Mercurial > hg > smallbox
changeset 200:69ce11724b1f luisf_dev
Added dictionary decorrelation for multiple dictionaries
| author | bmailhe |
|---|---|
| date | Tue, 20 Mar 2012 12:25:50 +0000 |
| parents | d50f5bdbe14c |
| children | 5140b0e06c22 |
| files | DL/two-step DL/dico_color_separate.m DL/two-step DL/dico_decorr_symetric.m |
| diffstat | 2 files changed, 201 insertions(+), 28 deletions(-) [+] |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/DL/two-step DL/dico_color_separate.m Tue Mar 20 12:25:50 2012 +0000 @@ -0,0 +1,95 @@ +function [colors nbColors] = dico_color_separate(dico, mu) + % DICO_COLOR cluster several dictionaries in pairs of high correlation + % atoms. Called by dico_decorr. + % + % Parameters: + % -dico: the dictionaries + % -mu: the correlation threshold + % + % Result: + % -colors: a cell array of indices. Two atoms with the same color have + % a correlation greater than mu + + + numDico = length(dico); + colors = cell(numDico,1); + for i = 1:numDico + colors{i} = zeros(length(dico{i}),1); + end + + G = cell(numDico); + + % compute the correlations + for i = 1:numDico + for j = i+1:numDico + G{i,j} = abs(dico{i}'*dico{j}); + end + end + + % iterate on the correlations higher than mu + c = 1; + [maxCorr, i, j, m, n] = findMaxCorr(G); + while maxCorr > mu + % find the highest correlated pair + + % color them + colors{i}(m) = c; + colors{j}(n) = c; + c = c+1; + + % make sure these atoms never get selected again + % Set to zero relevant lines in the Gram Matrix + for j2 = i+1:numDico + G{i,j2}(m,:) = 0; + end + + for i2 = 1:i-1 + G{i2,i}(:,m) = 0; + end + + for j2 = j+1:numDico + G{j,j2}(n,:) = 0; + end + + for i2 = 1:j-1 + G{i2,j}(:,n) = 0; + end + + % find the next correlation + [maxCorr, i, j, m, n] = findMaxCorr(G); + end + + % complete the coloring with singletons + % index = find(colors==0); + % colors(index) = c:c+length(index)-1; + nbColors = c-1; +end + +function [val, i, j, m, n] = findMaxCorr(G) + %FINDMAXCORR find the maximal correlation in the cellular Gram matrix + % + % Input: + % -G: the Gram matrix + % + % Output: + % -val: value of the correlation + % -i,j,m,n: indices of the argmax. The maximal correlation is reached + % for the m^th atom of the i^th dictionary and the n^h atom of the + % j^h dictionary + + val = -1; + for tmpI = 1:length(G) + for tmpJ = tmpI+1:length(G) + [tmpVal tmpM] = max(G{tmpI,tmpJ},[],1); + [tmpVal tmpN] = max(tmpVal); + if tmpVal > val + val = tmpVal; + i = tmpI; + j = tmpJ; + n = tmpN; + m = tmpM(n); + end + end + end +end + \ No newline at end of file
--- a/DL/two-step DL/dico_decorr_symetric.m Wed Mar 14 14:42:52 2012 +0000 +++ b/DL/two-step DL/dico_decorr_symetric.m Tue Mar 20 12:25:50 2012 +0000 @@ -1,15 +1,17 @@ -function dico = dico_decorr_symetric(dico, mu, amp) +function dico = dico_decorr_symetric(dico, mu) %DICO_DECORR decorrelate a dictionary % Parameters: - % dico: the dictionary + % dico: the dictionary, either a matrix or a cell array of matrices. % mu: the coherence threshold - % amp: the amplitude coefficients, only used to decide which atom to - % project % % Result: - % dico: a dictionary close to the input one with coherence mu. + % dico: if the input dico was a matrix, then a matrix close to the + % input one with coherence mu. + % If the input was a cell array, a cell array of the same size + % containing matrices such that the coherence between different cells + % is lower than mu. - eps = 1e-6; % define tolerance for normalisation term alpha + eps = 1e-3; % define