Learning Machines: Foundations of Trainable Pattern-classifying Systems |
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Sivu 32
2.13 The number of linear dichotomies of N points of d dimensions We shall begin by calculating the number of dichotomies of N patterns achievable by a linear discriminant function ( i.e. , a TLU ) . Recall that each of these ...
2.13 The number of linear dichotomies of N points of d dimensions We shall begin by calculating the number of dichotomies of N patterns achievable by a linear discriminant function ( i.e. , a TLU ) . Recall that each of these ...
Sivu 33
Assume that we have a set X ' of 1 points X1 , X2 , XN - 1 in general position in Ed . There are L ( N1 , d ) linear dichotomies of X ' . We wish to find out by how much this number of linear dichotomies is increased if the set X ' is ...
Assume that we have a set X ' of 1 points X1 , X2 , XN - 1 in general position in Ed . There are L ( N1 , d ) linear dichotomies of X ' . We wish to find out by how much this number of linear dichotomies is increased if the set X ' is ...
Sivu 37
Since any linear dichotomy of F in Ž space corresponds to a dichotomy of X in the pattern space , § ( N , d ) is equal to L ( N , M ) , which is the number of linear dichotomies of the set F of N points in space .
Since any linear dichotomy of F in Ž space corresponds to a dichotomy of X in the pattern space , § ( N , d ) is equal to L ( N , M ) , which is the number of linear dichotomies of the set F of N points in space .
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Sisältö
TRAINABLE PATTERN CLASSIFIERS | 1 |
SOME NONPARAMETRIC TRAINING METHODS | 65 |
TRAINING THEOREMS | 79 |
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adjusted apply assume bank called cells changes Chapter cluster column committee machine components consider consists contains correction corresponding covariance decision surfaces define denote density depends described dichotomies discriminant functions discussed distance distributions elements equal error-correction estimates example exist expression FIGURE fixed given implemented important initial layered machine linear machine linearly separable lines majority matrix mean measurements modes negative networks nonparametric normal Note optimum origin parameters partition pattern classifier pattern hyperplane pattern space pattern vector piecewise linear plane points positive presented probability problem properties PWL machine quadric regions respect response rule selection separable sequence side solution space Stanford step subsidiary discriminant Suppose theorem theory threshold training methods training patterns training procedure training sequence training subsets transformation values weight vectors X1 and X2 Y₁ zero
Viitteet tähän teokseen
A Probabilistic Theory of Pattern Recognition Luc Devroye,Lįszló Györfi,Gabor Lugosi Rajoitettu esikatselu - 1997 |