ajout du TP3 - Lundi Fin TP

Semestre1/IML/TP/TP3/George.m

+X = load("george.dat");
+
+figure, plot(X(:,1), X(:,2), 'o', 'markersize', 8, 'markerfacecolor', 'r')
+hold on
+title('George','fontsize', 14)
+
+ltlX = mydownsampling(X, 10);
+M = distance(ltlX);
+
+%%
+
+method='complete'; 
+level_max = aggclust(M, method);
+
+figure
+dendro(level_max);
+title('Clustering avec distance max', 'fontsize', 24)
+
+K=2; % nombre de clusters voulus
+% recuperation des indices des points de chaque cluster
+N = size(ltlX, 1);
+clusters=level_max(N-K+1).cluster;
+
+% trace des clusters obtenus
+plotclusters(clusters, X, K);
+title('Clustering avec distance max', 'fontsize', 24)
\ No newline at end of file

Semestre1/IML/TP/TP3/George.m~

+X = load("george.dat");
+
+figure, plot(X(:,1), X(:,2), 'ro', 'markersize', 8, 'markerfacecolor', 'r')
+hold on
+title('George','fontsize', 14)
+
+ltlX = mydownsampling()
\ No newline at end of file

Semestre1/IML/TP/TP3/TP3.m

+%%% les données
+vmu1 = [0 0]';
+vmu2 = [3 3]';
+SIGMA = eye(2);
+
+n = 50; % nombre de points par classe
+
+% generation de donnees aleatoires suivant lois gaussiennes
+X1 =  mvnrnd(vmu1,SIGMA,n);   % classe 1
+X2 =  mvnrnd(vmu2,SIGMA,n);    % classe 2
+
+
+figure, plot(X1(:,1), X1(:,2), 'ro', 'markersize', 8, 'markerfacecolor', 'r')
+hold on
+plot(X2(:,1), X2(:,2), 'bv', 'markersize', 8, 'markerfacecolor', 'b')
+title('La vérité vraie','fontsize', 14)
+
+% on concatene les données (on suppose qu'on ne sait pas quel point est de la classe 1 ou 2
+% Dans la suite on ne travaillera qu'avec X1
+X = [X1; X2]; clear X1 X2
\ No newline at end of file

Semestre1/IML/TP/TP3/aggclust.m

+function level = aggclust(distance, method)
+% AGGCLUST Hierarchical (agglomerative) clustering
+%	Usage: level = aggclust(distance, method)
+%
+%	distance: 2D distance matrix of data points, with diagonal elements
+%		of "INF"
+%	method: "single" for single-linkage
+%		"complete" for complete-linkage
+%	level: data structure for a hierarchical clustering result
+%	level(i).distance: distance matrix at level i
+%	level(i).height: the minimum distance measure to form level i 
+%	level(i).merged: the two clusters (of level i-1) being merged to form
+%		level i 
+%	level(i).cluster{j}: a vector denotes the data points in j-th cluster
+%		of level i 
+%
+%	Type "aggclust" to see a demo of a hierarchical clustering
+%	cluster(single-linkage) of 50 random patterns of dimensionality 2.
+%
+%	See also DENDRO, LINKCLU.
+
+% Roger Jang, 981027
+
+if nargin == 0, selfdemo; return; end
+if nargin < 2, method = 'complete'; end
+
+data_n = size(distance, 1);
+level(1).distance = distance;
+level(1).height = 0;
+level(1).merged = [];
+for i = 1:data_n,
+	level(1).cluster{i} = [i];
+end
+
+for i = 2:data_n,
+	level(i) = merge(level(i-1), method);
+end
+
+% ====== Merge clusters
+function level_out = merge(level, method)
+% MERGE Merge a level of n clusters into n-1 clusters
+
+cluster_n = length(level.cluster);
+[min_i, min_j, min_value] = minxy(level.distance);
+% Reorder to have min_i < min_j
+if min_i > min_j,
+	temp = min_i;
+	min_i = min_j; 
+	min_j = temp;
+end
+
+level_out = level;
+
+% Update height
+level_out.height = min_value;
+
+% Update merged cluster
+level_out.merged = [min_i min_j];
+
+% Update cluster
+level_out.cluster{min_i} = [level_out.cluster{min_i} level_out.cluster{min_j}];
+level_out.cluster(min_j) = [];	% delete cluster{min_j}
+%keyboard
+% New distance matrix
+distance2 = level.distance;
+% "min" for single-linkage; "max" for complete-linkage
+if strcmp(method, 'single'),
+	distance2(:, min_i) = min(distance2(:, min_i), distance2(:, min_j)); 
+	distance2(min_i, :) = min(distance2(min_i, :), distance2(min_j, :)); 
+elseif strcmp(method, 'complete'),
+	distance2(:, min_i) = max(distance2(:, min_i), distance2(:, min_j)); 
+	distance2(min_i, :) = max(distance2(min_i, :), distance2(min_j, :)); 
+else
+	error('Unsupported method in AGGCLUST!');
+end
+
+distance2(min_j, :) = [];
+distance2(:, min_j) = [];
+distance2(min_i, min_i) = inf;
+
+level_out.distance = distance2;
+
+% ====== Find the minimum value in a matrix
+function [i, j, min_value] = minxy(A)
+[value_row, index_row] = min(A);
+[min_value, j] = min(value_row);
+i = index_row(j);
+
+% ====== Self demo ======
+function selfdemo
+data_n = 50;
+dimension = 2;
+points = rand(data_n, dimension);
+for i = 1:data_n,
+	for j = 1:data_n,
+		distance(i, j) = norm(points(i,:)-points(j,:));
+	end
+end
+
+% Diagonal elements should always be inf.
+for i = 1:data_n, distance(i, i) = inf; end
+
+level = aggclust(distance);
+
+% Plot heights w.r.t. levels
+figure;
+plot([level.height], 'r:o');
+xlabel('Level');
+ylabel('Height');
+title('Height vs. level');
+
+% Plot the dendrogram
+figure;
+dendro(level);
+
+% View the formation of clusters
+figure;
+linkclu(points, distance, level);

