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Supervised and Unsupervised MFA learning Self-organization Classification

Supervised and Unsupervised MFA learning Self-organization Classification Independent component analysis. Outline. MFA learning Mixed integer and linear programming (MILP) Classification Independent component analysis Self-organization MATLAB demo Face recognition Fetal ECG extraction

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Supervised and Unsupervised MFA learning Self-organization Classification

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  1. Supervised and Unsupervised MFA learning • Self-organization • Classification • Independent component analysis Advanced Numerical Computation 2008, AM NDHU

  2. Outline • MFA learning • Mixed integer and linear programming (MILP) • Classification • Independent component analysis • Self-organization • MATLAB demo • Face recognition • Fetal ECG extraction • Automatic microarray image analysis • Conclusions Advanced Numerical Computation 2008, AM NDHU

  3. MILP • Variables • Binary discrete variables • Real continuous variables • The objective function is not differentiable with respect to discrete variables • MILP is solved by MFA learning Advanced Numerical Computation 2008, AM NDHU

  4. Learning self-organizing map • MILP • Solve a MILP by the AEM method Advanced Numerical Computation 2008, AM NDHU

  5. A generative model for Gaussian mixtures Advanced Numerical Computation 2008, AM NDHU

  6. Multivariate Gaussian Advanced Numerical Computation 2008, AM NDHU

  7. Membership Standard basis Advanced Numerical Computation 2008, AM NDHU

  8. Membership vector Advanced Numerical Computation 2008, AM NDHU

  9. Fitting Gaussian mixtures Advanced Numerical Computation 2008, AM NDHU

  10. Griding Kohonen SOM algorithm Advanced Numerical Computation 2008, AM NDHU

  11. SOM Advanced Numerical Computation 2008, AM NDHU

  12. Energy function Advanced Numerical Computation 2008, AM NDHU

  13. MILP • E is not differentiable with respect to discrete variables • Boltzmann assumption Advanced Numerical Computation 2008, AM NDHU

  14. Free energy • Mean energy combined with negative entropy • Entropy: Advanced Numerical Computation 2008, AM NDHU

  15. Approximation to mean energy Advanced Numerical Computation 2008, AM NDHU

  16. Free energy Advanced Numerical Computation 2008, AM NDHU

  17. Unsupervised MFA • E step • M step Advanced Numerical Computation 2008, AM NDHU

  18. E step Advanced Numerical Computation 2008, AM NDHU

  19. Numerical procedure Advanced Numerical Computation 2008, AM NDHU

  20. Numerical results Advanced Numerical Computation 2008, AM NDHU

  21. Numerical results Advanced Numerical Computation 2008, AM NDHU

  22. Micro-Array image Advanced Numerical Computation 2008, AM NDHU

  23. Griding Kohonen SOM algorithm Advanced Numerical Computation 2008, AM NDHU

  24. T s(v) a b s(v) T c d s(v) T Advanced Numerical Computation 2008, AM NDHU e f

  25. s(v) T Advanced Numerical Computation 2008, AM NDHU

  26. Unsupervised MFA Learning Advanced Numerical Computation 2008, AM NDHU

  27. Face classification Advanced Numerical Computation 2008, AM NDHU

  28. Data sets Training set Testing set Advanced Numerical Computation 2008, AM NDHU

  29. Data flow Training set Learning a classifier Parameters of a classifier: A,y Classification Testing set Error rate for testing Advanced Numerical Computation 2008, AM NDHU

  30. p K A generative model Flip Coin … … … … Advanced Numerical Computation 2008, AM NDHU

  31. Classification Advanced Numerical Computation 2008, AM NDHU

  32. Maternal ECG Advanced Numerical Computation 2008, AM NDHU

  33. Fetal ECG extraction PottsICA MECG Advanced Numerical Computation 2008, AM NDHU

  34. Blind source separation Advanced Numerical Computation 2008, AM NDHU

  35. BSS Convolutive ICA Advanced Numerical Computation 2008, AM NDHU

  36. Convolutive mixtures Advanced Numerical Computation 2008, AM NDHU

  37. Recovered sources Advanced Numerical Computation 2008, AM NDHU

  38. Advanced Numerical Computation 2008, AM NDHU

  39. Advanced Numerical Computation 2008, AM NDHU

  40. Advanced Numerical Computation 2008, AM NDHU

  41. ICA of mixed facial images Advanced Numerical Computation 2008, AM NDHU

  42. ICA Advanced Numerical Computation 2008, AM NDHU

  43. Demo • Demo_face_nda • Jade_K5 • Microarray_nen Advanced Numerical Computation 2008, AM NDHU

  44. Conclusions • Successfully develop MILP modeling for self-organization, independent component analysis, classification • Well verify effectiveness of AEM for relevant bio-signal analysis Advanced Numerical Computation 2008, AM NDHU

  45. References • Jiann-Ming Wu & Lin, Neural Networks, Vol 15, No. 3(2002) • Jiann-Ming Wu, Neural Computation,Vol. 14, No. 3(2002) • Jiann-Ming Wu & Chiu, IEEE Trans. On Neural Networks, Vol. 12, No. 2, March (2001) Advanced Numerical Computation 2008, AM NDHU

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