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# Em

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### Em

1. 1. 2 (a)02 2 0 2
2. 2. 2 (b)02 2 0 2
3. 3. 2 (b)02 2 0 2
4. 4. 2 (c) (b)02 2 0 2
5. 5. 2 (c) (d) (b)02 2 0 2
6. 6. 2 (c) (e) (d) (b)02 2 0 2
7. 7. 2 (f) (c) (e) (d) (b)02 2 0 2
8. 8. 2 (g) (f) (c) (e) (d) (b)02 2 0 2
9. 9. 2 (h) (g) (f) (c) (e) (d) (b)02 2 0 2
10. 10. 2 (i) (h) (g) (f) (c) (e) (d) (b)02 2 0 2
11. 11. 1000 J500 0 1 2 3 4
12. 12. … …
13. 13. 202 2 0 (a) 2
14. 14. 202 2 0 (b) (a) 2
15. 15. 2 L=102 2 0 (b) (a) (c) 2
16. 16. 2 1 L=202 2 0 (d) (b) (a) (c) 2
17. 17. 2 1 L=2 502 2 0 (e) (d) (b) (a) (c) 2
18. 18. 2 1 L = 20 5 202 2 0 (e) (d) (b) (a) (c) (f) 2
19. 19. ln p(X|θ) = ln p(X, Z|θ) z
20. 20. Q(θ, θold ) = p(Z|X, θold )p(X, Z|θ) Z θnew = argmaxθ Q(θ, θold )
21. 21. Q(θ, θold ) znk p(X, Z|µ, Σ, π) = πk N (xn |µk , Σk )znk i kln p(X, Z|µ, Σ, π) = znk {ln πk + ln N (xn |µk , Σk )} i,k Z =
22. 22. p(zk = 1)p(x|zk = 1)γ(zk ) ≡ p(zk = 1|x) = K j=1 p(zj = 1)p(x|zj = 1) πk N (x|µk , Σk ) = K j πj N (x|µj , Σj ) N N 1 µk = γ(zik )xi Nk = γ(zik ) Nk i=1 i=1 N 1 Σk = γ(zik )(xi − µk )(xi − µk )T Nk i=1