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

Adavanced Numerical Computation 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

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

Adavanced Numerical Computation Interpolation Adavanced Numerical Computation

Adavanced Numerical Computation Function approximation Adavanced Numerical Computation

Adavanced Numerical Computation Function approximation Adavanced Numerical Computation

Adavanced Numerical Computation Initial Value Problem for ODEs Adavanced Numerical Computation

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

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

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

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

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

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

Adavanced Numerical Computation Marginal Density Estimation Adavanced Numerical Computation

Adavanced Numerical Computation Clustering analysis Adavanced Numerical Computation

Adavanced Numerical Computation Clustering analysis Adavanced Numerical Computation

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

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

Adavanced Numerical Computation Generative models of natural images Adavanced Numerical Computation

Adavanced Numerical Computation Traveling salesman problems Adavanced Numerical Computation

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

Adavanced Numerical Computation Independent component analysis Adavanced Numerical Computation

Adavanced Numerical Computation Independent component analysis Observations Adavanced Numerical Computation

Adavanced Numerical Computation Independent component analysis Recovered sources Adavanced Numerical Computation

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

Adavanced Numerical Computation sources mixed images AemICA JadeICA Adavanced Numerical Computation

Adavanced Numerical Computation Fz Cz Pz Oz C3 F4 F3 P2 P3 Adavanced Numerical Computation

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

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

Adavanced Numerical Computation Convolutive mixtures Adavanced Numerical Computation

Adavanced Numerical Computation Recovered sources Adavanced Numerical Computation

Adavanced Numerical Computation

Adavanced Numerical Computation

Adavanced Numerical Computation

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

Adavanced Numerical Computation Classification- Face detection Adavanced Numerical Computation

Adavanced Numerical Computation Classification- Face detection Adavanced Numerical Computation

Adavanced Numerical Computation Classification- Face detection Adavanced Numerical Computation

Adavanced Numerical Computation Classification- Face recognition Adavanced Numerical Computation

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

Adavanced Numerical Computation Function Approximation a. Adavanced Numerical Computation

Adavanced Numerical Computation Function Approximation b. Adavanced Numerical Computation

Adavanced Numerical Computation Function Approximation Adavanced Numerical Computation

Adavanced Numerical Computation Density estimation Adavanced Numerical Computation

Adavanced Numerical Computation Density estimation Adavanced Numerical Computation

Adavanced Numerical Computation Density estimation Adavanced Numerical Computation

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

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

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

Adavanced Numerical Computation Density estimation a b Adavanced Numerical Computation

Adavanced Numerical Computation Density estimation Adavanced Numerical Computation

Adavanced Numerical Computation Density estimation Adavanced Numerical Computation

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

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

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

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

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

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