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Numerical Analysis

Numerical Analysis. MATLAB programming Numerical Methods I Numerical Methods II Marginal density estimation Expectation and maximization(EM) Annealed EM AEM for Clustering analysis Traveling salesman problem Numerical Methods III Independent component analysis Classification

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Numerical Analysis

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  1. Numerical Analysis • MATLAB programming • Numerical Methods I • Numerical Methods II • Marginal density estimation • Expectation and maximization(EM) • Annealed EM • AEM for Clustering analysis • Traveling salesman problem • Numerical Methods III • Independent component analysis • Classification • Function approximation • Density estimation Adavanced Numerical Computation

  2. References • Numerical mathematics and computing, • fourth Edition, Cheney&Kincaid, 1999 • Lecture slides • ftp://134.208.26.61 user:ndhu passwd:ndhu port:4810 • G. Rechtenwald, Numerical methods with MATLAB: • Implementation and application. Adavanced Numerical Computation

  3. Numerical Methods I • Numerical interpolation and approximation • Numerical integration and differentiation • Linear system and least square method • Approximation by spline functions Adavanced Numerical Computation

  4. Interpolation Adavanced Numerical Computation

  5. Function approximation Adavanced Numerical Computation

  6. Function approximation Adavanced Numerical Computation

  7. Initial Value Problem for ODEs Adavanced Numerical Computation

  8. Numerical integration • Lower sum and upper sum • Trapezoid rule • Simpson rule Adavanced Numerical Computation

  9. Linear system Ax=b Given A and b, find x Ex. Adavanced Numerical Computation

  10. Approximation by spline functions • Quadratic spline • Cubic spline • Natural cubic spline • B-splines Adavanced Numerical Computation

  11. Smoothing and the least square method Adavanced Numerical Computation

  12. Numerical methods II • Expectation and maximization(EM) • Marginal density estimation • Annealed EM • Marginal density estimation(AEM) • AEM for Clustering analysis • Traveling salesman problem Adavanced Numerical Computation

  13. Generator . . . Generator . . . Generator A generative model for Gaussian mixtures Multiplexer Adavanced Numerical Computation

  14. Marginal Density Estimation Adavanced Numerical Computation

  15. Clustering analysis Adavanced Numerical Computation

  16. Clustering analysis Adavanced Numerical Computation

  17. Density estimation- Gaussian Mixtures p 2 M Flip Coin … … … … Adavanced Numerical Computation

  18. Generative models of natural images Adavanced Numerical Computation Figure 5

  19. Generative models of natural images Adavanced Numerical Computation

  20. Traveling salesman problems Adavanced Numerical Computation

  21. Numerical Methods III • Independent component analysis • Linear ICA • Convolutive ICA • Classification • Data driven function approximation • Multivariate density estimation Adavanced Numerical Computation

  22. Independent component analysis Adavanced Numerical Computation

  23. Independent component analysis Observations Adavanced Numerical Computation

  24. Independent component analysis Recovered sources Adavanced Numerical Computation

  25. Blind source separation – fetal ECG BSS Adavanced Numerical Computation

  26. sources mixed images AemICA JadeICA Adavanced Numerical Computation

  27. Fz F3 F4 Cz C3 Pz Oz N1 N2 P2 P3 Adavanced Numerical Computation

  28. Fz F3 F4 Cz C3 Pz Oz P2 N1 N2 P3 Figure 12 Adavanced Numerical Computation

  29. Blind source separation by convolutive ICA music and speech Adavanced Numerical Computation

  30. Convolutive mixtures Adavanced Numerical Computation

  31. Recovered sources Adavanced Numerical Computation

  32. Adavanced Numerical Computation

  33. Adavanced Numerical Computation

  34. Adavanced Numerical Computation

  35. Numerical methods III • Independent component analysis • Classification • Function approximation • Multivariate density estimation Adavanced Numerical Computation

  36. Classification- Face detection Adavanced Numerical Computation

  37. Classification- Face detection Adavanced Numerical Computation

  38. Classification- Face detection Adavanced Numerical Computation

  39. Classification- Face recognition Adavanced Numerical Computation

  40. Classification – breast cancer diagnosis Breast Cancer Diagnosis FNA細胞樣本 Features: clump thickness uniformity of cell size uniformity of cell shape marginal adhesion single epithelial cell size bare nuclei bland chromatin normal nucleoli and mitoses A camera on a Microscope Benign Or Malignant Feature extractor Adavanced Numerical Computation

  41. Function Approximation a. Adavanced Numerical Computation

  42. Function Approximation b. Adavanced Numerical Computation

  43. Function Approximation Adavanced Numerical Computation

  44. Density estimation Adavanced Numerical Computation

  45. Density estimation Adavanced Numerical Computation

  46. Density estimation Adavanced Numerical Computation

  47. a b d c Density estimation Adavanced Numerical Computation

  48. a b d c Density estimation Adavanced Numerical Computation

  49. Density estimation b a c d Adavanced Numerical Computation

  50. Density estimation a b Adavanced Numerical Computation

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