1. Random Swap EM algorithm for GMM and Image Segmentation
Qinpei Zhao, Ville Hautamäki, Ismo Kärkkäinen, Pasi Fränti
Speech & Image Processing Unit
Department of Computer Science, University of Joensuu
Box 111, Fin Joensuu
FINLAND

2. Outline
Background & Status
RS-EM
Application

3. Background: Mixture Model

4. Background: EM algorithm
E-step (Expectation):
M-step (Maximization):
Iterate E,M step until convergence
α- mixing coefficient
Θ- model parameters, eg. {μ,∑}

5. Local Maxima
Let’s describe it as mountain climbing……

6. 2160m
3099m
600km

8. Initialization Effect
Initialization and Result(1)
Initialization and Result(2)

9. The situation of local maxima trap
Sub-optimal Example
The situation of local maxima trap

10. Status Standard EM for Mixture Models(1977)
Deterministic Annealing EM (DAEM) (1998)
Split-Merge EM (SMEM) (2000)
Greedy EM (2002)
RS-EM coming…

11. Outline
Background & Status
RS-EM (Random Swap)
Application

12. RSEM: Motivations Random manner
Prevent from staying near the unstable or hyperbolic fixed points of EM.
Prevent from its stable fixed points corresponding to insignificant local maxima of the likelihood function
Avoid the slow convergence of EM algorithm
Less sensitive to its initialization

13. Formulas
SMEM
Greedy EM
RSEM

14. Random Swap EM
After EM
After EM
After Swap

15. Comparisons(1)

16. Comparisons(2) Q1 Q2 S1 S4

17. Outline
Background & Status
RS-EM
Application

18. Application
Image Segmentation
Color Quantization
Image Retrieval ……

19. Conclusion Thanks!☺ Introduce Randomization into algorithm
Performs better
Without heavy time complexity
Wider applications
Thanks!☺