├── Fair_SC_normalized.m
├── Fair_SC_unnormalized.m
├── README.md
├── SC_normalized.m
├── SC_unnormalized.m
├── clustering_accuracy.m
├── experiments_Figure2_Row1.m
├── experiments_Figure2_Row2.m
├── experiments_Figure3.m
├── experiments_Figure4.m
└── generate_adja_SB_model.m


/Fair_SC_normalized.m:
--------------------------------------------------------------------------------
 1 | function clusterLabels = Fair_SC_normalized(adj,k,sensitive)
 2 | %implementation of fair normalized SC as stated in Alg. 3 
 3 | %
 4 | %INPUT:
 5 | %adj ... (weighted) adjacency matrix of size n x n
 6 | %k ... number of clusters
 7 | %sensitive ... vector of length n encoding the sensitive attribute 
 8 | %
 9 | %OUTPUT:
10 | %clusterLabels ... vector of length n comprising the cluster label for each
11 | %                  data point
12 | 
13 | 
14 | n = size(adj, 1);
15 | 
16 | % converting sensitive to a vector with entries in [h] and building F %%%
17 | sens_unique=unique(sensitive);
18 | h = length(sens_unique);
19 | sens_unique=reshape(sens_unique,[1,h]);
20 | 
21 | sensitiveNEW=sensitive;
22 | 
23 | temp=1;
24 | for ell=sens_unique
25 |     sensitiveNEW(sensitive==ell)=temp;
26 |     temp=temp+1;
27 | end
28 |     
29 | F=zeros(n,h-1);
30 | 
31 | for ell=1:(h-1)
32 |     temp=(sensitiveNEW == ell);
33 |     F(temp,ell)=1; 
34 |     groupSize = sum(temp);
35 |     F(:,ell) = F(:,ell)-groupSize/n;
36 | end
37 | %%%%
38 | 
39 | 
40 | 
41 | degrees = sum(adj, 1);
42 | D = diag(degrees);
43 | L = D-adj;
44 | 
45 | Z = null(F');
46 | Q=sqrtm(Z'*D*Z);
47 | Qinv=inv(Q);
48 | 
49 | 
50 | Msymm=Qinv'*Z'*L*Z*Qinv;
51 | Msymm=(Msymm+Msymm')/2;
52 | 
53 | try
54 |     [Y, eigValues] = eigs(Msymm,k,'smallestabs','MaxIterations',500,'SubspaceDimension',min(size(Msymm,1),max(2*k,25)));
55 | catch
56 |     [Y, eigValues] = eigs(Msymm,k,'smallestreal','MaxIterations',1000,'SubspaceDimension',min(size(Msymm,1),max(2*k,25)));
57 | end
58 | 
59 | H = Z*Qinv*Y;
60 | 
61 | clusterLabels = kmeans(H,k,'Replicates',10);
62 | end
63 | 
64 | 


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/Fair_SC_unnormalized.m:
--------------------------------------------------------------------------------
 1 | function clusterLabels = Fair_SC_unnormalized(adj,k,sensitive)
 2 | %implementation of fair unnormalized SC as stated in Alg. 2 
 3 | %
 4 | %INPUT:
 5 | %adj ... (weighted) adjacency matrix of size n x n
 6 | %k ... number of clusters
 7 | %sensitive ... vector of length n encoding the sensitive attribute 
 8 | %
 9 | %OUTPUT:
10 | %clusterLabels ... vector of length n comprising the cluster label for each
11 | %                  data point
12 | 
13 | 
14 | n = size(adj, 1);
15 | 
16 | % converting sensitive to a vector with entries in [h] and building F %%%
17 | sens_unique=unique(sensitive);
18 | h = length(sens_unique);
19 | sens_unique=reshape(sens_unique,[1,h]);
20 | 
21 | sensitiveNEW=sensitive;
22 | 
23 | temp=1;
24 | for ell=sens_unique
25 |     sensitiveNEW(sensitive==ell)=temp;
26 |     temp=temp+1;
27 | end
28 |     
29 | F=zeros(n,h-1);
30 | 
31 | for ell=1:(h-1)
32 |     temp=(sensitiveNEW == ell);
33 |     F(temp,ell)=1; 
34 |     groupSize = sum(temp);
35 |     F(:,ell) = F(:,ell)-groupSize/n;
36 | end
37 | %%%%
38 | 
39 | 
40 | 
41 | degrees = sum(adj, 1);
42 | D = diag(degrees);
43 | L = D-adj;
44 | 
45 | Z = null(F');
46 | 
47 | Msymm=Z'*L*Z;
48 | Msymm=(Msymm+Msymm')/2;
49 | 
50 | try
51 |     [Y, eigValues] = eigs(Msymm,k,'smallestabs','MaxIterations',500,'SubspaceDimension',min(size(Msymm,1),max(2*k,25)));
52 | catch
53 |     [Y, eigValues] = eigs(Msymm,k,'smallestreal','MaxIterations',1000,'SubspaceDimension',min(size(Msymm,1),max(2*k,25)));
54 | end
55 | 
56 | H = Z*Y;
57 | 
58 | clusterLabels = kmeans(H,k,'Replicates',10);
59 | end
60 | 
61 | 


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/README.md:
--------------------------------------------------------------------------------
1 | # fair_spectral_clustering
2 | 
3 | MATLAB code for our paper "Guarantees for Spectral Clustering with Fairness Constraints" (https://arxiv.org/abs/1901.08668).
4 | 
5 | To reproduce the experiments shown in Figures 2 to 4, simply run *experiments_Figure2_Row1.m*, *experiments_Figure2_Row2.m*, *experiments_Figure3.m* or *experiments_Figure4.m*. In the first line of the scripts, one can set the number of runs over which to average the results.
6 | 
7 | The code has been tested in MATLAB R2017b.
8 | 


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/SC_normalized.m:
--------------------------------------------------------------------------------
 1 | function clusterLabels = SC_normalized(adj,k)
 2 | %implementation of normalized SC as described in Appendix A 
 3 | %
 4 | %INPUT:
 5 | %adj ... (weighted) adjacency matrix of size n x n
 6 | %k ... number of clusters
 7 | %
 8 | %OUTPUT:
 9 | %clusterLabels ... vector of length n comprising the cluster label for each
10 | %                  data point
11 | 
12 | 
13 | n=size(adj,1);
14 | 
15 | degrees = sum(adj, 1);
16 | D = diag(degrees);
17 | Dsqinv=diag(1./sqrt(degrees));
18 | 
19 | L = D-adj;
20 | 
21 | Msymm=Dsqinv*L*Dsqinv;
22 | Msymm=(Msymm+Msymm')/2;
23 | 
24 | 
25 | try
26 |     [H, eigValues] = eigs(Msymm,k,'smallestabs','MaxIterations',500,'SubspaceDimension',min(n,max(2*k,25)));
27 | catch
28 |     [H, eigValues] = eigs(Msymm,k,'smallestreal','MaxIterations',1000,'SubspaceDimension',min(n,max(2*k,25)));
29 | end
30 | 
31 | clusterLabels = kmeans(Dsqinv*H,k,'Replicates',10);
32 | end
33 | 
34 | 
35 | 
36 | 
37 | 


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/SC_unnormalized.m:
--------------------------------------------------------------------------------
 1 | function clusterLabels = SC_unnormalized(adj,k)
 2 | %implementation of unnormalized SC as stated in Alg. 1 
 3 | %
 4 | %INPUT:
 5 | %adj ... (weighted) adjacency matrix of size n x n
 6 | %k ... number of clusters
 7 | %
 8 | %OUTPUT:
 9 | %clusterLabels ... vector of length n comprising the cluster label for each
10 | %                  data point
11 | 
12 | 
13 | n=size(adj,1);
14 | 
15 | degrees = sum(adj, 1);
16 | D = diag(degrees);
17 | L = D-adj;
18 | 
19 | try
