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with_cent_passed_noise.m
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% 0.0819 0.0726 0.0846 0.0765
% 0.0921 0.0800 0.1101 0.1191
% 0.0693 0.0904 0.0289 0.0141
%fetching data from file to matrix
% data_org=csvread('./Data/rand_square.csv');
% data_org(:,[1,2]) = [];
a = 0.2;
b = 0.4;
x1 = (b -a)*rand(150,1) + a;
a = 0.6;
b = 0.8;
x2 = (b -a)*rand(150,1) + a;
a = 0.4;
b = 0.6;
y1 = (b - a)*rand(150,1) + a;
x = [x1;x2];
y = [y1;y1];
noise_x = rand(30,1);
a = 0.1;
b = 0.3;
noise_y1 = (b -a)*rand(15,1) + a;
a = 0.7;
b = 0.9;
noise_y2 = (b -a)*rand(15,1) + a;
noise_y = [noise_y1;noise_y2];
x = [x;noise_x];
y = [y;noise_y];
data_org = [x y];
% data_org=normc(data_org);
% data_org = ( data_org-min(data_org) ) ./ ( max(data_org) - min(data_org) );
% plot(data_org([1:9],1),data_org([1:9],2),'ob');
% xlim([-5 5]);
% ylim([-5 5]);
% hold on;
% plot(data_org([10:end],1),data_org([10:end],2),'or');
% xlim([-5 5]);
% ylim([-5 5]);
% hold on;
% plot(data_org([101:150],1),data_org([101:150],2),'og');
% hold on;
scatter(x1,y1,20,'k');
xlim([0 1]);
ylim([0 1]);
hold on;
scatter(x2,y1,20,'k');
scatter(noise_x,noise_y,10,'k','d');
% scatter(data_org([51:100],1),data_org([51:100],2),25,'k');
% scatter(data_org([101:150],1),data_org([101:150],2),25,'k');
% No. of clusters(c)
c = 2;
eps = 10^(-5);
V_old = zeros(c,size(data_org,2));
V_new = [0.1 0.2;0.7 0.2];
% V_new = rand(c,size(data_org,2));
Vl = zeros(c,size(data_org,2));
Vr = zeros(c,size(data_org,2));
u_l = zeros(c,size(data_org,1));
u_r = zeros(c,size(data_org,1));
itr = 0;
%m,m1 and m2 values
m1=1.1;
m2=10;
% m=(m1+m2)/2;
%center path
c1 = [];
c2 = [];
% c3 = [];
c1 = [c1;V_new(1,:)];
c2 = [c2;V_new(2,:)];
% c3 = [c3;V_new(3,:)];
h_m1_m2_idx = zeros(c,size(data_org,1));
l_m1_m2_idx = zeros(c,size(data_org,1));
while(1)
itr = itr + 1;
old_diff = norm(V_new - V_old);
V_old = V_new;
% plot(V_new(1,1),V_new(1,2),'sb','MarkerSize',5,'LineWidth',3);
% plot(V_new(2,1),V_new(2,2),'sr','MarkerSize',5,'LineWidth',3);
% plot(V_new(3,1),V_new(3,2),'sg','MarkerSize',5,'LineWidth',3);
% plot(V_new(1,1),V_new(1,2),'MarkerSize',5,'LineWidth',1);
% plot(V_new(2,1),V_new(2,2),'MarkerSize',5,'LineWidth',1);
% plot(V_new(3,1),V_new(3,2),'MarkerSize',5,'LineWidth',1);
% step ------> 1
% Estimating FCM membership using m1
[U_m1,~] = cal_U(data_org,V_old,m1,c);
% Estimating FCM membership using m2
[U_m2,~] = cal_U(data_org,V_old,m2,c);
% step ------> 2
%Determine Upper and lower membership using U_m1 and U_m2
for i=1:c
for j=1:length(data_org)
if( U_m1(i,j) > U_m2(i,j) )
Uh(i,j) = U_m1(i,j);
Ul(i,j) = U_m2(i,j);
h_m1_m2_idx(i,j) = m1;
l_m1_m2_idx(i,j) = m2;
else
Ul(i,j) = U_m1(i,j);
Uh(i,j) = U_m2(i,j);
h_m1_m2_idx (i,j) = m2;
l_m1_m2_idx(i,j) = m1;
end
end
end
% U = (Uh + Ul) / 2;
% step ------> 3
%Type reduction and Defuzzification using KM algorithm
