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Unformatted text preview: P X U x = 1 U x t m 1 exp Um t dt where U is the gamma function. The complement of the incomplete gamma distribution is correspondingly defined by U , x = x t m 1 exp Um t dt . Using these two formulas, derive the cumulative distribution function of random variable R that is defined in Eq. (9.43). This propagates the error found in 9.8. (b) Using the formula of the incomplete gamma distribution as the definition of the averaged neural output y i , derive Eq. (9.51) for the partial derivative y i U r / r . 5. (Problem 9.10 Haykin) In developing the approximate update formula of Eq. (9.55) for the weight vector of the kernel SOM algorithm, we justified ignoring the second term in Eq. (9.52). Yet, in deriving the update formula of Eq. (9.58) for the kernel width i , no approximation was made. Justify this latter choice....
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 Spring '08
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