20 |     [H, eigValues] = eigs(L,k,'smallestabs','MaxIterations',500,'SubspaceDimension',min(n,max(2*k,25)));
21 | catch   
22 |     [H, eigValues] = eigs(L,k,'smallestreal','MaxIterations',1000,'SubspaceDimension',min(n,max(2*k,25)));
23 | end
24 | 
25 | clusterLabels = kmeans(H,k,'Replicates',10);
26 | end
27 | 
28 | 
29 | 
30 | 
31 | 


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/clustering_accuracy.m:
--------------------------------------------------------------------------------
 1 | function error=clustering_accuracy(labels,clustering)
 2 | %computes the error of a clustering with respect to the ground-truth
 3 | %clustering (see Section 4)
 4 | %
 5 | %INPUT:
 6 | %labels ... vector of length n comprising ground-truth cluster labels
 7 | %clustering ... vector of length n comprising cluster labels provided by a
 8 | %               clustering algorithm
 9 | %
10 | %OUTPUT:
11 | %error ... error of the clustering
12 | 
13 | 
14 | n=length(labels);
15 | 
16 | 
17 | if sum(size(labels)==[n,1])==2
18 |     labels=reshape(labels,[1,n]);
19 | end
20 | 
21 | if sum(size(clustering)==[n,1])==2
22 |     clustering=reshape(clustering,[1,n]);
23 | end
24 | 
25 | 
26 | aa=unique(labels);
27 | J=length(aa);
28 | 
29 | bb=unique(clustering);
30 | K=length(bb);
31 | 
32 | 
33 | if sum(aa==(1:J))<J
34 |     labels_old=labels;
35 |     temp=1;
36 |     for ell=aa
37 |         labels(labels_old==ell)=temp;
38 |         temp=temp+1;
39 |     end
40 | end
41 | 
42 | if sum(bb==(1:K))<K
43 |     clustering_old=clustering;
44 |     temp=1;
45 |     for ell=bb
46 |         clustering(clustering_old==ell)=temp;
47 |         temp=temp+1;
48 |     end
49 | end
50 | 
51 | 
52 | 
53 | permut=perms(1:max(K,J));
54 | Kfac=size(permut,1);
55 | 
56 | error=Inf;
57 | clustering_temp=clustering;
58 | 
59 | for ell=1:Kfac
60 |     for mmm=1:K
61 |         clustering_temp(clustering==mmm)=permut(ell,mmm);
62 |     end    
63 |     error_temp=sum(clustering_temp~=labels)/n;
64 |     if error_temp<error
65 |         error=error_temp;
66 |     end
67 | end
68 |     
69 |     


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/experiments_Figure2_Row1.m:
--------------------------------------------------------------------------------
  1 | anz_runs=10;
  2 | n_range=1000:1000:10000;
  3 | n_range_fair_norm=1000:1000:4000;
  4 | 
  5 | 
  6 | 
  7 | %%%% FIRST PLOT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  8 | 
  9 | k=5;
 10 | h=5;
 11 | 
 12 | a=0.4;
 13 | b=0.3;
 14 | c=0.2;
 15 | d=0.1;
 16 | 
 17 | 
 18 | 
 19 | error_SC=zeros(anz_runs,length(n_range));
 20 | error_SC_Normalized=zeros(anz_runs,length(n_range));
 21 | error_Fair_SC=zeros(anz_runs,length(n_range));
 22 | error_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
 23 | 
 24 | time_SC=zeros(anz_runs,length(n_range));
 25 | time_SC_Normalized=zeros(anz_runs,length(n_range));
 26 | time_Fair_SC=zeros(anz_runs,length(n_range));
 27 | time_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
 28 | 
 29 | for mmm=1:length(n_range)
 30 |     
 31 |     n=n_range(mmm);
 32 |         
 33 |     disp('-------------------------------------------------')
 34 |     n
 35 |     
 36 |     
 37 |     block_sizes=(n/(k*h))*ones(1,k*h);
 38 |        
 39 |     sensitive=zeros(n,1);
 40 |     labels=zeros(n,1);
 41 |     for yyy=1:k
 42 |         for zzz=1:h
 43 |             sensitive(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=zzz;
 44 |             labels(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=yyy;
 45 |         end
 46 |     end
 47 |         
 48 |     
 49 |     
 50 |     for ell=1:anz_runs
 51 |     
 52 |         adja=generate_adja_SB_model(n,a,b,c,d,k,h,block_sizes);
 53 |         
 54 |         tstart=tic;
 55 |         clustering_SC=SC_unnormalized(adja,k);
 56 |         time_SC(ell,mmm)=toc(tstart);
 57 |         error_SC(ell,mmm)=clustering_accuracy(labels,clustering_SC);
 58 |         
 59 |         
 60 |         tstart=tic;
 61 |         clustering_SC_NORMALIZED=SC_normalized(adja,k);
 62 |         time_SC_Normalized(ell,mmm)=toc(tstart);
 63 |         error_SC_Normalized(ell,mmm)=clustering_accuracy(labels,clustering_SC_NORMALIZED);
 64 |         
 65 |         
 66 |         tstart=tic;
 67 |         FAIR_clustering_SC=Fair_SC_unnormalized(adja,k,sensitive);
 68 |         time_Fair_SC(ell,mmm)=toc(tstart);
 69 |         error_Fair_SC(ell,mmm)=clustering_accuracy(labels, FAIR_clustering_SC);
 70 |         
 71 |         
 72 |         if mmm<=length(n_range_fair_norm)
 73 |             tstart=tic;
 74 |             FAIR_clustering_SC_NORMALIZED=Fair_SC_normalized(adja,k,sensitive);
 75 |             time_Fair_SC_Normalized(ell,mmm)=toc(tstart);
 76 |             error_Fair_SC_Normalized(ell,mmm)=clustering_accuracy(labels,FAIR_clustering_SC_NORMALIZED);
 77 |         end
 78 |         
 79 |     end
 80 | end
 81 | 
 82 | 
 83 |         
 84 | %set default sizes for figures:
 85 | ulesfontsize = 24;
 86 | set(0, 'DefaultAxesFontSize', ulesfontsize);
 87 | set(0, 'DefaultTextFontSize', ulesfontsize);
 88 | set(0, 'DefaultUIControlFontSize', ulesfontsize);
 89 | set(0,'DefaultLineMarkerSize',ulesfontsize);
 90 | set(0,'DefaultLineLineWidth',1.5) 
 91 | set(gcf, 'PaperPositionMode','auto')
 92 | close all;
 93 |     
 94 | 
 95 | sfname=strcat('_SB_model_as_function_of_n_with_k=',num2str(k),'_h=',num2str(h),'_runs=',num2str(anz_runs),'_Row1Plot1');    
 96 | 
 97 | %save(strcat('DATA',sfname,'.mat'))
 98 | 
 99 | figure(1);clf;
100 | plot(n_range,mean(error_SC,1),'mo-.',n_range,mean(error_SC_Normalized,1),'gs-.',n_range,mean(error_Fair_SC,1),'rx-',n_range_fair_norm,mean(error_Fair_SC_Normalized,1),'bx-')
101 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)')
102 | xlabel('n')
103 | ylabel('Error')
104 | ylim([0,1])
105 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a=',num2str(a),', b=',num2str(b),', c=',num2str(c),', d=',num2str(d)),'FontWeight','normal')
106 | saveas(1,strcat('Error',sfname))
107 | print(1,'-dpdf',strcat('Error',sfname))
108 | 
109 | figure(2);clf;
110 | plot(n_range,mean(time_SC,1),'mo-.',n_range,mean(time_SC_Normalized,1),'gs-.',n_range,mean(time_Fair_SC,1),'rx-',n_range_fair_norm,mean(time_Fair_SC_Normalized,1),'bx-',...
