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demo_conditional_correlation.m
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demo_conditional_correlation.m
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function results = demo_conditional_covariance(X,Y,varargin)
opts = struct();
opts.exportfig = true;
opts.exportfun = @(fname)(print('-dpng','-r300',fname));
% if(exist('process_options'))
% [exportfig exportfun opts] = process_options(varargin, ...
% 'exportfig', opts.exportfig, ...
% 'exportfun', opts.exportfun ...
% );
% else
% warning('KPMTools from matlab-library needed to process optional arguments');
% end
exportfig = opts.exportfig;
exportfun = opts.exportfun;
fname = ['tmp' filesep datestr(now,'dd-mmm-yyyy-HHMM')];
if(~exist(fname,'dir'))
mkdir(fname)
end
opts.outputdir = fname;
results = {};
results{1}.method = 'Sample Correlation';
results{1}.output = standard_correlation(X);
results{2}.method = 'RC, Sample Correlation';
results{2}.output = standard_correlation_sn(X);
results{3}.method = 'Nuisance Correlation';
results{3}.output = conditional_correlation(X,Y);
results{4}.method = 'Denoised Sample Correlation';
results{4}.output = results{3}.output;
results{4}.output.corr = results{3}.output.corr;
disp(sprintf('Frob. MSE: Sigma_std - Sigma_cond = %.3f', ...
norm(abs(results{1}.output.corr-results{3}.output.corr),'fro')));
disp(sprintf('Frob. SSE: Sigma_std - Sigma_cond = %.3f', ...
sum(sum((results{1}.output.corr-results{3}.output.corr).^2)) ));
if(exist('brewermap'))
colormapfun = @()(brewermap(length(colormap),'RdYlBu'));
close all;
else
colormapfun = @winter;
end
addpath(genpath('../MATLAB/packages/spreadFigures/tightfig/'));
figure(1);
set(gcf,'Position',[10 150 1200 650]);
subplot(2,2,1);
imagesc(results{1}.output.corr);
colormap(colormapfun()); axis image; colorbar;;
title(results{1}.method);
set(gca,'fontsize',16);
subplot(2,2,2);
imagesc(results{3}.output.nuisance);
colormap(colormapfun()); axis image; colorbar;
title(results{3}.method);
set(gca,'fontsize',16);
subplot(2,2,3);
imagesc(results{4}.output.corr);
colormap(colormapfun()); axis image; colorbar;;
title(results{4}.method);
set(gca,'fontsize',16);
subplot(2,2,4);
imagesc(results{2}.output.corr);
colormap(colormapfun()); axis image; colorbar;
title(results{2}.method);
set(gca,'fontsize',16);
exportfun(fullfile(fname,mfilename));
% if(exist('tightfig'))
% tightfig;
% end
figure(2)
set(gcf,'Position',[10 150 1200 650]);
subplot(2,2,1);
upper_idx = find(reshape(triu(ones(size(results{1}.output.corr)),1), ...
[1 numel(results{1}.output.corr)]));
histogram(results{1}.output.corr(upper_idx),'Normalization','probability');
ylim([-1.2 1.2]);axis tight;
title(results{1}.method); xlabel('correlation'); ylabel('pdf')
set(gca,'fontsize',16);
subplot(2,2,2);
histogram(results{3}.output.nuisance(upper_idx),'Normalization','probability');
ylim([-1.2 1.2]);axis tight;
title(results{3}.method);xlabel('correlation'); ylabel('pdf')
set(gca,'fontsize',16);
subplot(2,2,3);
histogram(results{4}.output.corr(upper_idx),'Normalization','probability');
ylim([-1.2 1.2]);axis tight;
title(results{4}.method);xlabel('correlation'); ylabel('pdf')
set(gca,'fontsize',16);
subplot(2,2,4);
histogram(results{2}.output.corr(upper_idx),'Normalization','probability');
ylim([-1.2 1.2]);axis tight;
title(results{2}.method);xlabel('correlation'); ylabel('pdf')
set(gca,'fontsize',16);
% if(exist('tightfig'))
% tightfig;
% end
exportfun(fullfile(fname,[mfilename '2']));
end
function output = standard_correlation(X)
% Usual standard correlation matrix
output = struct();
[Sigma results] = covariance.mle_sample_covariance(X, ...
struct('standardize',false));
output.corr = Sigma;
end
function output = standard_correlation_sn(X)
% Automatically applies row-first successive norm
%standardize.successive_normalize(X');
output = struct();
[Sigma results] = covariance.mle_sample_covariance(X, ...
struct('standardize',true));
output.corr = Sigma;
end
function output = conditional_correlation(X,Y)
% Only uses usual column standardize (i.e. correlation)
output = struct();
%[Sigma results] = covariance.conditional_sample_covariance_separate(X);
[~, results] = covariance.conditional_sample_covariance_separate(X, ...
struct('verbose',true,...
'nuisance',Y) ...
);
output.corr = results.Sigma;
output.nuisance = results.nCov;
output.corr2 = covariance.mle_sample_covariance(results.X_perpY, ...
struct('standardize',false));
end