tolerance for normalisation term alpha % convert mu to the to the mean direction theta = acos(mu)/2; @@ -23,39 +25,115 @@ % rank = randperm(length(dico)); % end - % several decorrelation iterations might be needed to reach global - % coherence mu. niter can be adjusted to needs. - niter = 1; - while max(max(abs(dico'*dico -eye(length(dico))))) > mu + 0.01 - % find pairs of high correlation atoms - colors = dico_color(dico, mu); + % if only one dictionary is provided, then decorrelate it + if ~iscell(dico) + % several decorrelation iterations might be needed to reach global + % coherence mu. niter can be adjusted to needs. + niter = 1; + while max(max(abs(dico'*dico -eye(length(dico))))) > mu + eps + % find pairs of high correlation atoms + colors = dico_color(dico, mu); + + % iterate on all pairs + nbColors = max(colors); + for c = 1:nbColors + index = find(colors==c); + if numel(index) == 2 + if dico(:,index(1))'*dico(:,index(2)) > 0 + %build the basis vectors + v1 = dico(:,index(1))+dico(:,index(2)); + v1 = v1/norm(v1); + v2 = dico(:,index(1))-dico(:,index(2)); + v2 = v2/norm(v2); + + dico(:,index(1)) = ctheta*v1+stheta*v2; + dico(:,index(2)) = ctheta*v1-stheta*v2; + else + v1 = dico(:,index(1))-dico(:,index(2)); + v1 = v1/norm(v1); + v2 = dico(:,index(1))+dico(:,index(2)); + v2 = v2/norm(v2); + + dico(:,index(1)) = ctheta*v1+stheta*v2; + dico(:,index(2)) = -ctheta*v1+stheta*v2; + end + end + end + niter = niter+1; + end + %if a cell array of dictionaries is provided, decorrelate among + %different dictionaries only + else + niter = 1; + numDicos = length(dico); + G = cell(numDicos); + maxCorr = 0; + for i = 1:numDicos + for j = i+1:numDicos + G{i,j} = dico{i}'*dico{j}; + maxCorr = max(maxCorr,max(max(abs(G{i,j})))); + end + end - % iterate on all pairs - nbColors = max(colors); - for c = 1:nbColors - index = find(colors==c); - if numel(index) == 2 - if dico(:,index(1))'*dico(:,index(2)) > 0 + while maxCorr > mu + eps + % find pairs of high correlation atoms + [colors nbColors] = dico_color_separate(dico, mu); + + % iterate on all pairs + for c = 1:nbColors + for tmpI = 1:numDicos + index = find(colors{tmpI}==c); + if ~isempty(index) + i = tmpI; + m = index; + break; + end + end + for tmpJ = i+1:numDicos + index = find(colors{tmpJ}==c); + if ~isempty(index) + j = tmpJ; + n = index; + break; + end + end + + if dico{i}(:,m)'*dico{j}(:,n) > 0 %build the basis vectors - v1 = dico(:,index(1))+dico(:,index(2)); + v1 = dico{i}(:,m)+dico{j}(:,n); v1 = v1/norm(v1); - v2 = dico(:,index(1))-dico(:,index(2)); + v2 = dico{i}(:,m)-dico{j}(:,n); v2 = v2/norm(v2); - dico(:,index(1)) = ctheta*v1+stheta*v2; - dico(:,index(2)) = ctheta*v1-stheta*v2; + dico{i}(:,m) = ctheta*v1+stheta*v2; + dico{j}(:,n) = ctheta*v1-stheta*v2; else - v1 = dico(:,index(1))-dico(:,index(2)); + v1 = dico{i}(:,m)-dico{j}(:,n); v1 = v1/norm(v1); - v2 = dico(:,index(1))+dico(:,index(2)); + v2 = dico{i}(:,m)+dico{j}(:,n); v2 = v2/norm(v2); - dico(:,index(1)) = ctheta*v1+stheta*v2; - dico(:,index(2)) = -ctheta*v1+stheta*v2; + dico{i}(:,m) = ctheta*v1+stheta*v2; + dico{j}(:,n) = -ctheta*v1+stheta*v2; + end + end + niter = niter+1; + + % Remove noegative components and renormalize + for i = 1:length(dico) + dico{i} = max(dico{i},0); + for m = 1:size(dico{i},2) + dico{i}(:,m) = dico{i}(:,m)/norm(dico{i}(:,m)); + end + end + + maxCorr = 0; + for i = 1:numDicos + for j = i+1:numDicos + G{i,j} = dico{i}'*dico{j}; + maxCorr = max(maxCorr,max(max(abs(G{i,j})))); end end end - niter = niter+1; end end -