111 |     n_range_fair_norm,1.2*(time_Fair_SC_Normalized(1)/(n_range_fair_norm(1)^3))*n_range_fair_norm.^3,'c-')
112 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)','~ n^3')
113 | xlabel('n')
114 | ylabel('Running time [s]')
115 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a=',num2str(a),', b=',num2str(b),', c=',num2str(c),', d=',num2str(d)),'FontWeight','normal')
116 | saveas(2,strcat('Time',sfname))
117 | print(2,'-dpdf',strcat('Time',sfname))
118 | 
119 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
120 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
121 | 
122 | 
123 | 
124 | 
125 | 
126 | 
127 | 
128 | 
129 | 
130 | %%%% SECOND PLOT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
131 | 
132 | k=5;
133 | h=5;
134 | 
135 | a=0.2;
136 | b=0.15;
137 | c=0.1;
138 | d=0.05;
139 | 
140 | 
141 | 
142 | error_SC=zeros(anz_runs,length(n_range));
143 | error_SC_Normalized=zeros(anz_runs,length(n_range));
144 | error_Fair_SC=zeros(anz_runs,length(n_range));
145 | error_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
146 | 
147 | time_SC=zeros(anz_runs,length(n_range));
148 | time_SC_Normalized=zeros(anz_runs,length(n_range));
149 | time_Fair_SC=zeros(anz_runs,length(n_range));
150 | time_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
151 | 
152 | for mmm=1:length(n_range)
153 |     
154 |     n=n_range(mmm);
155 |         
156 |     disp('-------------------------------------------------')
157 |     n
158 |     
159 |     
160 |     block_sizes=(n/(k*h))*ones(1,k*h);
161 |        
162 |     sensitive=zeros(n,1);
163 |     labels=zeros(n,1);
164 |     for yyy=1:k
165 |         for zzz=1:h
166 |             sensitive(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=zzz;
167 |             labels(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=yyy;
168 |         end
169 |     end
170 |         
171 |     
172 |     
173 |     for ell=1:anz_runs
174 |     
175 |         adja=generate_adja_SB_model(n,a,b,c,d,k,h,block_sizes);
176 |         
177 |         tstart=tic;
178 |         clustering_SC=SC_unnormalized(adja,k);
179 |         time_SC(ell,mmm)=toc(tstart);
180 |         error_SC(ell,mmm)=clustering_accuracy(labels,clustering_SC);
181 |         
182 |         
183 |         tstart=tic;
184 |         clustering_SC_NORMALIZED=SC_normalized(adja,k);
185 |         time_SC_Normalized(ell,mmm)=toc(tstart);
186 |         error_SC_Normalized(ell,mmm)=clustering_accuracy(labels,clustering_SC_NORMALIZED);
187 |         
188 |         
189 |         tstart=tic;
190 |         FAIR_clustering_SC=Fair_SC_unnormalized(adja,k,sensitive);
191 |         time_Fair_SC(ell,mmm)=toc(tstart);
192 |         error_Fair_SC(ell,mmm)=clustering_accuracy(labels, FAIR_clustering_SC);
193 |         
194 |         
195 |         if mmm<=length(n_range_fair_norm)
196 |             tstart=tic;
197 |             FAIR_clustering_SC_NORMALIZED=Fair_SC_normalized(adja,k,sensitive);
198 |             time_Fair_SC_Normalized(ell,mmm)=toc(tstart);
199 |             error_Fair_SC_Normalized(ell,mmm)=clustering_accuracy(labels,FAIR_clustering_SC_NORMALIZED);
200 |         end
201 |         
202 |     end
203 | end
204 | 
205 | 
206 | 
207 |         
208 | %set default sizes for figures:
209 | ulesfontsize = 24;
210 | set(0, 'DefaultAxesFontSize', ulesfontsize);
211 | set(0, 'DefaultTextFontSize', ulesfontsize);
212 | set(0, 'DefaultUIControlFontSize', ulesfontsize);
213 | set(0,'DefaultLineMarkerSize',ulesfontsize);
214 | set(0,'DefaultLineLineWidth',1.5) 
215 | set(gcf, 'PaperPositionMode','auto')
216 | close all;
217 |     
218 | 
219 | sfname=strcat('_SB_model_as_function_of_n_with_k=',num2str(k),'_h=',num2str(h),'_runs=',num2str(anz_runs),'_Row1Plot2');
220 |     
221 | %save(strcat('DATA',sfname,'.mat'))
222 | 
223 | figure(1);clf;
224 | plot(n_range,mean(error_SC,1),'mo-.',n_range,mean(error_SC_Normalized,1),'gs-.',n_range,mean(error_Fair_SC,1),'rx-',n_range_fair_norm,mean(error_Fair_SC_Normalized,1),'bx-')
225 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)')
226 | xlabel('n')
227 | ylabel('Error')
228 | ylim([0,1])
229 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a=',num2str(a),', b=',num2str(b),', c=',num2str(c),', d=',num2str(d)),'FontWeight','normal')
230 | saveas(1,strcat('Error',sfname))
231 | print(1,'-dpdf',strcat('Error',sfname))
232 | 
233 | figure(2);clf;
234 | plot(n_range,mean(time_SC,1),'mo-.',n_range,mean(time_SC_Normalized,1),'gs-.',n_range,mean(time_Fair_SC,1),'rx-',n_range_fair_norm,mean(time_Fair_SC_Normalized,1),'bx-',...
235 |     n_range_fair_norm,1.2*(time_Fair_SC_Normalized(1)/(n_range_fair_norm(1)^3))*n_range_fair_norm.^3,'c-')
236 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)','~ n^3')
237 | xlabel('n')
238 | ylabel('Running time [s]')
239 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a=',num2str(a),', b=',num2str(b),', c=',num2str(c),', d=',num2str(d)),'FontWeight','normal')
240 | saveas(2,strcat('Time',sfname))
241 | print(2,'-dpdf',strcat('Time',sfname))
242 | 
243 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
244 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
245 | 
246 | 
247 | 
248 | 
249 | 
250 | 
251 | 
252 | 
253 | 
254 | %%%% THIRD AND FOURTH PLOT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
255 | 
256 | k=5;
257 | h=5;
258 | 
259 | af=10;
260 | bf=7;
261 | cf=4;
262 | df=1;
263 | 
264 | 
265 | 
266 | error_SC=zeros(anz_runs,length(n_range));
267 | error_SC_Normalized=zeros(anz_runs,length(n_range));
268 | error_Fair_SC=zeros(anz_runs,length(n_range));
269 | error_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
270 | 
271 | time_SC=zeros(anz_runs,length(n_range));
272 | time_SC_Normalized=zeros(anz_runs,length(n_range));
273 | time_Fair_SC=zeros(anz_runs,length(n_range));
274 | time_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
275 | 
276 | for mmm=1:length(n_range)
277 |     
278 |     n=n_range(mmm);
279 |     
280 |     a=af*(log(n)/n)^(2/3);
281 |     b=bf*(log(n)/n)^(2/3);
282 |     c=cf*(log(n)/n)^(2/3);
283 |     d=df*(log(n)/n)^(2/3);
284 |     
285 |     expo1=2;
286 |     expo2=3;
287 |     
288 |     disp('-------------------------------------------------')
289 |     n
290 |     
291 |     
292 |     block_sizes=(n/(k*h))*ones(1,k*h);
293 |     
294 |     sensitive=zeros(n,1);
295 |     labels=zeros(n,1);
296 |     for yyy=1:k
297 |         for zzz=1:h
298 |             sensitive(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=zzz;
299 |             labels(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=yyy;
300 |         end
301 |     end
302 |         
303 |     
304 |     
305 |     for ell=1:anz_runs
306 |     
307 |         adja=generate_adja_SB_model(n,a,b,c,d,k,h,block_sizes);
308 |         
309 |         tstart=tic;
310 |         clustering_SC=SC_unnormalized(adja,k);
311 |         time_SC(ell,mmm)=toc(tstart);
312 |         error_SC(ell,mmm)=clustering_accuracy(labels,clustering_SC);
313 |         
314 |         
315 |         tstart=tic;
316 |         clustering_SC_NORMALIZED=SC_normalized(adja,k);
317 |         time_SC_Normalized(ell,mmm)=toc(tstart);
318 |         error_SC_Normalized(ell,mmm)=clustering_accuracy(labels,clustering_SC_NORMALIZED);
319 |         
320 |         
321 |         tstart=tic;
322 |         FAIR_clustering_SC=Fair_SC_unnormalized(adja,k,sensitive);
323 |         time_Fair_SC(ell,mmm)=toc(tstart);
324 |         error_Fair_SC(ell,mmm)=clustering_accuracy(labels, FAIR_clustering_SC);
325 |         
326 |         
327 |         if mmm<=length(n_range_fair_norm)
328 |             tstart=tic;
329 |             FAIR_clustering_SC_NORMALIZED=Fair_SC_normalized(adja,k,sensitive);
330 |             time_Fair_SC_Normalized(ell,mmm)=toc(tstart);
331 |             error_Fair_SC_Normalized(ell,mmm)=clustering_accuracy(labels,FAIR_clustering_SC_NORMALIZED);
332 |         end   
333 | 
334 |     end
335 | end
336 | 
337 | 
338 | 
339 |         
340 | %set default sizes for figures:
341 | ulesfontsize = 24;
342 | set(0, 'DefaultAxesFontSize', ulesfontsize);
343 | set(0, 'DefaultTextFontSize', ulesfontsize);
344 | set(0, 'DefaultUIControlFontSize', ulesfontsize);
345 | set(0,'DefaultLineMarkerSize',ulesfontsize);
346 | set(0,'DefaultLineLineWidth',1.5) 
347 | set(gcf, 'PaperPositionMode','auto')
348 | close all;
349 |     
350 | 
351 | sfname=strcat('_SB_model_as_function_of_n_with_k=',num2str(k),'_h=',num2str(h),'_runs=',num2str(anz_runs),'_Row1Plot3and4');
352 | 
353 | %save(strcat('DATA',sfname,'.mat'))
354 | 
355 | figure(1);clf;
356 | plot(n_range,mean(error_SC,1),'mo-.',n_range,mean(error_SC_Normalized,1),'gs-.',n_range,mean(error_Fair_SC,1),'rx-',n_range_fair_norm,mean(error_Fair_SC_Normalized,1),'bx-')
357 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)')
358 | xlabel('n')
359 | ylabel('Error')
360 | ylim([0,1])
361 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a,b,c,d ~ (log(n)/n)\^(',num2str(expo1),'/',num2str(expo2),')'),'FontWeight','normal')
362 | saveas(1,strcat('Error',sfname))
363 | print(1,'-dpdf',strcat('Error',sfname))
364 | 
365 | figure(2);clf;
366 | plot(n_range,mean(time_SC,1),'mo-.',n_range,mean(time_SC_Normalized,1),'gs-.',n_range,mean(time_Fair_SC,1),'rx-',n_range_fair_norm,mean(time_Fair_SC_Normalized,1),'bx-',...