for j=1:c
temp_l = zeros(1,size(data_org,1));
temp_r = zeros(1,size(data_org,1));
for d=1:size(data_org,2)
[V_new(j,d),Vl(j,d),Vr(j,d),u_left,u_right] = KM_withchange(data_org(:,d)',Ul(j,:),Uh(j,:),h_m1_m2_idx(j,:),l_m1_m2_idx(j,:));
temp_l = temp_l + u_left;
temp_r = temp_r + u_right;
end
u_l(j,:) = temp_l ./ size(data_org,2);
u_r(j,:) = temp_r ./ size(data_org,2);
end
c1 = [c1;V_new(1,:)];
c2 = [c2;V_new(2,:)];
% c3 = [c3;V_new(3,:)];
% flag1 = [1;2;3];
% gscatter(V_new(:,1),V_new(:,2),flag1,['y' 'y' 'y']);
%
%
% plot(V_new(3,1),V_new(3,2),'xg','MarkerSize',15,'LineWidth',3);
% disp(V_new);
new_diff = norm(V_new - V_old);
disp(norm(V_new - V_old));
% step ------> 4
if( new_diff > old_diff || itr>100 || new_diff < eps )
break;
end
end
fprintf("Final centers are:");
disp(V_new);
% disp(u_l);
% disp(u_r);
u = (u_l + u_r) ./ 2;
% hard_partition(data_org,u);
% plot(V_new(1,1),V_new(1,2),'xb','MarkerSize',10,'LineWidth',3);
% plot(V_new(2,1),V_new(2,2),'xr','MarkerSize',10,'LineWidth',3);
% plot(V_new(1,1),V_new(1,2),'sb','MarkerSize',5,'LineWidth',3);
% plot(V_new(2,1),V_new(2,2),'sr','MarkerSize',5,'LineWidth',3);
% plot(V_new(3,1),V_new(3,2),'sg','MarkerSize',5,'LineWidth',3);
% flag1 = [1;2;3];
% gscatter(V_new(:,1),V_new(:,2),flag1,['y' 'y' 'y']);
% for i=1:length(c1)
% plot(c1(1,1),c1(1,2),'sb','MarkerSize',5,'LineWidth',3);
plot(c1(:,1),c1(:,2),'r+-');
plot(c1(end,1),c1(end,2),'xr','MarkerSize',5,'LineWidth',1);
% plot(c2(1,1),c2(1,2),'sb','MarkerSize',5,'LineWidth',3);
plot(c2(:,1),c2(:,2),'r+-');
plot(c2(end,1),c2(end,2),'xr','MarkerSize',5,'LineWidth',1);
% plot(c3(1,1),c3(1,2),'sb','MarkerSize',5,'LineWidth',3);
% plot(c3(:,1),c3(:,2),'r+-');
% plot(c3(end,1),c3(end,2),'xr','MarkerSize',5,'LineWidth',1);
% hold off;
function [U,dist] = cal_U(X,V,m,c)
dist = zeros(length(X),c);
U = zeros(c,length(X));
% Calculating distance of jth point from ith center
for i=1:c
for j=1:length(X)
dist(j,i) = norm( X(j,:) - V(i,:) );
end
end
% Calclulating uij
for i=1:c
for j=1:length(X)
if( dist(j,i) == 0 )
U(i,j) = 1;
continue;
end
temp = 0;
done = 0;
for k=1:c
if( dist(j,k) == 0 )
U(i,j) = 0;
done = 1;
break;
end
temp = temp + ( dist( j,i) / dist(j,k) )^ (2 /(m-1));
end
if ( ~done == 1 )
U(i,j) = 1/temp;
end
end
end
end
function [] = hard_partition(X,u)
cent_test = zeros(length(X),1);
count = 0;
for i=1:length(X)
[~,cent_test(i)] = max(u(:,i));
end
check1 = cent_test([1:50],1);
count = count + length(find(check1 == mode(check1)));
check2 = cent_test([51:100],1);
temp1 = check2(check2 == mode(check2));
temp2 = temp1(temp1 ~= mode(check1));
count = count + length(temp2);
check3 = cent_test([101:150],1);
temp1 = check3(check3 == mode(check3));
temp2 = temp1(temp1 ~= mode(check2));
temp3 = temp2(temp2 ~= mode(check1));
count = count + length(temp3);
fprintf('Performance of algorithm is %f',count/length(X)*100);
end