updated demos for ch01~06

chapter01/demo.m

@@ -1,5 +1,5 @@
-% Done
-% demo for information theory toolbox
+
+% demos for ch01
 clear;
 k = 10;  % variable range
 n = 100;  % number of variables
@@ -10,20 +10,20 @@
 % x = randi(k,1,n);  % need statistics toolbox
 % y = randi(k,1,n);
 
-%% entropy H(x), H(y)
+%% Entropy H(x), H(y)
 Hx = entropy(x);
 Hy = entropy(y);
-%% joint entropy H(x,y)
+%% Joint entropy H(x,y)
 Hxy = jointEntropy(x,y);
-%% conditional entropy H(x|y)
+%% Conditional entropy H(x|y)
 Hx_y = condEntropy(x,y);
-%% mutual information I(x,y)
+%% Mutual information I(x,y)
 Ixy = mutInfo(x,y);
-%% relative entropy (KL divergence) KL(p(x)|p(y))
+%% Relative entropy (KL divergence) KL(p(x)|p(y))
 Dxy = relatEntropy(x,y);
-%% normalized mutual information I_n(x,y)
+%% Normalized mutual information I_n(x,y)
 nIxy = nmi(x,y);
-%% nomalized variation information I_v(x,y)
+%% Nomalized variation information I_v(x,y)
 vIxy = nvi(x,y);
 %% H(x|y) = H(x,y)-H(y)
 isequalf(Hx_y,Hxy-Hy)

chapter03/demo.m

@@ -1,10 +1,9 @@
-% Done
-% demo for chapter 03
+% demos for ch03
 clear; close all;
 d = 1;
 n = 200;
 [x,t] = linRnd(d,n);
-%% linear regression
+%% Linear regression
 model = linReg(x,t);
 plotBar(model,x,t);
 %% Empirical Bayesian linear regression via EM

chapter04/demo.m

@@ -1,5 +1,6 @@
-% TODO: multiPlot: plot multiclass decison boundary
-% 
+% demos for ch04
+
+%% Logistic logistic regression for binary classification
 clear; close all;
 k = 2;
 n = 1000;
@@ -8,7 +9,7 @@
 plot(llh);
 y = logitBinPred(model,X)+1;
 binPlot(model,X,y)
-%%
+%% Logistic logistic regression for multiclass classification
 clear
 k = 3;
 n = 1000;

chapter06/demo.m

@@ -1,74 +1,77 @@
+% demos for ch06
+
+
+%% Kernel regression with gaussian kernel
 clear; close all;
 n = 100;
 x = linspace(0,2*pi,n);   % test data
 t = sin(x)+rand(1,n)/2;
-
 model = knReg(x,t,1e-4,@knGauss);
 knRegPlot(model,x,t);
 
-%% kernel regression with linear kernel is linear regression
-% clear; close all;
-% n = 100;
-% x = linspace(0,2*pi,n);   % test data
-% t = sin(x)+rand(1,n)/2;
-% lambda = 1e-4;
-% model_kn = knReg(x,t,lambda,@knLin);
-% model_lin = linReg(x,t,lambda);
-% 
-% idx = 1:2:n;
-% xt = x(:,idx);
-% tt = t(idx);
-% 
-% [y_kn, sigma_kn,p_kn] = knRegPred(model_kn,xt,tt);
-% [y_lin, sigma_lin,p_lin] = linPred(model_lin,xt,tt);
-% 
-% maxabsdiff(y_kn,y_lin)
-% maxabsdiff(sigma_kn,sigma_lin)
-% maxabsdiff(p_kn,p_lin)
-%% kernel kmeans with linear kernel is kmeans
-% clear; close all;
-% d = 2;
-% k = 3;
-% n = 500;
-% [X,y] = kmeansRnd(d,k,n);
-% init = ceil(k*rand(1,n));
-% [y_kn,en_kn,model_kn] = knKmeans(X,init,@knLin);
-% [y_lin,en_lin,model_lin] = kmeans(X,init);
-% 
-% idx = 1:2:n;
-% Xt = X(:,idx);
-% 
-% [t_kn,ent_kn] = knKmeansPred(model_kn, Xt);
-% [t_lin,ent_lin] = kmeansPred(model_lin, Xt);
-% 
-% maxabsdiff(y_kn,y_lin)
-% maxabsdiff(en_kn,en_lin)
-% 
-% maxabsdiff(t_kn,t_lin)
-% maxabsdiff(ent_kn,ent_lin)
-%% kernel PCA with linear kernel is PCA
+%% Kernel regression with linear kernel is EQUIVALENT to linear regression
+lambda = 1e-4;
+model_kn = knReg(x,t,lambda,@knLin);
+model_lin = linReg(x,t,lambda);
+
+idx = 1:2:n;
+xt = x(:,idx);
+tt = t(idx);
+
+[y_kn, sigma_kn,p_kn] = knRegPred(model_kn,xt,tt);
+[y_lin, sigma_lin,p_lin] = linPred(model_lin,xt,tt);
+
+maxdiff(y_kn,y_lin)
+maxdiff(sigma_kn,sigma_lin)
+maxdiff(p_kn,p_lin)
+%% Kernel kmeans with linear kernel is EQUIVALENT to kmeans
+clear; close all;
+d = 2;
+k = 3;
+n = 500;
+[X,y] = kmeansRnd(d,k,n);
+init = ceil(k*rand(1,n));
+[y_kn,en_kn,model_kn] = knKmeans(X,init,@knLin);
+[y_lin,en_lin,model_lin] = kmeans(X,init);
+
+idx = 1:2:n;
+Xt = X(:,idx);
+
+[t_kn,ent_kn] = knKmeansPred(model_kn, Xt);
+[t_lin,ent_lin] = kmeansPred(model_lin, Xt);
+
+maxdiff(y_kn,y_lin)
+maxdiff(en_kn,en_lin)
+
+maxdiff(t_kn,t_lin)
+maxdiff(ent_kn,ent_lin)
+%% Kernel PCA with linear kernel is EQUIVALENT TO PCA
 clear; close all;
 d = 10;
-p = 2;
+q = 2;
 n = 500;
 X = randn(d,n);
 
-model_lin = pca(X,p);
-model_kn = knPca(X,p,@knLin);
 
+model_kn = knPca(X,q,@knLin);
 idx = 1:2:n;
 Xt = X(:,idx);
-Y_lin = pcaPred(model_lin,Xt);
+
 Y_kn = knPcaPred(model_kn,Xt);
 
-R = Y_lin/Y_kn    % the results are equivalent up to a rotation.
-
-%% test case for knCenter
-% clear; close all;
-% kn = @knGauss;
-% X=rand(2,100);
-% X1=rand(2,10);
-% X2=rand(2,5);
-% 
-% isequalf(knCenter(kn,X,X1),diag(knCenter(kn,X,X1,X1)))
-% isequalf(knCenter(kn,X),knCenter(kn,X,X,X));
+[U,L,mu,err1] = pca(X,q);
+Y_lin = U'*bsxfun(@minus,Xt,mu);   % projection
+
+
+R = Y_lin/Y_kn;    % the results are equivalent up to a rotation.
+maxdiff(R*R', eye(q))
+
+%% demo for knCenter
+clear; close all;
+kn = @knGauss;
+X=rand(2,100);
+X1=rand(2,10);
+X2=rand(2,5);
+
+maxdiff(knCenter(kn,X,X1),diag(knCenter(kn,X,X1,X1)))
+maxdiff(knCenter(kn,X),knCenter(kn,X,X,X))