Learning Machines: Foundations of Trainable Pattern-classifying Systems |
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Any pattern can be represented by a point in a d - dimensional Euclidean space Ed called the pattern space . ... thus a device which maps the points of Ed into the category numbers , 1 , ... , R. Let the symbol Pi denote the set of a .
Any pattern can be represented by a point in a d - dimensional Euclidean space Ed called the pattern space . ... thus a device which maps the points of Ed into the category numbers , 1 , ... , R. Let the symbol Pi denote the set of a .
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 function will depend only on the number of patterns N and the number of parameters M ...
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 function will depend only on the number of patterns N and the number of parameters M ...
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 ...
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 ...
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Sisältö
I | 1 |
SOME NONPARAMETRIC TRAINING METHODS | 65 |
APPENDIX | 127 |
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 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 specific Stanford step Suppose theorem theory threshold training methods training patterns 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 |