Learning Machines: Foundations of Trainable Pattern-classifying Systems |
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Sivu 5
Any pattern can be represented by a point in a d - dimensional Euclidean space
Ed called the pattern space . ... denote both the pattern point and the pattern
vector by the symbol X . A pattern classifier is thus a device which maps the
points of ...
Any pattern can be represented by a point in a d - dimensional Euclidean space
Ed called the pattern space . ... denote both the pattern point and the pattern
vector by the symbol X . A pattern classifier is thus a device which maps the
points of ...
Sivu 32
We shall show that if the positions of the N pattern points satisfy some quite mild
conditions , the number of dichotomies that can be implemented by a o function
will depend only on the number of patterns N and the number of parameters M +
1 ...
We shall show that if the positions of the N pattern points satisfy some quite mild
conditions , the number of dichotomies that can be implemented by a o function
will depend only on the number of patterns N and the number of parameters M +
1 ...
Sivu 36
Suppose that we have a set X of N points and a set Z of K points ( K < d ) in Ed .
We desire to know the number Lz ( N , d ) of linear dichotomies of X achievable
by a hyperplane constrained to contain all the points of Z . We shall assume that ...
Suppose that we have a set X of N points and a set Z of K points ( K < d ) in Ed .
We desire to know the number Lz ( N , d ) of linear dichotomies of X achievable
by a hyperplane constrained to contain all the points of Z . We shall assume that ...
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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