refined doc for ch09

chapter07/rvmBinFp.m

@@ -1,6 +1,13 @@
 function [model, llh] = rvmBinFp(X, t, alpha)
-% Relevance Vector Machine (ARD sparse prior) for binary classification
-% training by empirical bayesian (type II ML) using fix point update (Mackay update)
+% Relevance Vector Machine (ARD sparse prior) for binary classification.
+% trained by empirical bayesian (type II ML) using Mackay fix point update.
+% Input:
+%   X: d x n data matrix
+%   t: 1 x n label (0/1)
+%   alpha: prior parameter
+% Output:
+%   model: trained model structure
+%   llh: loglikelihood
 % Written by Mo Chen ([email protected]).
 if nargin < 3
     alpha = 1;

chapter09/demo.m

@@ -1,70 +1,70 @@
+% demos for ch09
 
+%% Empirical Bayesian linear regression via EM
+close all; clear;
+d = 5;
+n = 200;
+[x,t] = linRnd(d,n);
+[model,llh] = linRegEm(x,t);
+plot(llh);
 
-%% demo: EM linear regression
-% close all; clear;
-% d = 5;
-% n = 200;
-% [x,t] = linRnd(d,n);
-% [model,llh] = linRegEm(x,t);
-% plot(llh);
+%% RVM classification via EM
+clear; close all
+k = 2;
+d = 2;
+n = 1000;
+[X,t] = kmeansRnd(d,k,n);
+[x1,x2] = meshgrid(linspace(min(X(1,:)),max(X(1,:)),n), linspace(min(X(2,:)),max(X(2,:)),n));
 
-%% classification
-% clear; close all
-% k = 2;
-% d = 2;
-% n = 1000;
-% [X,t] = kmeansRnd(d,k,n);
-% [x1,x2] = meshgrid(linspace(min(X(1,:)),max(X(1,:)),n), linspace(min(X(2,:)),max(X(2,:)),n));
-% 
-% [model, llh] = rvmBinEm(X,t-1);
-% plot(llh);
-% y = rvmBinPred(model,X)+1;
-% figure;
-% binPlot(model,X,y);
-%% demo: kmeans 
-% close all; clear;
-% d = 2;
-% k = 3;
-% n = 500;
-% [X,label] = kmeansRnd(d,k,n);
-% y = kmeans(X,k);
-% plotClass(X,label);
-% figure;
-% plotClass(X,y);
+[model, llh] = rvmBinEm(X,t-1);
+plot(llh);
+y = rvmBinPred(model,X)+1;
+figure;
+binPlot(model,X,y);
+%% kmeans 
+close all; clear;
+d = 2;
+k = 3;
+n = 500;
+[X,label] = kmeansRnd(d,k,n);
+y = kmeans(X,k);
+plotClass(X,label);
+figure;
+plotClass(X,y);
 
-%% demo: Em for Gauss Mixture 
-% close all; clear;
-% d = 2;
-% k = 3;
-% n = 1000;
-% [X,label] = mixGaussRnd(d,k,n);
-% plotClass(X,label);
-% 
-% m = floor(n/2);
-% X1 = X(:,1:m);
-% X2 = X(:,(m+1):end);
-% % train
-% [z1,model,llh] = mixGaussEm(X1,k);
-% figure;
-% plot(llh);
-% figure;
-% plotClass(X1,z1);
-% % predict
-% z2 = mixGaussPred(X2,model);
-% figure;
-% plotClass(X2,z2);
-%% demo: Em for Gauss mixture initialized with kmeans;
-% close all; clear;
-% d = 2;
-% k = 3;
-% n = 500;
-% [X,label] = mixGaussRnd(d,k,n);
-% init = kmeans(X,k);
-% [z,model,llh] = mixGaussEm(X,init);
-% plotClass(X,label);
-% figure;
-% plotClass(X,init);
-% figure;
-% plotClass(X,z);
-% figure;
-% plot(llh);
+%% Gausssian Mixture via EM
+close all; clear;
+d = 2;
+k = 3;
+n = 1000;
+[X,label] = mixGaussRnd(d,k,n);
+plotClass(X,label);
+
+m = floor(n/2);
+X1 = X(:,1:m);
+X2 = X(:,(m+1):end);
+% train
+[z1,model,llh] = mixGaussEm(X1,k);
+figure;
+plot(llh);
+figure;
+plotClass(X1,z1);
+% predict
+z2 = mixGaussPred(X2,model);
+figure;
+plotClass(X2,z2);
+%% Gauss mixture initialized by kmeans
+close all; clear;
+d = 2;
+k = 3;
+n = 500;
+[X,label] = mixGaussRnd(d,k,n);
+init = kmeans(X,k);
+[z,model,llh] = mixGaussEm(X,init);
+plotClass(X,label);
+figure;
+plotClass(X,init);
+figure;
+plotClass(X,z);
+figure;
+plot(llh);

