtained by comparing the squared distances ( X –
P : / ? , i = 1 , . . . , R . Squaring both sides of Eq . ( 2 . ... 4 ) The minimum -
distance classification can be effected by comparing the expressions X · Pi – 12P
; .
Sivu 23
Pis the normal Euclidean distance from the origin to the hyperplane . We shall
denote this distance by the symbol Aw , which we set equal to wd + 1 / / wl . ( If
Aw > 0 , the origin is on the positive side of the hyperplane . ) The equation X n +
Aw ...
Pis the normal Euclidean distance from the origin to the hyperplane . We shall
denote this distance by the symbol Aw , which we set equal to wd + 1 / / wl . ( If
Aw > 0 , the origin is on the positive side of the hyperplane . ) The equation X n +
Aw ...
Sivu 24
Let us define the Euclidean distance d ( X , Pi ) from an arbitrary point X to the
point set Pi by d ( X , P : ) = min j = 1 , . . . , Li ... ( 0 ) | ( 2 : 16 ) That is , the distance
between X and Pi is the smallest of the distances between X and each point in Pi
.
Let us define the Euclidean distance d ( X , Pi ) from an arbitrary point X to the
point set Pi by d ( X , P : ) = min j = 1 , . . . , Li ... ( 0 ) | ( 2 : 16 ) That is , the distance
between X and Pi is the smallest of the distances between X and each point in Pi
.
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Sisältö
Preface vii | 1 |
PARAMETRIC TRAINING METHODS | 43 |
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 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 mean vector 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 Stanford step Suppose theorem theory threshold training methods 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 |