Learning Machines: Foundations of Trainable Pattern-classifying SystemsMcGraw-Hill, 1965 - 137 sivua |
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Sivu 54
... vector representing the pattern . is ad X1 column vector . It has the property of being equal to the expected value of X ( i.e. , M = E [ X ] ) and is therefore called the mean vector . ma Old σ11 012 σij Odd σdi is a symmetric ...
... vector representing the pattern . is ad X1 column vector . It has the property of being equal to the expected value of X ( i.e. , M = E [ X ] ) and is therefore called the mean vector . ma Old σ11 012 σij Odd σdi is a symmetric ...
Sivu 59
... mean vectors are assumed to be random variables . Suppose the pattern vectors belonging to category i are normal with known covariance matrix Σ ; and unknown mean vector . Thus , the d com- ponents of the mean vector are the only ...
... mean vectors are assumed to be random variables . Suppose the pattern vectors belonging to category i are normal with known covariance matrix Σ ; and unknown mean vector . Thus , the d com- ponents of the mean vector are the only ...
Sivu 61
... mean vector . We note the asymptotic results lim = UN ( X ) lim KN = 0 N → ∞ ( 3.51 ) Further insight into the process of learning the mean vector can be obtained by considering the special case where K = ( 1 / a ) , where a is a ...
... mean vector . We note the asymptotic results lim = UN ( X ) lim KN = 0 N → ∞ ( 3.51 ) Further insight into the process of learning the mean vector can be obtained by considering the special case where K = ( 1 / a ) , where a is a ...
Sisältö
TRAINABLE PATTERN CLASSIFIERS | 1 |
SOME NONPARAMETRIC TRAINING METHODS | 65 |
TRAINING THEOREMS | 79 |
Tekijänoikeudet | |
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assume augmented pattern belonging to category Chapter cluster committee machine committee TLUS components correction increment covariance matrix d-dimensional decision surfaces denote diagonal matrix discussed dot products error-correction procedure Euclidean distance example Fix and Hodges function g(X given Hodges method hypersphere image-space implemented initial weight vectors ith bank layer of TLUS layered machine linear dichotomies linear discriminant functions linearly separable loss function mean vector minimum-distance classifier mode-seeking networks nonparametric number of patterns p₁ parameters partition pattern classifier pattern hyperplane pattern space pattern vector patterns belonging perceptron piecewise linear plane point sets positive probability distributions prototype pattern PWL machine quadratic form quadric function rule sample covariance matrix shown in Fig solution weight vectors Stanford subsets X1 subsidiary discriminant functions Suppose terns TLU response training patterns training sequence training set training subsets transformation two-layer machine values W₁ Wa+1 weight point weight space weight-vector sequence X1 and X2 zero
Viitteet tähän teokseen
A Probabilistic Theory of Pattern Recognition Luc Devroye,László Györfi,Gabor Lugosi Rajoitettu esikatselu - 1997 |