MLVQ(EM 演算法 )

1. MLVQ(EM演算法) Speaker:楊志民 Date:96.10.4

2. training Feature extraction Test data 411.C Remove Dc_bias Speech feature Breath.c Feature extraction train model recognize Silence.c Recognize rate Duration.c Initial models

3. Initialize VQ Initial state loop VQ (get mixture means) Initialize MLVQ MLVQ (get mean ,variance weight, determin)

4. Mixture Gaussian density function The mixture Gaussian can fit any kinds of distribution f(x) x

5. Estimation theory • Bayes’ theorem • our goal is to maximize the log-likelihood of the observable，

6. We take the conditional expectation of over X computed with parameter vector : • The following expression is obtained

7. by Jensen’s inequality : • The convergence of the EM algorithm lies in the fact that if we • choose • so that then

8. Jensen’s inequality 對數函數 (f(x)=log(x)) 為一凸函數， 其滿足下列不等式 推廣上式， 其中 必須滿足

9. Jensen’s inequality

10. Thus, we can • The EM method is an iterative method, and we need a initial model Q0Q1Q2 … Maximization

11. Step of implement EM initialization: Choose an initial estimate Φ E-Step Estimate unobserved data using auxiliary Q-function M-step: Compute to maximize the auxiliary Q-function. Iteration: Set repeat from step2 until convergence. No Yes