367 |     n_range_fair_norm,1.2*(time_Fair_SC_Normalized(1)/(n_range_fair_norm(1)^3))*n_range_fair_norm.^3,'c-')
368 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)','~ n^3')
369 | xlabel('n')
370 | ylabel('Running time [s]')
371 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a,b,c,d ~ (log(n)/n)\^(',num2str(expo1),'/',num2str(expo2),')'),'FontWeight','normal')
372 | saveas(2,strcat('Time',sfname))
373 | print(2,'-dpdf',strcat('Time',sfname))
374 | 
375 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
376 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
377 | 
378 | 
379 | 


--------------------------------------------------------------------------------
/experiments_Figure2_Row2.m:
--------------------------------------------------------------------------------
  1 | anz_runs=10;
  2 | n_range=1000:1000:10000;
  3 | n_range_fair_norm=1000:1000:4000;
  4 | 
  5 | 
  6 | 
  7 | %%%% FIRST PLOT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  8 | 
  9 | k=3;
 10 | h=5;
 11 | 
 12 | a=0.4;
 13 | b=0.3;
 14 | c=0.2;
 15 | d=0.1;
 16 | 
 17 | 
 18 | 
 19 | error_SC=zeros(anz_runs,length(n_range));
 20 | error_SC_Normalized=zeros(anz_runs,length(n_range));
 21 | error_Fair_SC=zeros(anz_runs,length(n_range));
 22 | error_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
 23 | 
 24 | time_SC=zeros(anz_runs,length(n_range));
 25 | time_SC_Normalized=zeros(anz_runs,length(n_range));
 26 | time_Fair_SC=zeros(anz_runs,length(n_range));
 27 | time_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
 28 | 
 29 | for mmm=1:length(n_range)
 30 |     
 31 |     n=n_range(mmm);
 32 |         
 33 |     disp('-------------------------------------------------')
 34 |     n
 35 |     
 36 |     block_sizes=[7*(n/10)*[0.2,0.2,0.2,0.2,0.2],15*(n/100)*[0.2,0.2,0.2,0.2,0.2],15*(n/100)*[0.2,0.2,0.2,0.2,0.2]];
 37 |     
 38 |     sensitive=zeros(n,1);
 39 |     labels=zeros(n,1);
 40 |     for yyy=1:k
 41 |         for zzz=1:h
 42 |             block=(yyy-1)*h+zzz;
 43 |             sensitive((sum(block_sizes(1:(block-1)))+1):sum(block_sizes(1:block)))=zzz;
 44 |             labels((sum(block_sizes(1:(block-1)))+1):sum(block_sizes(1:block)))=yyy;
 45 |         end
 46 |     end
 47 |         
 48 |     
 49 |     
 50 |     for ell=1:anz_runs
 51 |         
 52 |         adja=generate_adja_SB_model(n,a,b,c,d,k,h,block_sizes);
 53 |         
 54 |         tstart=tic;
 55 |         clustering_SC=SC_unnormalized(adja,k);
 56 |         time_SC(ell,mmm)=toc(tstart);
 57 |         error_SC(ell,mmm)=clustering_accuracy(labels,clustering_SC);
 58 |         
 59 |         
 60 |         tstart=tic;
 61 |         clustering_SC_NORMALIZED=SC_normalized(adja,k);
 62 |         time_SC_Normalized(ell,mmm)=toc(tstart);
 63 |         error_SC_Normalized(ell,mmm)=clustering_accuracy(labels,clustering_SC_NORMALIZED);
 64 |         
 65 |         
 66 |         tstart=tic;
 67 |         FAIR_clustering_SC=Fair_SC_unnormalized(adja,k,sensitive);
 68 |         time_Fair_SC(ell,mmm)=toc(tstart);
 69 |         error_Fair_SC(ell,mmm)=clustering_accuracy(labels, FAIR_clustering_SC);
 70 |         
 71 |         
 72 |         if mmm<=length(n_range_fair_norm)
 73 |             tstart=tic;
 74 |             FAIR_clustering_SC_NORMALIZED=Fair_SC_normalized(adja,k,sensitive);
 75 |             time_Fair_SC_Normalized(ell,mmm)=toc(tstart);
 76 |             error_Fair_SC_Normalized(ell,mmm)=clustering_accuracy(labels,FAIR_clustering_SC_NORMALIZED);
 77 |         end
 78 |         
 79 |     end
 80 | end
 81 | 
 82 | 
 83 | 
 84 | %set default sizes for figures:
 85 | ulesfontsize = 24;
 86 | set(0, 'DefaultAxesFontSize', ulesfontsize);
 87 | set(0, 'DefaultTextFontSize', ulesfontsize);
 88 | set(0, 'DefaultUIControlFontSize', ulesfontsize);
 89 | set(0,'DefaultLineMarkerSize',ulesfontsize);
 90 | set(0,'DefaultLineLineWidth',1.5) 
 91 | set(gcf, 'PaperPositionMode','auto')
 92 | close all;
 93 |     
 94 | 
 95 | sfname=strcat('_SB_model_as_function_of_n_with_k=',num2str(k),'_h=',num2str(h),'_runs=',num2str(anz_runs),'_Row2Plot1');    
 96 | 
 97 | %save(strcat('DATA',sfname,'.mat'))
 98 | 
 99 | figure(1);clf;
100 | plot(n_range,mean(error_SC,1),'mo-.',n_range,mean(error_SC_Normalized,1),'gs-.',n_range,mean(error_Fair_SC,1),'rx-',n_range_fair_norm,mean(error_Fair_SC_Normalized,1),'bx-')
101 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)')
102 | xlabel('n')
103 | ylabel('Error')
104 | ylim([0,1])
105 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a=',num2str(a),', b=',num2str(b),', c=',num2str(c),', d=',num2str(d)),'FontWeight','normal')
106 | saveas(1,strcat('Error',sfname))
107 | print(1,'-dpdf',strcat('Error',sfname))
108 | 
109 | figure(2);clf;
110 | plot(n_range,mean(time_SC,1),'mo-.',n_range,mean(time_SC_Normalized,1),'gs-.',n_range,mean(time_Fair_SC,1),'rx-',n_range_fair_norm,mean(time_Fair_SC_Normalized,1),'bx-',...
