Learning Machines: Foundations of Trainable Pattern-classifying Systems |
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3.6 The bivariate normal probability - density function In the example of Sec . 3.5 , we assumed that the pattern components were statistically independent , binary , random variables . Such an assumption permitted a straightforward ...
3.6 The bivariate normal probability - density function In the example of Sec . 3.5 , we assumed that the pattern components were statistically independent , binary , random variables . Such an assumption permitted a straightforward ...
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Contours of equal probability density ( z12 20122122 +222 = constant ) are ellipses , cen- tered on the origin , whose major axes lie along the line 21 eccentricities of the ellipses are equal to 2012 VI + 012 = 22.
Contours of equal probability density ( z12 20122122 +222 = constant ) are ellipses , cen- tered on the origin , whose major axes lie along the line 21 eccentricities of the ellipses are equal to 2012 VI + 012 = 22.
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The unconditional density for X can now be obtained by inspection , since Z and M are independent . Then X will have mean u and covariance matrix + K. That is , p ( X ) ~ N ( μ , Σ + K ) ( 3.41 ) The net effect of the uncertainty in M ...
The unconditional density for X can now be obtained by inspection , since Z and M are independent . Then X will have mean u and covariance matrix + K. That is , p ( X ) ~ N ( μ , Σ + K ) ( 3.41 ) The net effect of the uncertainty in M ...
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Sisältö
TRAINABLE PATTERN CLASSIFIERS | 1 |
PARAMETRIC TRAINING METHODS | 43 |
SOME NONPARAMETRIC TRAINING METHODS | 65 |
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adjusted apply assume bank called cells changes Chapter classifier cluster column committee machine components consider consists contains correction corresponding covariance decision surfaces define denote density depends described discriminant functions discussed distance distributions elements equal error-correction estimates example exist expression FIGURE fixed given implemented initial layered machine linear machine linearly separable lines majority matrix mean measurements modes negative networks nonparametric normal Note optimum origin parameters partition pattern hyperplane pattern space pattern vector pattern-classifying piecewise linear plane points positive presented probability problem properties PWL machine quadric regions respect response rule selection separable sequence side solution space step subsidiary discriminant Suppose terns 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 |