chapter09/kmeans.m

@@ -1,7 +1,12 @@
 function [label, energy, model] = kmeans(X, init)
-%  Perform k-means clustering.
+% Perform k-means clustering.
+% Input:
 %   X: d x n data matrix
-%   k: number of seeds
+%   init: k number of clusters or label (1 x n vector)
+% Output:
+%   label: 1 x n cluster label
+%   energy: optimization target value
+%   model: trained model structure
 % Written by Mo Chen ([email protected]).
 n = size(X,2);
 if numel(init)==1

chapter09/kmeansPred.m

@@ -1,7 +1,11 @@
 function [label, energy] = kmeansPred(model, Xt)
 % Prediction for kmeans clusterng
+% Input:
 %   model: trained model structure
 %   Xt: d x n testing data
+% Output:
+%   label: 1 x n cluster label
+%   energy: optimization target value
 % Written by Mo Chen ([email protected]).
 [val,label] = min(sqdist(model.means, Xt));
 energy = sum(val);

chapter09/kmeansRnd.m

@@ -1,6 +1,14 @@
 function [X, z, center] = kmeansRnd(d, k, n)
-% Sampling from a Gaussian mixture distribution with common variances (kmeans model).
-% Written by Michael Chen ([email protected]).
+% Generate samples from a Gaussian mixture distribution with common variances (kmeans model).
+% Input:
+%   d: dimension of data
+%   k: number of components
+%   n: number of data
+% Output:
+%   X: d x n data matrix
+%   z: 1 x n response variable
+%   center: d x k centers of clusters
+% Written by Mo Chen ([email protected]).
 alpha = 1;
 beta = nthroot(k,d); % in volume x^d there is k points: x^d=k
 

chapter09/linRegEm.m

@@ -4,7 +4,7 @@
 %   X: d x n data
 %   t: 1 x n response
 %   alpha: prior parameter
-%   beta? prior parameter
+%   beta: prior parameter
 % Output:
 %   model: trained model structure
 %   llh: loglikelihood

chapter09/mixBernEm.m

@@ -1,7 +1,12 @@
 function [label, model, llh] = mixBernEm(X, k)
 % Perform EM algorithm for fitting the Bernoulli mixture model.
+% Input: 
 %   X: d x n data matrix
-%   init: k (1 x 1) or label (1 x n, 1<=label(i)<=k) or center (d x k)
+%   k: number of cluster (1 x 1) or label (1 x n, 1<=label(i)<=k) or model structure
+% Output:
+%   label: 1 x n cluster label
+%   model: trained model structure
+%   llh: loglikelihood
 % Written by Mo Chen ([email protected]).
 %% initialization
 fprintf('EM for mixture model: running ... \n');