111 |     n_range_fair_norm,1.2*(time_Fair_SC_Normalized(1)/(n_range_fair_norm(1)^3))*n_range_fair_norm.^3,'c-')
112 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)','~ n^3')
113 | xlabel('n')
114 | ylabel('Running time [s]')
115 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a=',num2str(a),', b=',num2str(b),', c=',num2str(c),', d=',num2str(d)),'FontWeight','normal')
116 | saveas(2,strcat('Time',sfname))
117 | print(2,'-dpdf',strcat('Time',sfname))
118 | 
119 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
120 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
121 | 
122 | 
123 | 
124 | 
125 | 
126 | 
127 | 
128 | 
129 | 
130 | %%%% SECOND PLOT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
131 | 
132 | k=2;
133 | h=2;
134 | 
135 | af=10;
136 | bf=7;
137 | cf=4;
138 | df=1;
139 | 
140 | 
141 | 
142 | error_SC=zeros(anz_runs,length(n_range));
143 | error_SC_Normalized=zeros(anz_runs,length(n_range));
144 | error_Fair_SC=zeros(anz_runs,length(n_range));
145 | error_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
146 | 
147 | time_SC=zeros(anz_runs,length(n_range));
148 | time_SC_Normalized=zeros(anz_runs,length(n_range));
149 | time_Fair_SC=zeros(anz_runs,length(n_range));
150 | time_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
151 | 
152 | for mmm=1:length(n_range)
153 |     
154 |     n=n_range(mmm);
155 |     
156 |     disp('-------------------------------------------------')
157 |     n    
158 | 
159 |     a=af*(log(n)/n)^(2/3);
160 |     b=bf*(log(n)/n)^(2/3);
161 |     c=cf*(log(n)/n)^(2/3);
162 |     d=df*(log(n)/n)^(2/3);
163 |     
164 |     expo1=2;
165 |     expo2=3;
166 |     
167 |     
168 |     block_sizes=[6*(n/10)*[0.6,0.4],4*(n/10)*[0.6,0.4]];
169 |     
170 |     sensitive=zeros(n,1);
171 |     labels=zeros(n,1);
172 |     for yyy=1:k
173 |         for zzz=1:h
174 |             block=(yyy-1)*h+zzz;
175 |             sensitive((sum(block_sizes(1:(block-1)))+1):sum(block_sizes(1:block)))=zzz;
176 |             labels((sum(block_sizes(1:(block-1)))+1):sum(block_sizes(1:block)))=yyy;
177 |         end
178 |     end
179 |         
180 |     
181 |     
182 |     for ell=1:anz_runs
183 |     
184 |         adja=generate_adja_SB_model(n,a,b,c,d,k,h,block_sizes);
185 |         
186 |         tstart=tic;
187 |         clustering_SC=SC_unnormalized(adja,k);
188 |         time_SC(ell,mmm)=toc(tstart);
189 |         error_SC(ell,mmm)=clustering_accuracy(labels,clustering_SC);
190 |         
191 |         
192 |         tstart=tic;
193 |         clustering_SC_NORMALIZED=SC_normalized(adja,k);
194 |         time_SC_Normalized(ell,mmm)=toc(tstart);
195 |         error_SC_Normalized(ell,mmm)=clustering_accuracy(labels,clustering_SC_NORMALIZED);
196 |         
197 |         
198 |         tstart=tic;
199 |         FAIR_clustering_SC=Fair_SC_unnormalized(adja,k,sensitive);
200 |         time_Fair_SC(ell,mmm)=toc(tstart);
201 |         error_Fair_SC(ell,mmm)=clustering_accuracy(labels, FAIR_clustering_SC);
202 |         
203 |         
204 |         if mmm<=length(n_range_fair_norm)
205 |             tstart=tic;
206 |             FAIR_clustering_SC_NORMALIZED=Fair_SC_normalized(adja,k,sensitive);
207 |             time_Fair_SC_Normalized(ell,mmm)=toc(tstart);
208 |             error_Fair_SC_Normalized(ell,mmm)=clustering_accuracy(labels,FAIR_clustering_SC_NORMALIZED);
209 |         end
210 | 
211 |     end
212 | end
213 | 
214 | 
215 | 
216 | %set default sizes for figures:
217 | ulesfontsize = 24;
218 | set(0, 'DefaultAxesFontSize', ulesfontsize);
219 | set(0, 'DefaultTextFontSize', ulesfontsize);
220 | set(0, 'DefaultUIControlFontSize', ulesfontsize);
221 | set(0,'DefaultLineMarkerSize',ulesfontsize);
222 | set(0,'DefaultLineLineWidth',1.5) 
223 | set(gcf, 'PaperPositionMode','auto')
224 | close all;
225 |     
226 | 
227 | sfname=strcat('_SB_model_as_function_of_n_with_k=',num2str(k),'_h=',num2str(h),'_runs=',num2str(anz_runs),'_Row2Plot2');    
228 | 
229 | %save(strcat('DATA',sfname,'.mat'))
230 | 
231 | figure(1);clf;
232 | plot(n_range,mean(error_SC,1),'mo-.',n_range,mean(error_SC_Normalized,1),'gs-.',n_range,mean(error_Fair_SC,1),'rx-',n_range_fair_norm,mean(error_Fair_SC_Normalized,1),'bx-')
233 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)')
234 | xlabel('n')
235 | ylabel('Error')
236 | ylim([0,1])
237 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a,b,c,d ~ (log(n)/n)\^(',num2str(expo1),'/',num2str(expo2),')'),'FontWeight','normal')
238 | saveas(1,strcat('Error',sfname))
239 | print(1,'-dpdf',strcat('Error',sfname))
240 | 
241 | figure(2);clf;
242 | plot(n_range,mean(time_SC,1),'mo-.',n_range,mean(time_SC_Normalized,1),'gs-.',n_range,mean(time_Fair_SC,1),'rx-',n_range_fair_norm,mean(time_Fair_SC_Normalized,1),'bx-',...
243 |     n_range_fair_norm,1.2*(time_Fair_SC_Normalized(1)/(n_range_fair_norm(1)^3))*n_range_fair_norm.^3,'c-')
244 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)','~ n^3')
245 | xlabel('n')
246 | ylabel('Running time [s]')
247 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a,b,c,d ~ (log(n)/n)\^(',num2str(expo1),'/',num2str(expo2),')'),'FontWeight','normal')
248 | saveas(2,strcat('Time',sfname))
249 | print(2,'-dpdf',strcat('Time',sfname))
250 | 
251 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
252 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
253 | 
254 | 
255 | 
256 | 
257 | 
258 | 
259 | %%%% THIRD PLOT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
260 | 
261 | k=5;
262 | h=3;
263 | 
264 | a=0.4;
265 | b=0.3;
266 | c=0.2;
267 | d=0.1;
268 | 
269 | 
270 | 
271 | error_SC=zeros(anz_runs,length(n_range));
272 | error_SC_Normalized=zeros(anz_runs,length(n_range));
273 | error_Fair_SC=zeros(anz_runs,length(n_range));
274 | error_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
275 | 
276 | time_SC=zeros(anz_runs,length(n_range));
277 | time_SC_Normalized=zeros(anz_runs,length(n_range));
278 | time_Fair_SC=zeros(anz_runs,length(n_range));
279 | time_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
280 | 
281 | for mmm=1:length(n_range)
282 |     
283 |     n=n_range(mmm);
284 |         
285 |     disp('-------------------------------------------------')
286 |     n
287 |     
288 |     block_sizes=[3*(n/10)*[0.5,0.3,0.2],3*(n/10)*[0.5,0.3,0.2],2*(n/10)*[0.5,0.3,0.2],1*(n/10)*[0.5,0.3,0.2],1*(n/10)*[0.5,0.3,0.2]];
289 |     
290 |     sensitive=zeros(n,1);
291 |     labels=zeros(n,1);
292 |     for yyy=1:k
293 |         for zzz=1:h
294 |             block=(yyy-1)*h+zzz;
295 |             sensitive((sum(block_sizes(1:(block-1)))+1):sum(block_sizes(1:block)))=zzz;
296 |             labels((sum(block_sizes(1:(block-1)))+1):sum(block_sizes(1:block)))=yyy;
297 |         end
298 |     end
299 |         
300 |     
301 |     
302 |     for ell=1:anz_runs
303 |         
304 |         adja=generate_adja_SB_model(n,a,b,c,d,k,h,block_sizes);
305 |         
306 |         tstart=tic;
307 |         clustering_SC=SC_unnormalized(adja,k);
308 |         time_SC(ell,mmm)=toc(tstart);
309 |         error_SC(ell,mmm)=clustering_accuracy(labels,clustering_SC);
310 |         
311 |         
312 |         tstart=tic;
313 |         clustering_SC_NORMALIZED=SC_normalized(adja,k);
314 |         time_SC_Normalized(ell,mmm)=toc(tstart);
315 |         error_SC_Normalized(ell,mmm)=clustering_accuracy(labels,clustering_SC_NORMALIZED);
316 |         
317 |         
318 |         tstart=tic;
319 |         FAIR_clustering_SC=Fair_SC_unnormalized(adja,k,sensitive);
320 |         time_Fair_SC(ell,mmm)=toc(tstart);
321 |         error_Fair_SC(ell,mmm)=clustering_accuracy(labels, FAIR_clustering_SC);
322 |         
323 |         
324 |         if mmm<=length(n_range_fair_norm)
325 |             tstart=tic;
326 |             FAIR_clustering_SC_NORMALIZED=Fair_SC_normalized(adja,k,sensitive);
327 |             time_Fair_SC_Normalized(ell,mmm)=toc(tstart);
328 |             error_Fair_SC_Normalized(ell,mmm)=clustering_accuracy(labels,FAIR_clustering_SC_NORMALIZED);
329 |         end
330 |         
331 |     end
332 | end
333 | 
334 | 
335 | 
336 | %set default sizes for figures:
337 | ulesfontsize = 24;
338 | set(0, 'DefaultAxesFontSize', ulesfontsize);
339 | set(0, 'DefaultTextFontSize', ulesfontsize);
340 | set(0, 'DefaultUIControlFontSize', ulesfontsize);
341 | set(0,'DefaultLineMarkerSize',ulesfontsize);
342 | set(0,'DefaultLineLineWidth',1.5) 
343 | set(gcf, 'PaperPositionMode','auto')
344 | close all;
345 |     
346 | 
347 | sfname=strcat('_SB_model_as_function_of_n_with_k=',num2str(k),'_h=',num2str(h),'_runs=',num2str(anz_runs),'_Row2Plot3');    
348 | 
349 | %save(strcat('DATA',sfname,'.mat'))
350 | 
351 | figure(1);clf;
352 | plot(n_range,mean(error_SC,1),'mo-.',n_range,mean(error_SC_Normalized,1),'gs-.',n_range,mean(error_Fair_SC,1),'rx-',n_range_fair_norm,mean(error_Fair_SC_Normalized,1),'bx-')
353 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)')
354 | xlabel('n')
355 | ylabel('Error')
356 | ylim([0,1])
357 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a=',num2str(a),', b=',num2str(b),', c=',num2str(c),', d=',num2str(d)),'FontWeight','normal')
358 | saveas(1,strcat('Error',sfname))
359 | print(1,'-dpdf',strcat('Error',sfname))
360 | 
361 | figure(2);clf;
362 | plot(n_range,mean(time_SC,1),'mo-.',n_range,mean(time_SC_Normalized,1),'gs-.',n_range,mean(time_Fair_SC,1),'rx-',n_range_fair_norm,mean(time_Fair_SC_Normalized,1),'bx-',...
