jordan@2: function [asig pval a a_] = do_correlation(megacube, songs, metrics, algos, algo_groups, merge_algos, merge_songs, merge_dsets, metric_labels, bonferroni)
jordan@2: 
jordan@2: % function [asig pval a a_] = do_correlation(megacube, songs, metrics, algos, algo_groups, merge_algos, merge_songs, merge_dsets, metric_labels, bonferroni)
jordan@2: %
jordan@2: % Script to make and analyze correlation plot.
jordan@2: % Example usage:
jordan@2: %    To run your first experiment (Fig 1a) request:
jordan@2: %    do_correlation(megacube, lab_measures, sind_manual1, [1:9], -1, 0, 1, -1, s_manual1)
jordan@2: %
jordan@2: % MEGACUBE is the giant (N songs) x (M metrics) x (L algorithms) matrix of evaluation results.
jordan@2: % SONGS, METRICS and ALGOS are the indices into these three dimensions desired.
jordan@2: % ALGO_GROUPS indicates groups of algorithms that should be averaged together rather than counted separately.
jordan@2: %    (this has not yet been implemented)
jordan@2: % Set MERGE_ALGOS > 0 in order to compute the median score across algorithms.
jordan@2: % Set MERGE_SONGS > 0 in order to compute the median score across songs.
jordan@2: % MERGE_DSETS is also not yet implemented.
jordan@2: % METRIC_LABELS is a matrix of strings, one for each of the METRICS, for use in plotting.
jordan@2: % Set BONFERRONI > 0 in order to apply a bonferroni correction of BONFERRONI. (Default value: 0.05.)
jordan@2: % Note a few hard-coded decisions, such as:
jordan@2: %   - significance level hard coded as 0.05.
jordan@2: %   - in the image, decision that tau > 0.8 is strong, tau > 0.33 is weak, and tau < 0.33 is nothing.
jordan@2: 
jordan@2: % Defaults and hard coding values:
jordan@2: if nargin<10,
jordan@2:     bonferroni = 0.05;
jordan@2: end
jordan@2: significant_p = 0.05;
jordan@2: maxtau = 0.8;
jordan@2: mintau = 0.33;
jordan@2: 
jordan@2: 
jordan@2: 
jordan@2: tmpcube = megacube(songs,metrics,algos);
jordan@2: 
jordan@2: % if exist('algo_groups'),
jordan@2: %     for i=1:length(algo_groups),
jordan@2: %         merge the groups somehow...
jordan@2: %     end
jordan@2: % end
jordan@2: 
jordan@2: if merge_algos>0,                   % If we merge algorithms, take the median score across algorithms.
jordan@2:     tmpcube = median(tmpcube,3);
jordan@2: elseif merge_songs>0,               % If we merge songs, take the median score across songs.
jordan@2:     tmpcube = median(tmpcube,1);    % Then, resize the matrix to be 2-d:
jordan@2:     tmpcube = transpose(reshape(tmpcube,size(tmpcube,2),size(tmpcube,3)));
jordan@2: end
jordan@2: 
jordan@2: % Compute Kendall tau correlation:
jordan@2: [a pval] = corr(tmpcube,'type','Kendall');
jordan@2: % Apply bonferroni correction:
jordan@2: m = length(a)*(length(a)-1)/2;
jordan@2: asig = pval<significant_p;
jordan@2: if bonferroni>0,
jordan@2:     fprintf('Bonferroni applied.\n')
jordan@2:     asig = (pval*m)<bonferroni; % This is the matrix of values that are significant.
jordan@2: end
jordan@2: a_ = (abs(a)>=maxtau) + (abs(a)>=mintau);
jordan@2: a_ = tril(a_,-1);
jordan@2: 
jordan@2: % A contains the correlation values themselves.
jordan@2: % ASIG is a binary matrix that states whether the correlation is statistically significant.
jordan@2: % A_ is a matrix of -2, -1, 0, 1 and 2s that says whether a correlation is qualitatively strong (2), qualitatively weak (1), or nada (0).
jordan@2: % Sometimes values will be statistically significant, but qualitatively insignificant. We do not want to bother looking at these, so
jordan@2: % let us make our pretty picture carefully.
jordan@2: 
jordan@2: % The values we display will always be straight from A. The colour we display, to emphasize the strong correlations,
jordan@2: % should be the element-wise product of A, ASIG, and A_.
jordan@2: % Also:
jordan@2: %   Iff tau>0.33 (a_>0), include text.
jordan@2: %   Iff tau is significant (asig=1), include background.
jordan@2: %   Iff tau>0.8 (a_=2), put in bold.
jordan@2: %   Iff tau>0.8 AND tau is significant, invert the color of the text (because the colour will be darker).
jordan@2: 
jordan@2: img = a_.*a.*asig;
jordan@2: img = img(2:end,1:end-1);   % ignore the diagonal
jordan@2: clf
jordan@2: imagesc(img, [-1 1])
jordan@2: for i=1:length(a_),
jordan@2:     for j=1:length(a_),
jordan@2:         if a_(i,j)>0,
jordan@2:             % tau is >0.33 so we definitely write the value. need to determine fontface and colour.
jordan@2:             % if tau>.8, put in bold
jordan@2:             if abs(a_(i,j))>1,
jordan@2:                 fontw = 'bold';
jordan@2:             else
jordan@2:                 fontw = 'normal';
jordan@2:             end
jordan@2:             if abs(a_(i,j))>1 & asig(i,j)==1,
jordan@2:                 textcolor = [1 1 1];
jordan@2:             else
jordan@2:                 textcolor = [0 0 0];
jordan@2:             end
jordan@2:             % h = text(j-.35,i-1,num2str(a(i,j),2),'Color',textcolor);
jordan@2:             h = text(j,i-1,sprintf('%.2f',a(i,j)),'Color',textcolor,'FontWeight',fontw,'FontSize',12,'HorizontalAlignment','center');
jordan@2:             set(h,'HorizontalAlignment','center')
jordan@2:         end
jordan@2:     end
jordan@2: end
jordan@2: cmap_el = transpose([linspace(.3,1,50)]);
jordan@2: cmap = repmat(cmap_el,1,3);
jordan@2: cmap = [cmap; flipud(cmap)];
jordan@2: % Alternatively:
jordan@2: cmap = [ones(size(cmap_el)) cmap_el cmap_el; flipud([cmap_el cmap_el ones(size(cmap_el))])];
jordan@2: colormap(cmap);
jordan@2: 
jordan@2: set(gca,'YTickLabel',metric_labels(2:end),'YTick',(1:length(a)-1),'FontAngle','italic','FontSize',12)
jordan@2: set(gca,'XTickLabel',metric_labels(1:end-1),'XTick',(1:length(a)-1),'FontAngle','italic','FontSize',12)
jordan@2: % set(gcf,'Position',[1000,1000,700,300])
jordan@2: % set(gca,'XTickLabel',metric_labels(2:2:end),'YTick',(1:length(a)/2))
jordan@2: 
jordan@2: % axis([0.5, length(a)-.5, 1.5, length(a)+.5])