chapter09/mixGaussEm.m

@@ -2,7 +2,7 @@
 % Perform EM algorithm for fitting the Gaussian mixture model.
 % Input: 
 %   X: d x n data matrix
-%   init: k (1 x 1) or label (1 x n, 1<=label(i)<=k) or model structure
+%   init: k (1 x 1) number of components or label (1 x n, 1<=label(i)<=k) or model structure
 % Output:
 %   label: 1 x n cluster label
 %   model: trained model structure

chapter09/mixGaussPred.m

@@ -1,7 +1,11 @@
 function [label, R] = mixGaussPred(X, model)
 % Predict label and responsibility for Gaussian mixture model.
+% Input:
 %   X: d x n data matrix
 %   model: trained model structure outputed by the EM algirthm
+% Output:
+%   label: 1 x n cluster label
+%   R: k x n responsibility
 % Written by Mo Chen ([email protected]).
 mu = model.mu;
 Sigma = model.Sigma;

chapter09/mixGaussRnd.m

@@ -1,6 +1,14 @@
 function [X, z, model] = mixGaussRnd(d, k, n)
 % Sampling form a Gaussian mixture distribution.
-% Written by Michael Chen ([email protected]).
+% Input:
+%   d: dimension of data
+%   k: number of components
+%   n: number of data
+% Output:
+%   X: d x n data matrix
+%   z: 1 x n response variable
+%   model: model structure
+% Written by Mo Chen ([email protected]).
 alpha0 = 1;  % hyperparameter of Dirichlet prior
 W0 = eye(d);  % hyperparameter of inverse Wishart prior of covariances
 v0 = d+1;  % hyperparameter of inverse Wishart prior of covariances

chapter09/mixMnEm.m

@@ -1,7 +1,12 @@
 function [label, model, llh] = mixMnEm(X, k)
 % Perform EM algorithm for fitting the multinomial mixture model.
+% Input: 
 %   X: d x n data matrix
-%   init: k (1 x 1) or label (1 x n, 1<=label(i)<=k) or center (d x k)
+%   k: number of cluster (1 x 1) or label (1 x n, 1<=label(i)<=k) or model structure
+% Output:
+%   label: 1 x n cluster label
+%   model: trained model structure
+%   llh: loglikelihood
 % Written by Mo Chen ([email protected]).
 %% initialization
 fprintf('EM for mixture model: running ... \n');

chapter09/rvmBinEm.m

@@ -1,6 +1,13 @@
 function [model, llh] = rvmBinEm(X, t, alpha)
-% Relevance Vector Machine (ARD sparse prior) for binary classification
-% training by empirical bayesian (type II ML) using fix point update (Mackay update)
+% Relevance Vector Machine (ARD sparse prior) for binary classification.
+% trained by empirical bayesian (type II ML) using EM.
+% Input:
+%   X: d x n data matrix
+%   t: 1 x n label (0/1)
+%   alpha: prior parameter
+% Output:
+%   model: trained model structure
+%   llh: loglikelihood
 % Written by Mo Chen ([email protected]).
 if nargin < 3
     alpha = 1;

chapter09/rvmRegEm.m

@@ -1,6 +1,14 @@
 function [model, llh] = rvmRegEm(X, t, alpha, beta)
 % Relevance Vector Machine (ARD sparse prior) for regression
-% training by empirical bayesian (type II ML) using standard EM update 
+% trained by empirical bayesian (type II ML) using EM
+% Input:
+%   X: d x n data
+%   t: 1 x n response
+%   alpha: prior parameter
+%   beta: prior parameter
+% Output:
+%   model: trained model structure
+%   llh: loglikelihood
 % Written by Mo Chen ([email protected]).
 if nargin < 3
     alpha = 0.02;

chapter14/mixLinRnd.m

@@ -9,7 +9,6 @@
 %   y: 1 x n response variable
 %   W: d+1 x k weight matrix 
 % Written by Mo Chen ([email protected]).
-% Written by Mo Chen ([email protected]).
 W = randn(d+1,k);
 [X, z] = kmeansRnd(d, k, n);
 y = zeros(1,n);