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

3. Adavanced Numerical Computation
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. Adavanced Numerical Computation
Interpolation
Adavanced Numerical Computation

5. Adavanced Numerical Computation
Function approximation
Adavanced Numerical Computation

6. Adavanced Numerical Computation
Function approximation
Adavanced Numerical Computation

7. Adavanced Numerical Computation
Initial Value Problem for ODEs
Adavanced Numerical Computation

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

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

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

11. Adavanced Numerical Computation
Smoothing and the least square method
Adavanced Numerical Computation

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

14. Adavanced Numerical Computation
Marginal Density Estimation
Adavanced Numerical Computation

15. Adavanced Numerical Computation
Clustering analysis
Adavanced Numerical Computation

16. Adavanced Numerical Computation
Clustering analysis
Adavanced Numerical Computation

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

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

19. Adavanced Numerical Computation
Generative models of natural images
Adavanced Numerical Computation

20. Adavanced Numerical Computation
Traveling salesman problems
Adavanced Numerical Computation

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

22. Adavanced Numerical Computation
Independent component analysis
Adavanced Numerical Computation

23. Adavanced Numerical Computation
Independent component analysis
Observations
Adavanced Numerical Computation

24. Adavanced Numerical Computation
Independent component analysis
Recovered
sources
Adavanced Numerical Computation

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

26. Adavanced Numerical Computation
sources
mixed images
AemICA
JadeICA
Adavanced Numerical Computation

27. Adavanced Numerical ComputationFz Cz Pz Oz C3 F4 F3 P2 P3
Adavanced Numerical Computation

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

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

30. Adavanced Numerical Computation
Convolutive mixtures
Adavanced Numerical Computation

31. Adavanced Numerical Computation
Recovered sources
Adavanced Numerical Computation

32. Adavanced Numerical Computation

33. Adavanced Numerical Computation

34. Adavanced Numerical Computation

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

36. Adavanced Numerical Computation
Classification- Face detection
Adavanced Numerical Computation

37. Adavanced Numerical Computation
Classification- Face detection
Adavanced Numerical Computation

38. Adavanced Numerical Computation
Classification- Face detection
Adavanced Numerical Computation

39. Adavanced Numerical Computation
Classification- Face recognition
Adavanced Numerical Computation

40. Adavanced Numerical Computation
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. Adavanced Numerical Computation
Function Approximation a.
Adavanced Numerical Computation

42. Adavanced Numerical Computation
Function Approximation b.
Adavanced Numerical Computation

43. Adavanced Numerical Computation
Function Approximation
Adavanced Numerical Computation

44. Adavanced Numerical Computation
Density estimation
Adavanced Numerical Computation

45. Adavanced Numerical Computation
Density estimation
Adavanced Numerical Computation

46. Adavanced Numerical Computation
Density estimation
Adavanced Numerical Computation

47. Adavanced Numerical Computation
Density estimation a b c d
Adavanced Numerical Computation

48. Adavanced Numerical Computation
Density estimation a b c d
Adavanced Numerical Computation

49. Adavanced Numerical Computation
Density estimation a b c d
Adavanced Numerical Computation

50. Adavanced Numerical Computation
Density estimation a b
Adavanced Numerical Computation

51. Adavanced Numerical Computation
Density estimation
Adavanced Numerical Computation

52. Adavanced Numerical Computation
Density estimation
Adavanced Numerical Computation

53. Adavanced Numerical Computation
MATLAB Programming
Input your data, including texts, images, and sounds
Output: 2D plots & output messages
Basic control: if, for, while statements
Matrix manipulations
Function calling
Speeding-up of programs
Adavanced Numerical Computation

54. Adavanced Numerical Computation
Basic structure of a flowchart or a program
One by one sequential execution
A statement can be
an assignment: A = B*C-D
: x = sort(x)
a function for I/O : plot(x,y)
: imread(X)
a control statement
-- if statement
-- if else statement
-- for statement
-- while statement
start
statements
end
Adavanced Numerical Computation

55. Adavanced Numerical Computation
Control statements
If statement
false
condition
tag = 0;
if ~ tag
tag = tag+1;
end
true
statements
Adavanced Numerical Computation

56. Adavanced Numerical Computation
Control statements
If else statement
false or 0
condition
if ~ tag
tag = tag +1;
else
tag = tag –1;
end
true or 1
statements
statements
Adavanced Numerical Computation

57. Adavanced Numerical Computation
Control statements
for statement
i =1
Example
x=2;
for i = 1:10
x = x*x;
end
false
true
statements
i=i+1
Adavanced Numerical Computation

58. Adavanced Numerical Computation
Control statements
while statement
Example
a=1;
b=2;
while a < 100
a = a*b;
end
false
a<100
true
statements
Adavanced Numerical Computation