Semestre1/IML/TP/TP3/dendro.m

+function dendro(level)
+% DENDRO Dendrogrma plot for the result from hierarchical clustering.
+%
+%	Usage: dendro(level)
+%	level: the hierarchical clustering output from AGGCLUST
+%
+%	Type "dendro" to see a demo of a hierarchical clustering
+%	(single-linkage) of 50 random patterns of dimensionality 2.
+%
+%	See also AGGCLUST, HCLUSTDM.
+
+%	Roger Jang, 981027
+
+if nargin == 0, selfdemo; return, end
+
+set(gca, 'xticklabel', []);
+xticklabel = level(end).cluster{1};
+data_n = length(level);
+axis([1, data_n, 0, level(end).height]); 
+xlabel('Data index');
+ylabel('Distance');
+title('Dendrogram');
+for i=1:data_n,
+	h = text(i, 0, num2str(level(end).cluster{1}(i)));
+	set(h, 'rot', 90, 'fontsize', 8, 'hori', 'right');
+end
+
+% Generate necessary information for plotting dendrogram
+% cap_center is the leg position for future cluster
+cap_center(xticklabel) = 1:data_n;
+levelinfo(1).cap_center = cap_center; 
+% cap_height is the height for each cap
+levelinfo(1).cap_height = zeros(1, data_n);
+for i = 2:data_n,
+	m = level(i).merged(1);
+	n = level(i).merged(2);
+	% Find cap_center
+	levelinfo(i).cap_center = levelinfo(i-1).cap_center;
+	levelinfo(i).cap_center(m) = ...
+		(levelinfo(i).cap_center(m)+levelinfo(i).cap_center(n))/2; 
+	levelinfo(i).cap_center(n) = [];
+	% Find cap_height
+	levelinfo(i).cap_height = levelinfo(i-1).cap_height;
+	levelinfo(i).cap_height(m) = level(i).height;
+	levelinfo(i).cap_height(n) = [];
+end
+
+% Plot caps for the dendrogram
+center = 1:data_n;	% center for each cluster
+for i = 2:data_n,
+	height = level(i).height;
+	m = level(i).merged(1);
+	n = level(i).merged(2);
+	cluster1 = level(i-1).cluster{m};
+	cluster2 = level(i-1).cluster{n};
+	left_point = cluster1(end);
+	right_point = cluster2(1);
+	left = find(xticklabel==left_point);
+	right = find(xticklabel==right_point);
+
+	left_x = levelinfo(i-1).cap_center(m);
+	left_y = levelinfo(i-1).cap_height(m);
+	right_x = levelinfo(i-1).cap_center(n);
+	right_y = levelinfo(i-1).cap_height(n);
+	line([left_x left_x], [left_y, height]);
+	line([right_x right_x], [right_y, height]);
+	line([left_x right_x], [height, height]);
+end
+
+% Plot level lines for the dendrogram
+%for i = 1:data_n,
+%	line([1 data_n], [level(i).height level(i).height], ...
+%		'color', 'c', 'linestyle', ':');
+%end
+
+% ====== Self demo ======
+function selfdemo
+data_n = 50;
+dimension = 2;
+points = rand(data_n, dimension);
+% Compute the distance matrix
+for i = 1:data_n,
+	for j = 1:data_n,
+		distance(i, j) = norm(points(i,:)-points(j,:));
+	end
+end
+% Diagonal elements should always be inf.
+for i = 1:data_n, distance(i, i) = inf; end
+
+level = aggclust(distance);
+
+% Plot the dendrogram
+figure;
+dendro(level);
+fprintf('The figure is a dendrogram (single-linkage) of 50 random points in 2D\n');

