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102 lines
3.8 KiB
Matlab
102 lines
3.8 KiB
Matlab
function pcbc_prob_2integrate()
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%perform optimal feature integration given two Gaussian probability distributions
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inputs=[-180:10:180];
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centres=[-180:15:180];
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%define weights, to produce a 2d basis function network, where nodes have gaussian RFs.
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W=[];
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for c=centres
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W=[W;code(c,inputs,15,0,1),code(c,inputs,15,0,1)];
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end
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W=W./2;
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[n,m]=size(W);
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%define test cases
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stdx=20;
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X=zeros(m,4);
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X(:,1)=[code(-20,inputs,20,0,0,stdx),code(-10,inputs,20,0,0,stdx)]';
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X(:,2)=[code(-20,inputs,20,0,0,stdx),code(-10,inputs,40,0,0,stdx)]';
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X(:,3)=[code(-20,inputs,20,0,0,stdx),code(70,inputs,20,0,0,stdx)]';
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X(:,4)=[code(-20,inputs,20,0,0,stdx)+code(50,inputs,20,0,0,stdx),code(70,inputs,20,0,0,stdx)]';
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%present test cases to network and record results
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for k=1:size(X,2)
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x=X(:,k);
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[y,e,r]=dim_activation(W,x);
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figure(k),clf
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plot_result2(x,r,y,2,inputs,centres);
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if k<3, hold on, plot(x(1:length(inputs))'.*x(1+length(inputs):end)','LineWidth',3); end
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print(gcf, '-dpdf', ['probability_2integrate',int2str(k),'.pdf']);
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end
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%test accuracy across many random trials (Ma et al's method)
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numTrials=1008
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numTests=100
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compare_means=zeros(numTests,2);
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compare_vars=zeros(numTests,2);
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for k=1:numTests
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fprintf(1,'.%i.',k);
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%select parameters of input
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mu1=0;
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mu2=mu1+(24*rand-12);
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sigma1=20+40*rand;
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sigma2=20+40*rand;
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%for these parameters average estimates over many trials
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for trial=1:numTrials
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%batch together all trials fo faster execution of dim
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x(:,trial)=[code(mu1,inputs,sigma1,1,0,stdx),code(mu2,inputs,sigma2,1,0,stdx)]';
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end
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[y,e,r]=dim_activation(W,x);
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mu3Mean=[];
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var3Mean=[];
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mu3estMean=[];
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var3estMean=[];
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for trial=1:numTrials
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%analyse results from each trial
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[mu1act,var1act]=decode(x(1:length(inputs),trial)',inputs);
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[mu2act,var2act]=decode(x(1+length(inputs):end,trial)',inputs);
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[mu3Mean(trial),var3Mean(trial)]=stats_gaussian_combination([mu1act,mu2act],[var1act,var2act]);
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[mu3estMean(trial),var3estMean(trial)]=decode(r(1:length(inputs),trial)',inputs,2);
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end
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%take average results across trials
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compare_means(k,:)=[nanmean(mu3Mean),nanmean(mu3estMean)];
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compare_vars(k,:)=[nanmean(var3Mean),nanmean(var3estMean)];
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end
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disp(' ')
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figure(size(X,2)+1),clf
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plot(compare_means(:,1),compare_means(:,2),'o','MarkerFaceColor','b','MarkerSize',6);
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hold on
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plot([-10,10],[-10,10],'k--','LineWidth',2)
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set(gca,'YTick',[-8:8:8],'XTick',[-8:8:8],'FontSize',15)
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axis('equal','tight')
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xlabel('Optimal Estimate of Mean ');
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ylabel('Network Estimate of Mean ')
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set(gcf,'PaperSize',[10 8],'PaperPosition',[0 0.25 10 7.5],'PaperOrientation','Portrait');
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print(gcf, '-dpdf', ['probability_2integrate_mean_accuracy.pdf']);
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figure(size(X,2)+2),clf
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plot(compare_vars(:,1),compare_vars(:,2),'o','MarkerFaceColor','b','MarkerSize',6);
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hold on
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plot([100,1800],[100,1800],'k--','LineWidth',2)
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set(gca,'YTick',[500:500:1500],'YTickLabel',' ','XTick',[500:500:1500],'FontSize',15)
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text([100,100,100]-10,[500:500:1500],int2str([500:500:1500]'),'Rotation',90,'VerticalAlignment','bottom','HorizontalAlignment','center','FontSize',15)
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axis('equal','tight')
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xlabel({'Optimal Estimate of \sigma^2 ';' '});
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ylabel({'Network Estimate of \sigma^2 ';' '});
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set(gcf,'PaperSize',[10 8],'PaperPosition',[0 0.25 10 7.5],'PaperOrientation','Portrait');
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print(gcf, '-dpdf', ['probability_2integrate_var_accuracy.pdf']);
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error=abs(compare_means(:,1)-compare_means(:,2));
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disp('Comparing Means (difference between network and optimal estimate)')
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disp([' Max=',num2str(max(error)),' Median=',num2str(median(error)),' Mean=',num2str(mean(error))]);
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error=100.*abs(compare_vars(:,1)-compare_vars(:,2))./compare_vars(:,1);
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disp('Comparing Variances (% difference between network and optimal estimate)')
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disp([' Max=',num2str(max(error)),' Median=',num2str(median(error)),' Mean=',num2str(mean(error))]);
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