MLVQ(EM演算法) Speaker:楊志民 Date:96.10.4 training Test data Remove Dc_bias Feature extraction 411.C Speech feature Breath.c Feature extraction train model recognize Silence.c Recognize rate Duration.c Initial models Initialize VQ Initial state loop VQ (get mixture means) Initialize MLVQ MLVQ (get mean ,variance weight, determin) Mixture Gaussian density function The mixture Gaussian can fit any kinds of distribution K p y | Φ ck N k y | μk , k k 1 c p K k 1 k k y | Φk f(x) x Estimation theory Bayes’ theorem P X x, Y y | P X x | Y y , P Y y | our goal is to maximize the log-likelihood of the observable, P Y y | P X x, Y y | P X x | Y y, log P Y y | log P X x, Y y | log P X x | Y y, We take the conditional expectation of X computed with parameter vector : E log P Y y X Yy log P Y y over P X x Y y , log P Y y x log P Y y The following expression is obtained log P Y y E log P X , Y y X Q , H , Yy E log P X Y y, X Yy • by Jensen’s inequality : H , H , • The convergence of the EM algorithm lies in the fact that if we choose so that Q , Q , then log P Y y | log P Y y | Jensen’s inequality 對數函數 (f(x)=log(x)) 為一凸函數, 其滿足下列不等式 log[ x1 (1 ) x2 ] log( x1 ) (1 ) log( x2 ) n n 推廣上式, log[ x ] i 1 其中 i 必須滿足 i i i 1 n i 1 i i 1 log( xi ) H (, ) H (, ) P( X x | Y y, ) log P( X x | Y y, ) x P( X x | Y y, ) log P( X x | Y y, ) x Jensen’s inequality P( X x | Y y, ) log[ x P( X x | Y y, ) ] P( X x | Y y, ) P( X x | Y y, ) log [ P( X x | Y y, ) ] P( X x | Y y, ) x log P( X x | Y y, ) 0 x Thus, we can Max Q ( , ) Maximization The EM method is an iterative method, and we need a initial model Q0Q1Q2 … Step of implement EM initialization: Choose an initial estimate Φ E-Step Estimate unobserved data using auxiliary Q-function Q(, ) M-step: ^ Compute arg max Q(, ) to maximize the auxiliary Q-function. ^ Iteration: ^ Set repeat from step2 until convergence. Yes No
© Copyright 2024 Paperzz