Learning Machines: Foundations of Trainable Pattern-classifying Systems |
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Sivu 103
6.5 Transformation properties of layered machines We have seen in Secs . ... Another representation , to be discussed in this section , con- centrates on the nonlinear transformations implemented by each layer of TLUS .
6.5 Transformation properties of layered machines We have seen in Secs . ... Another representation , to be discussed in this section , con- centrates on the nonlinear transformations implemented by each layer of TLUS .
Sivu 104
For a given set of weights , the first layer will transform a finite set X of pattern vectors into a finite set g ( 1 ) of image ... The transformation from I space to I2 space depends on the values of the weights in the second layer .
For a given set of weights , the first layer will transform a finite set X of pattern vectors into a finite set g ( 1 ) of image ... The transformation from I space to I2 space depends on the values of the weights in the second layer .
Sivu 131
A 3 Transformation of normal patterns Consider the normal distribution expressed by where p ( X ) = 1 - - ( 2π ) d / 2 | | 31⁄2 exp { — 1⁄2 [ ( X — M ) ' Σ − 1 ( X — M ) ] } ( A.10 ) is the covariance matrix and M is the mean vector .
A 3 Transformation of normal patterns Consider the normal distribution expressed by where p ( X ) = 1 - - ( 2π ) d / 2 | | 31⁄2 exp { — 1⁄2 [ ( X — M ) ' Σ − 1 ( X — M ) ] } ( A.10 ) is the covariance matrix and M is the mean vector .
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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,László Györfi,Gabor Lugosi Rajoitettu esikatselu - 1997 |