/* MELODIC - Multivariate exploratory linear optimized decomposition into independent components melica.cc - ICA estimation Christian F. Beckmann, FMRIB Image Analysis Group Copyright (C) 1999-2008 University of Oxford */ /* Part of FSL - FMRIB's Software Library http://www.fmrib.ox.ac.uk/fsl fsl@fmrib.ox.ac.uk Developed at FMRIB (Oxford Centre for Functional Magnetic Resonance Imaging of the Brain), Department of Clinical Neurology, Oxford University, Oxford, UK LICENCE FMRIB Software Library, Release 4.0 (c) 2007, The University of Oxford (the "Software") The Software remains the property of the University of Oxford ("the University"). 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Contact details are: innovation@isis.ox.ac.uk quoting reference DE/1112. */ #include <stdlib.h> #include "newimage/newimageall.h" #include "utils/log.h" #include "meloptions.h" #include "meldata.h" #include "melodic.h" #include "newmatap.h" #include "newmatio.h" #include "melica.h" #include "melpca.h" #include "melhlprfns.h" #include "miscmaths/miscprob.h" using namespace Utilities; using namespace NEWIMAGE; namespace Melodic{ void MelodicICA::ica_fastica_symm(const Matrix &Data){ // based on Aapo Hyv�rinen's fastica method // see www.cis.hut.fi/projects/ica/fastica/ //initialize matrices Matrix redUMM_old, rank1_old; Matrix tmpU; //srand((unsigned int)timer(NULL)); redUMM = melodat.get_white()* unifrnd(melodat.get_white().Ncols(),dim); // got to start somewhere if(opts.debug.value()) cerr << "redUMM init submatrix : " << endl << redUMM.SubMatrix(1,2,1,2) << endl; if(opts.guessfname.value().size()>1){ message(" Use columns in " << opts.guessfname.value() << " as initial values for the mixing matrix " <<endl); Matrix guess ; guess = melodat.get_white()*read_ascii_matrix(opts.guessfname.value()); redUMM.Columns(1,guess.Ncols()) = guess; } symm_orth(redUMM); int itt_ctr,itt_ctr2=1,cum_itt=0,newmaxitts = opts.maxNumItt.value(); double minAbsSin = 1.0, minAbsSin2 = 1.0; if(opts.approach.value() == string("tica")) opts.maxNumItt.set_T(opts.rank1interval.value()); rank1_old = melodat.get_dewhite()*redUMM; rank1_old = melodat.expand_dimred(rank1_old); rank1_old = krapprox(rank1_old,int(rank1_old.Nrows()/melodat.get_numfiles())); do{// TICA loop itt_ctr = 1; do{ // da loop!!! redUMM_old = redUMM; //calculate IC estimates tmpU = Data.t() * redUMM; //update redUMM depending on nonlinearity if(opts.nonlinearity.value()=="pow4"){ redUMM = (Data * pow(tmpU,3.0)) / samples - 3 * redUMM; } if(opts.nonlinearity.value()=="pow3"){ tmpU /= opts.nlconst1.value(); redUMM = 3 * (Data * pow(tmpU,2.0)) / samples - (SP(ones(dim,1)*sum(tmpU,1),redUMM))/ samples; } if(opts.nonlinearity.value()=="tanh"){ Matrix hyptanh; hyptanh = tanh(opts.nlconst1.value()*tmpU); redUMM = (Data * hyptanh - opts.nlconst1.value()*SP(ones(dim,1)* sum(1-pow(hyptanh,2),1),redUMM))/samples; } if(opts.nonlinearity.value()=="gauss"){ Matrix tmpUsq; Matrix tmpU2; Matrix gauss; Matrix dgauss; tmpUsq = pow(tmpU,2); tmpU2 = exp(-(opts.nlconst2.value()/2) * tmpUsq); gauss = SP(tmpU,tmpU2); dgauss = SP(1-opts.nlconst2.value()*tmpUsq,tmpU2); redUMM = (Data * gauss - SP(ones(dim,1)* sum(dgauss,1),redUMM))/samples; } // orthogonalize the unmixing-matrix symm_orth(redUMM); if(opts.approach.value() == string("tica")){ message(""); } //termination condition : angle between old and new < epsilon minAbsSin = 1 - diag(abs(redUMM.t()*redUMM_old)).Minimum(); message(" Step no. " << cum_itt + itt_ctr << " change : " << minAbsSin << endl); // if((abs(minAbsSin) < opts.epsilon.value())&& // (opts.approach.value()!