Semestre1/IML/TP/TP3/distance.m

+function M = distance(X)
+
+% Calcul de la matrice de Distance pour l'algo CHA
+N = size(X,1);
+M = X*X';
+ps = diag(M);
+M = ps*ones(1,N)+ones(N,1)*ps' - 2*M;
+% mettre d(x_i, x_i) = infini
+for i=1:N 
+    M(i,i) = inf; 
+end
\ No newline at end of file

Semestre1/IML/TP/TP3/kmoyennes.m

+function [C,clusters,JWiter] = kmoyennes(X,K,Co)
+    C = Co;
+    MaxIter = 15;
+    JWiter = zeros(MaxIter,1);
+    iter = 1;
+    
+    while (iter <= MaxIter)
+        [clusters, Jw] = affectation(X,C,K);
+        JWiter(iter) = Jw;
+        C = nouveaux_centres(X,clusters);
+    end
+    
+end

Semestre1/IML/TP/TP3/mydownsampling.m

+
+function datalight = mydownsampling(data, step)
+
+[ndata, dim] = size(data);
+assert(step >=1, 'the downsampling step should be greater than 1')
+
+Nlight = ceil(ndata/step);
+datalight = zeros(Nlight, dim);
+ind = randperm(ndata);
+for i=1:Nlight
+    datalight(i,:) = data(ind(i), :);
+end
\ No newline at end of file

Semestre1/IML/TP/TP3/plotclusters.m

+
+function eff_clusters = plotclusters(clusters, X, K)
+
+% cluster : rsultat de clustering
+% X : donnees
+% K nombre de clusters voulus
+
+d = size(X, 2);
+if d ~=2
+    error('Affichage disponible uniquement en 2D')
+end
+
+couleur = 'rbgmckyrbg';
+symbole = 'ovpsh>xd<+';
+
+eff_clusters = zeros(K,1);
+
+figure;
+
+for i=1:K
+    if iscell(clusters)
+        ii=clusters{i};
+    else
+        ii = find(clusters==i);
+    end
+    eff_clusters(i) = length(ii);
+    
+    plot(X(ii,1), X(ii,2), [couleur(i), symbole(i)], 'markersize', 8, 'markerfacecolor', couleur(i));
+    %plot(X(ii,1), X(ii,2), [couleur(i), symbole(i)], 'markersize', 8);
+    hold on ;
+end;
+
+title('Rsultat clustering','fontsize', 14)
\ No newline at end of file

Semestre1/IML/TP/TP3/scriptcha_etud.m

+% ========================================================
+% Utilisation de AGGCLUST
+% ========================================================
+
+close all;
+clear all;
+clc
+
+%%% les donnees
+vmu1 = [0 0]';
+vmu2 = [3 3]';
+SIGMA = eye(2);
+
+n = 50; % nombre de points par cluster
+
+% generation de donnees aleatoires suivant lois gaussiennes
+X1 =  mvnrnd(vmu1,SIGMA,n);   % classe 1
+X2 =  mvnrnd(vmu2,SIGMA,n);    % classe 2
+
+figure, plot(X1(:,1), X1(:,2), 'ro', 'markersize', 8, 'markerfacecolor', 'r')
+hold on
+plot(X2(:,1), X2(:,2), 'bv', 'markersize', 8, 'markerfacecolor', 'b')
+title('La verite vraie','fontsize', 14)
+
+% on concatene les donnees (on suppose qu'on ne sait pas quel 
+% point est du cluster 1 ou 2
+X = [X1; X2];
+
+% Calcul de la matrice de distance
+M = distance(X);
+
+
+%% ========== CHA ===========
+% -------- ultra-metrique : diametre maximal -------
+method='complete'; 
+level_max = aggclust(M, method);
+
+% Affichage du dendogramme 
+figure
+dendro(level_max);
+title('Clustering avec distance max', 'fontsize', 24)
+
+K=3; % nombre de clusters voulus
+% recuperation des indices des points de chaque cluster
+N = size(X, 1);
+clusters=level_max(N-K+1).cluster;
+
+% trace des clusters obtenus
+plotclusters(clusters, X, K);
+title('Clustering avec distance max', 'fontsize', 24)
+
+% ------- ultra-metrique : diametre min -------
+method='single'; % saut minimal
+level_min = aggclust(M, method);
+
+
+% Affichage du dendogramme 
+figure
+dendro(level_min);
+title('Clustering avec distance mix', 'fontsize', 24)
+
+% recuperation des indices des points de chaque cluster
+N = size(X, 1);
+clusters=level_min(N-K+1).cluster;
+
+% trace des clusters obtenus
+plotclusters(clusters, X, K);
+title('Clustering avec distance min', 'fontsize', 24)
+