363 |     n_range_fair_norm,1.2*(time_Fair_SC_Normalized(1)/(n_range_fair_norm(1)^3))*n_range_fair_norm.^3,'c-')
364 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)','~ n^3')
365 | xlabel('n')
366 | ylabel('Running time [s]')
367 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a=',num2str(a),', b=',num2str(b),', c=',num2str(c),', d=',num2str(d)),'FontWeight','normal')
368 | saveas(2,strcat('Time',sfname))
369 | print(2,'-dpdf',strcat('Time',sfname))
370 | 
371 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
372 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
373 | 
374 | 
375 | 
376 | 
377 | 
378 | 
379 | %%%% FOURTH PLOT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
380 | 
381 | k=5;
382 | h=3;
383 | 
384 | a=0.4;
385 | b=0.3;
386 | c=0.2;
387 | d=0.1;
388 | 
389 | 
390 | 
391 | error_SC=zeros(anz_runs,length(n_range));
392 | error_SC_Normalized=zeros(anz_runs,length(n_range));
393 | error_Fair_SC=zeros(anz_runs,length(n_range));
394 | error_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
395 | 
396 | time_SC=zeros(anz_runs,length(n_range));
397 | time_SC_Normalized=zeros(anz_runs,length(n_range));
398 | time_Fair_SC=zeros(anz_runs,length(n_range));
399 | time_Fair_SC_Normalized=zeros(anz_runs,length(n_range_fair_norm));
400 | 
401 | for mmm=1:length(n_range)
402 |     
403 |     n=n_range(mmm);
404 |         
405 |     disp('-------------------------------------------------')
406 |     n
407 |     
408 |     block_sizes=[6*(n/10)*[0.5,0.3,0.2],1*(n/10)*[0.5,0.3,0.2],1*(n/10)*[0.5,0.3,0.2],1*(n/10)*[0.5,0.3,0.2],1*(n/10)*[0.5,0.3,0.2]];
409 |     
410 |     sensitive=zeros(n,1);
411 |     labels=zeros(n,1);
412 |     for yyy=1:k
413 |         for zzz=1:h
414 |             block=(yyy-1)*h+zzz;
415 |             sensitive((sum(block_sizes(1:(block-1)))+1):sum(block_sizes(1:block)))=zzz;
416 |             labels((sum(block_sizes(1:(block-1)))+1):sum(block_sizes(1:block)))=yyy;
417 |         end
418 |     end
419 |         
420 |     
421 |     
422 |     for ell=1:anz_runs
423 |          
424 |         adja=generate_adja_SB_model(n,a,b,c,d,k,h,block_sizes);
425 |         
426 |         tstart=tic;
427 |         clustering_SC=SC_unnormalized(adja,k);
428 |         time_SC(ell,mmm)=toc(tstart);
429 |         error_SC(ell,mmm)=clustering_accuracy(labels,clustering_SC);
430 |         
431 |         
432 |         tstart=tic;
433 |         clustering_SC_NORMALIZED=SC_normalized(adja,k);
434 |         time_SC_Normalized(ell,mmm)=toc(tstart);
435 |         error_SC_Normalized(ell,mmm)=clustering_accuracy(labels,clustering_SC_NORMALIZED);
436 |         
437 |         
438 |         tstart=tic;
439 |         FAIR_clustering_SC=Fair_SC_unnormalized(adja,k,sensitive);
440 |         time_Fair_SC(ell,mmm)=toc(tstart);
441 |         error_Fair_SC(ell,mmm)=clustering_accuracy(labels, FAIR_clustering_SC);
442 |         
443 |         
444 |         if mmm<=length(n_range_fair_norm)
445 |             tstart=tic;
446 |             FAIR_clustering_SC_NORMALIZED=Fair_SC_normalized(adja,k,sensitive);
447 |             time_Fair_SC_Normalized(ell,mmm)=toc(tstart);
448 |             error_Fair_SC_Normalized(ell,mmm)=clustering_accuracy(labels,FAIR_clustering_SC_NORMALIZED);
449 |         end
450 |         
451 |     end
452 | end
453 | 
454 | 
455 | 
456 | %set default sizes for figures:
457 | ulesfontsize = 24;
458 | set(0, 'DefaultAxesFontSize', ulesfontsize);
459 | set(0, 'DefaultTextFontSize', ulesfontsize);
460 | set(0, 'DefaultUIControlFontSize', ulesfontsize);
461 | set(0,'DefaultLineMarkerSize',ulesfontsize);
462 | set(0,'DefaultLineLineWidth',1.5) 
463 | set(gcf, 'PaperPositionMode','auto')
464 | close all;
465 |     
466 | 
467 | sfname=strcat('_SB_model_as_function_of_n_with_k=',num2str(k),'_h=',num2str(h),'_runs=',num2str(anz_runs),'_Row2Plot4');    
468 | 
469 | %save(strcat('DATA',sfname,'.mat'))
470 | 
471 | figure(1);clf;
472 | plot(n_range,mean(error_SC,1),'mo-.',n_range,mean(error_SC_Normalized,1),'gs-.',n_range,mean(error_Fair_SC,1),'rx-',n_range_fair_norm,mean(error_Fair_SC_Normalized,1),'bx-')
473 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)')
474 | xlabel('n')
475 | ylabel('Error')
476 | ylim([0,1])
477 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a=',num2str(a),', b=',num2str(b),', c=',num2str(c),', d=',num2str(d)),'FontWeight','normal')
478 | saveas(1,strcat('Error',sfname))
479 | print(1,'-dpdf',strcat('Error',sfname))
480 | 
481 | figure(2);clf;
482 | plot(n_range,mean(time_SC,1),'mo-.',n_range,mean(time_SC_Normalized,1),'gs-.',n_range,mean(time_Fair_SC,1),'rx-',n_range_fair_norm,mean(time_Fair_SC_Normalized,1),'bx-',...
