gmmROKI

%% Load data
clc;
clearvars;
close all;
load('dataGMM.mat');
%% Preprocess data
m = size(Data,2);
n = size(Data,1);
PIfunc = @(idx, c) length(idx(idx==c))/length(idx);
% meanfunc = @(x,n,theta) 1;
covfunc = @(x,mean) ((x-mean')*(x-mean')')/(length(x)-1);
covfuncMATLAB = @(x,mean) cov((x-mean')');
GaussDist = @(x,meanfunc,covfunc) 1;
loglklhd = @(PI,Mu,SIGMA) 1;

% plot data
X = Data;
figure(1);
plot(X(1,:),X(2,:),'k*','MarkerSize',5); hold on;
title 'Data';
xlabel 'X1';
ylabel 'X2';
K = 4; % num of clusters
%% Init parameters
[idx, MU] = kmeans(X', K);
% calc PI
PI =  zeros(K,1);
for c=1:K
    PI(c) = PIfunc(idx,c);
end
SIGMA = zeros(2,2,4);
for i=1:K
%     SIGMA(:,:,i) = covfuncMATLAB(X(idx==i),MU(i,:))
    SIGMA(:,:,i) = cov((X(:,idx==i))');
end

%%
%Evaluate the pdf of the normal distribution at the grid points.
for k=1:K
    mu = MU(k,:);
    sigma = SIGMA(:,:,k);
    % Create a grid of 100x100 evenly spaced points in two-dimensional space.
    dim_grid = 100;
    x1 = linspace(-0.1,0.1,dim_grid);
    x2 = linspace(-0.1,0.1,dim_grid);
    [X1,X2] = meshgrid(x1',x2'); % grid 100x100
    X = [X1(:) X2(:)];
    % Evaluate the cdf of the normal distribution at the grid points.
    p = PI(k)*mvnpdf(X,mu,sigma);
    % Plot the cdf values.
    Z = reshape(p,dim_grid,dim_grid);
    figure(2);
    surf(X1,X2,Z);
    caxis([min(Z(:))-0.5*range(Z(:)),max(Z(:))]); hold on;
    scatter(mu(1), mu(2),50,'r'); hold on;
end
view(0,90);
xlabel('x1')
ylabel('x2')
zlabel('Probability Density');