483 |     n_range_fair_norm,1.2*(time_Fair_SC_Normalized(1)/(n_range_fair_norm(1)^3))*n_range_fair_norm.^3,'c-')
484 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)','~ n^3')
485 | xlabel('n')
486 | ylabel('Running time [s]')
487 | title(strcat('k=',num2str(k),', h=',num2str(h),' --- a=',num2str(a),', b=',num2str(b),', c=',num2str(c),', d=',num2str(d)),'FontWeight','normal')
488 | saveas(2,strcat('Time',sfname))
489 | print(2,'-dpdf',strcat('Time',sfname))
490 | 
491 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
492 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
493 | 
494 | 


--------------------------------------------------------------------------------
/experiments_Figure3.m:
--------------------------------------------------------------------------------
  1 | anz_runs=10;
  2 | h=4;
  3 | k_range=2:8;
  4 | factor_range=1:0.5:3;
  5 | 
  6 | af=0.25;
  7 | bf=0.2;
  8 | cf=0.15;
  9 | df=0.1;
 10 | 
 11 | 
 12 | 
 13 | %%%% LEFT PLOT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 14 | 
 15 | n_app=5000;
 16 | 
 17 | error_Fair_SC=zeros(anz_runs,length(k_range),length(factor_range));
 18 | 
 19 | for mmm=1:length(k_range)
 20 |     
 21 |     k=k_range(mmm);
 22 |     n=ceil(n_app/(k*h))*(k*h);
 23 |     block_sizes=(n/(k*h))*ones(1,k*h);
 24 |         
 25 |     sensitive=zeros(n,1);
 26 |     labels=zeros(n,1);
 27 |     for yyy=1:k
 28 |         for zzz=1:h
 29 |             sensitive(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=zzz;
 30 |             labels(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=yyy;
 31 |         end
 32 |     end
 33 |     
 34 |     
 35 |     
 36 |     for hg=1:length(factor_range)
 37 |         
 38 |         a=af*factor_range(hg);
 39 |         b=bf*factor_range(hg);
 40 |         c=cf*factor_range(hg);
 41 |         d=df*factor_range(hg);
 42 |     
 43 |         for ell=1:anz_runs
 44 | 
 45 |             adja=generate_adja_SB_model(n,a,b,c,d,k,h,block_sizes);
 46 | 
 47 |             FAIR_clustering_SC=Fair_SC_unnormalized(adja,k,sensitive);
 48 |             
 49 |             error_Fair_SC(ell,mmm,hg)=clustering_accuracy(labels, FAIR_clustering_SC);
 50 | 
 51 |         end    
 52 | 
 53 |     end
 54 | end
 55 | 
 56 | 
 57 |         
 58 | %set default sizes for figures:
 59 | ulesfontsize = 24;
 60 | set(0, 'DefaultAxesFontSize', ulesfontsize);
 61 | set(0, 'DefaultTextFontSize', ulesfontsize);
 62 | set(0, 'DefaultUIControlFontSize', ulesfontsize);
 63 | set(0,'DefaultLineMarkerSize',ulesfontsize);
 64 | set(0,'DefaultLineLineWidth',1.5) 
 65 | set(gcf, 'PaperPositionMode','auto')
 66 | close all;
 67 |     
 68 | sfname=strcat('_SB_model_as_function_of_k_with_n~',num2str(n_app),'_h=',num2str(h),'_runs=',num2str(anz_runs),'_LeftPlot');
 69 | 
 70 | %save(strcat('DATA',sfname,'.mat'))
 71 | 
 72 | figure(1);clf;
 73 | plot(k_range,mean(error_Fair_SC(:,:,1),1),'Marker','x','DisplayName',strcat('F=',num2str(factor_range(1))))
 74 | hold on
 75 | for hg=2:length(factor_range)
 76 |     plot(k_range,mean(error_Fair_SC(:,:,hg),1),'Marker','x','DisplayName',strcat('F=',num2str(factor_range(hg))))
 77 | end  
 78 | hold off
 79 | legend
 80 | xlabel('k')
 81 | ylabel('Error')
 82 | ylim([0,1])
 83 | title(strcat('FAIR SC (Alg. 2) --- n~',num2str(n_app),', h=',num2str(h)),'FontWeight','normal')
 84 | saveas(1,strcat('Error',sfname))
 85 | print(1,'-dpdf',strcat('Error',sfname))
 86 | 
 87 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 88 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 89 | 
 90 | 
 91 | 
 92 | 
 93 | 
 94 | 
 95 | 
 96 | %%%% RIGHT PLOT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 97 |  
 98 | n_app=2000;
 99 | 
100 | error_Fair_SC_Normalized=zeros(anz_runs,length(k_range));
101 | 
102 | for mmm=1:length(k_range)
103 |     
104 |     k=k_range(mmm);
105 |     n=ceil(n_app/(k*h))*(k*h);
106 |     block_sizes=(n/(k*h))*ones(1,k*h);
107 |     
108 |     sensitive=zeros(n,1);
109 |     labels=zeros(n,1);
110 |     for yyy=1:k
111 |         for zzz=1:h
112 |             sensitive(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=zzz;
113 |             labels(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=yyy;
114 |         end
115 |     end
116 |         
117 |     
118 |     
119 |     for hg=1:length(factor_range)
120 |         
121 |         a=af*factor_range(hg);
122 |         b=bf*factor_range(hg);
123 |         c=cf*factor_range(hg);
124 |         d=df*factor_range(hg);
125 |     
126 |         for ell=1:anz_runs
127 | 
128 |             adja=generate_adja_SB_model(n,a,b,c,d,k,h,block_sizes);
129 | 
130 |             FAIR_clustering_SC_NORMALIZED=Fair_SC_normalized(adja,k,sensitive);
131 |             
132 |             error_Fair_SC_Normalized(ell,mmm,hg)=clustering_accuracy(labels,FAIR_clustering_SC_NORMALIZED);
133 | 
134 |         end    
135 | 
136 |     end
137 | end        
138 |         
139 |         
140 |         
141 | %set default sizes for figures:
142 | ulesfontsize = 24;
143 | set(0, 'DefaultAxesFontSize', ulesfontsize);
144 | set(0, 'DefaultTextFontSize', ulesfontsize);
145 | set(0, 'DefaultUIControlFontSize', ulesfontsize);
146 | set(0,'DefaultLineMarkerSize',ulesfontsize);
147 | set(0,'DefaultLineLineWidth',1.5) 
148 | set(gcf, 'PaperPositionMode','auto')
149 | close all;
150 | 
151 | sfname=strcat('_SB_model_as_function_of_k_with_n~',num2str(n_app),'_h=',num2str(h),'_runs=',num2str(anz_runs),'_RightPlot');
152 | 
153 | %save(strcat('DATA',sfname,'.mat'))
154 | 
155 | figure(1);clf;
156 | plot(k_range,mean(error_Fair_SC_Normalized(:,:,1),1),'Marker','x','DisplayName',strcat('F=',num2str(factor_range(1))))
157 | hold on
158 | for hg=2:length(factor_range)
159 |     plot(k_range,mean(error_Fair_SC_Normalized(:,:,hg),1),'Marker','x','DisplayName',strcat('F=',num2str(factor_range(hg))))
160 | end  
161 | hold off
162 | legend
163 | xlabel('k')
164 | ylabel('Error')
165 | ylim([0,1])
166 | title(strcat('FAIR Norm. SC (Alg. 3) --- n~',num2str(n_app),', h=',num2str(h)),'FontWeight','normal')
167 | saveas(1,strcat('Error',sfname))
168 | print(1,'-dpdf',strcat('Error',sfname))
169 | 
170 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
171 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
172 | 
173 | 
174 |     


--------------------------------------------------------------------------------
/experiments_Figure4.m:
--------------------------------------------------------------------------------
  1 | anz_runs=10;
  2 | perturbation_range=0:0.05:1;
  3 | k=4;
  4 | h=2;
  5 | 
  6 | 
  7 | 
  8 | %%%% LEFT PLOT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  9 | 
 10 | n=4000;
 11 | 
 12 | a=0.4;
 13 | b=0.3;
 14 | c=0.2;
 15 | d=0.1;
 16 | 
 17 | 
 18 | error_SC=zeros(anz_runs,length(perturbation_range));
 19 | error_SC_Normalized=zeros(anz_runs,length(perturbation_range));
 20 | error_Fair_SC=zeros(anz_runs,length(perturbation_range));
 21 | error_Fair_SC_Normalized=zeros(anz_runs,length(perturbation_range));
 22 | 
 23 | for mmm=1:length(perturbation_range)
 24 |     
 25 |     pp=perturbation_range(mmm);
 26 |     block_sizes=(n/(k*h))*ones(1,k*h);
 27 |     
 28 |         
 29 |     for ell=1:anz_runs
 30 |     
 31 |         sensitive=zeros(n,1);
 32 |         labels=zeros(n,1);
 33 |         for yyy=1:k
 34 |             for zzz=1:h
 35 |                 sensitive(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=zzz;
 36 |                 labels(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=yyy;
 37 |             end
 38 |         end
 39 |         
 40 |     
 41 |         temp1=random('binomial',1,pp,n,1);
 42 |         
 43 |         sensitive((temp1==1)&(sensitive==1))=2;
 44 |         
 45 |         adja=generate_adja_SB_model(n,a,b,c,d,k,h,block_sizes);
 46 |         
 47 |         clustering_SC=SC_unnormalized(adja,k);
 48 |         error_SC(ell,mmm)=clustering_accuracy(labels,clustering_SC);
 49 |         
 50 |         clustering_SC_NORMALIZED=SC_normalized(adja,k);
 51 |         error_SC_Normalized(ell,mmm)=clustering_accuracy(labels,clustering_SC_NORMALIZED);
 52 |         
 53 |         FAIR_clustering_SC=Fair_SC_unnormalized(adja,k,sensitive);
 54 |         error_Fair_SC(ell,mmm)=clustering_accuracy(labels, FAIR_clustering_SC);
 55 |         
 56 |         FAIR_clustering_SC_NORMALIZED=Fair_SC_normalized(adja,k,sensitive);
 57 |         error_Fair_SC_Normalized(ell,mmm)=clustering_accuracy(labels,FAIR_clustering_SC_NORMALIZED);
 58 |         
 59 |     end
 60 | end
 61 | 
 62 | 
 63 | %set default sizes for figures:
 64 | ulesfontsize = 24;
 65 | set(0, 'DefaultAxesFontSize', ulesfontsize);
 66 | set(0, 'DefaultTextFontSize', ulesfontsize);
 67 | set(0, 'DefaultUIControlFontSize', ulesfontsize);
 68 | set(0,'DefaultLineMarkerSize',ulesfontsize);
 69 | set(0,'DefaultLineLineWidth',1.5) 
 70 | set(gcf, 'PaperPositionMode','auto')
 71 | close all;
 72 | 
 73 | sfname=strcat('_SB_model_as_function_of_perturbation_with_n=',num2str(n),'_k=',num2str(k),'_h=',num2str(h),'_runs=',num2str(anz_runs),'_LeftPlot');
 74 | 
 75 | %save(strcat('DATA',sfname,'.mat'))
 76 | 
 77 | figure(1);clf;
 78 | plot(perturbation_range,mean(error_SC,1),'mo-.',perturbation_range,mean(error_SC_Normalized,1),'gs-.',perturbation_range,mean(error_Fair_SC,1),'rx-',perturbation_range,mean(error_Fair_SC_Normalized,1),'bx-')
 79 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)')
 80 | xlabel('p')
 81 | ylabel('Error')
 82 | ylim([0,1])
 83 | title(strcat('n=',num2str(n),', k=',num2str(k),', h=',num2str(h),' --- a=',num2str(a),', b=',num2str(b),', c=',num2str(c),', d=',num2str(d)),'FontWeight','normal')
 84 | saveas(1,strcat('Error',sfname))
 85 | print(1,'-dpdf',strcat('Error',sfname))
 86 | 
 87 | 
 88 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 89 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 90 | 
 91 | 
 92 | 
 93 | 
 94 | 
 95 | 
 96 | %%%% RIGHT PLOT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 97 | 
 98 | n=2000;
 99 | 
100 | a=0.5;
101 | b=0.4;
102 | c=0.3;
103 | d=0.1;
104 | 
105 | 
106 | error_SC=zeros(anz_runs,length(perturbation_range));
107 | error_SC_Normalized=zeros(anz_runs,length(perturbation_range));
108 | error_Fair_SC=zeros(anz_runs,length(perturbation_range));
109 | error_Fair_SC_Normalized=zeros(anz_runs,length(perturbation_range));
110 | 
111 | for mmm=1:length(perturbation_range)
112 |     
113 |     pp=perturbation_range(mmm);
114 |     block_sizes=(n/(k*h))*ones(1,k*h);
115 |     
116 |         
117 |     for ell=1:anz_runs
118 |     
119 |         sensitive=zeros(n,1);
120 |         labels=zeros(n,1);
121 |         for yyy=1:k
122 |             for zzz=1:h
123 |                 sensitive(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=zzz;
124 |                 labels(((n/k)*(yyy-1)+(n/(k*h))*(zzz-1)+1):((n/k)*(yyy-1)+(n/(k*h))*zzz))=yyy;
125 |             end
126 |         end
127 |         
128 |     
129 |         temp1=random('binomial',1,pp,n,1);
130 |         
131 |         sensitive((temp1==1)&(sensitive==1))=2;
132 |         
133 |         adja=generate_adja_SB_model(n,a,b,c,d,k,h,block_sizes);
134 |         
135 |         clustering_SC=SC_unnormalized(adja,k);
136 |         error_SC(ell,mmm)=clustering_accuracy(labels,clustering_SC);
137 |         
138 |         clustering_SC_NORMALIZED=SC_normalized(adja,k);
139 |         error_SC_Normalized(ell,mmm)=clustering_accuracy(labels,clustering_SC_NORMALIZED);
140 |         
141 |         FAIR_clustering_SC=Fair_SC_unnormalized(adja,k,sensitive);
142 |         error_Fair_SC(ell,mmm)=clustering_accuracy(labels, FAIR_clustering_SC);
143 |         
144 |         FAIR_clustering_SC_NORMALIZED=Fair_SC_normalized(adja,k,sensitive);
145 |         error_Fair_SC_Normalized(ell,mmm)=clustering_accuracy(labels,FAIR_clustering_SC_NORMALIZED);
146 |         
147 |     end
148 | end
149 | 
150 | 
151 | %set default sizes for figures:
152 | ulesfontsize = 24;
153 | set(0, 'DefaultAxesFontSize', ulesfontsize);
154 | set(0, 'DefaultTextFontSize', ulesfontsize);
155 | set(0, 'DefaultUIControlFontSize', ulesfontsize);
156 | set(0,'DefaultLineMarkerSize',ulesfontsize);
157 | set(0,'DefaultLineLineWidth',1.5) 
158 | set(gcf, 'PaperPositionMode','auto')
159 | close all;
160 | 
161 | sfname=strcat('_SB_model_as_function_of_perturbation_with_n=',num2str(n),'_k=',num2str(k),'_h=',num2str(h),'_runs=',num2str(anz_runs),'_RightPlot');
162 | 
163 | %save(strcat('DATA',sfname,'.mat'))
164 | 
165 | figure(1);clf;
166 | plot(perturbation_range,mean(error_SC,1),'mo-.',perturbation_range,mean(error_SC_Normalized,1),'gs-.',perturbation_range,mean(error_Fair_SC,1),'rx-',perturbation_range,mean(error_Fair_SC_Normalized,1),'bx-')
167 | legend('SC (Alg. 1)','Normalized SC','FAIR SC (Alg. 2)','FAIR Norm. SC (Alg. 3)')
168 | xlabel('p')
169 | ylabel('Error')
170 | ylim([0,1])
171 | title(strcat('n=',num2str(n),', k=',num2str(k),', h=',num2str(h),' --- a=',num2str(a),', b=',num2str(b),', c=',num2str(c),', d=',num2str(d)),'FontWeight','normal')
172 | saveas(1,strcat('Error',sfname))
173 | print(1,'-dpdf',strcat('Error',sfname))
174 | 
175 | 
176 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
177 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
178 | 
179 | 


--------------------------------------------------------------------------------
/generate_adja_SB_model.m:
--------------------------------------------------------------------------------
 1 | function A=generate_adja_SB_model(n,a,b,c,d,k,h,block_sizes)
 2 | %generates
 3 | %
 4 | %INPUT:
 5 | %n ... number of elements
 6 | %a,b,c,d ... parameters / probabilities
 7 | %k ... number of clusters
 8 | %h ... number of groups
 9 | %block_sizes ... vector of length k*h with sum(block_sizes)=n; the 
10 | %                first h entries correspond to the first cluster for 
11 | %                the h groups, and so on ... 
12 | %
13 | %OUTPUT
14 | %A ... adjacency matrix of size n x n
15 | 
16 | 
17 | if (sum(block_sizes)~=n)||(length(block_sizes)~=(k*h))
18 |     error('wrong input')
19 | end
20 | 
21 | adja=random('Binomial',1,d,n,n);
22 | 
23 | for ell=1:k
24 |     for mmm=1:k
25 |         for ggg=1:h
26 |             for fff=1:h
27 |                 if ell==mmm
28 |                     if ggg==fff
29 |                         adja((sum(block_sizes(1:((ell-1)*h+(ggg-1))))+1):(sum(block_sizes(1:((ell-1)*h+(ggg))))),...
30 |                             (sum(block_sizes(1:((ell-1)*h+(ggg-1))))+1):(sum(block_sizes(1:((ell-1)*h+(ggg))))))=random('Binomial',1,a,block_sizes((ell-1)*h+(ggg)),block_sizes((ell-1)*h+(ggg)));
31 |                     else
32 |                         adja((sum(block_sizes(1:((ell-1)*h+(ggg-1))))+1):(sum(block_sizes(1:((ell-1)*h+(ggg))))),...
33 |                             (sum(block_sizes(1:((ell-1)*h+(fff-1))))+1):(sum(block_sizes(1:((ell-1)*h+(fff))))))=random('Binomial',1,c,block_sizes((ell-1)*h+(ggg)),block_sizes((ell-1)*h+(fff)));
34 |                     end
35 |                     
36 |                 else
37 |                     if ggg==fff
38 |                         adja((sum(block_sizes(1:((ell-1)*h+(ggg-1))))+1):(sum(block_sizes(1:((ell-1)*h+(ggg))))),...
39 |                                 (sum(block_sizes(1:((mmm-1)*h+(ggg-1))))+1):(sum(block_sizes(1:((mmm-1)*h+(ggg))))))=random('Binomial',1,b,block_sizes((ell-1)*h+(ggg)),block_sizes((mmm-1)*h+(ggg)));
40 |                     end
41 |                 end
42 |             end
43 |         end
44 |     end
45 | end
46 |             
47 | 
48 | 
49 | 
50 | A=triu(adja,1);
51 | A=A+A';


--------------------------------------------------------------------------------