=string("tica"))){ break;} if((abs(minAbsSin) < opts.epsilon.value())){ break;} itt_ctr++; } while(itt_ctr < opts.maxNumItt.value()); cum_itt += itt_ctr; itt_ctr2++; if(opts.approach.value() == string("tica")){ message(" Rank-1 approximation of the time courses; "); Matrix temp(melodat.get_dewhite() * redUMM); temp = melodat.expand_dimred(temp); temp = krapprox(temp,int(temp.Nrows()/melodat.get_numfiles())); minAbsSin2 = 1 - diag(abs(corrcoef(temp,rank1_old))).Minimum(); rank1_old = temp; temp = melodat.reduce_dimred(temp); redUMM = melodat.get_white() * temp; message(" change : " << minAbsSin2 << endl); if(abs(minAbsSin2) < opts.epsilonS.value() && abs(minAbsSin) < opts.epsilon.value()){ break;} } } while( (itt_ctr2 < newmaxitts/opts.maxNumItt.value()) && (opts.approach.value() == string("tica")) && cum_itt < newmaxitts); if((itt_ctr>=opts.maxNumItt.value() && (opts.approach.value()!=string("tica"))) || (cum_itt >= newmaxitts && opts.approach.value()==string("tica"))){ cerr << " No convergence after " << cum_itt <<" steps "<<endl; } else { message(" Convergence after " << cum_itt <<" steps " << endl << endl); no_convergence = false; {Matrix temp(melodat.get_dewhite() * redUMM); melodat.set_mix(temp);} {Matrix temp(redUMM.t()*melodat.get_white()); melodat.set_unmix(temp);} } } void MelodicICA::ica_fastica_defl(const Matrix &Data){ if(!opts.explicitnums || opts.numICs.value()>dim){ opts.numICs.set_T(dim); message(" Using numICs:" << opts.numICs.value() << endl); } //redUMM = zeros(dim); // got to start somewhere redUMM = melodat.get_white()* unifrnd(melodat.get_white().Ncols(),opts.numICs.value()); redUMM = zeros(melodat.get_white().Nrows(),opts.numICs.value()); Matrix guess; int guesses=0; if(opts.guessfname.value().size()>1){ message(" Use columns in " << opts.guessfname.value() << " as initial values for the mixing matrix " <<endl); guess = melodat.get_white()*read_ascii_matrix(opts.guessfname.value()); guesses = guess.Ncols(); } int ctrIC = 1; int numRestart = 0; while(ctrIC<=opts.numICs.value()){ message(" Extracting IC " << ctrIC << " ... "); ColumnVector w; ColumnVector w_old; ColumnVector tmpU; if(ctrIC <= guesses){ w = w - redUMM * redUMM.t() * w; w = w / norm2(w); w_old = zeros(w.Nrows(),1); int itt_ctr = 1; do{ w_old = w; tmpU = Data.t() * w; if(opts.nonlinearity.value()=="pow4"){ w = (Data * pow(tmpU,3.0)) / samples - 3 * w; } if(opts.nonlinearity.value()=="tanh"){ ColumnVector hyptanh; hyptanh = tanh(opts.nlconst1.value()*tmpU); w = (Data * hyptanh - opts.nlconst1.value()*SP(ones(dim,1)* sum(1-pow(hyptanh,2),1),w))/samples; } if(opts.nonlinearity.value()=="pow3"){ tmpU /= opts.nlconst1.value(); w = 3*(Data * pow(tmpU,2.0)) / samples - 2*(SP(ones(dim,1)* sum(tmpU,1),w))/samples; } if(opts.nonlinearity.value()=="gauss"){ ColumnVector tmpUsq; ColumnVector tmpU2; ColumnVector gauss; ColumnVector dgauss; tmpUsq = pow(tmpU,2); tmpU2 = exp(-(opts.nlconst2.value()/2) * tmpUsq); gauss = SP(tmpU,tmpU2); dgauss = SP(1-opts.nlconst2.value()*tmpUsq,tmpU2); w = (Data * gauss - SP(ones(dim,1)* sum(dgauss,1),w))/samples; } // orthogonalize w w = w - redUMM * redUMM.t() * w; w = w / norm2(w); //termination condition : angle between old and new < epsilon if((norm2(w-w_old) < 0.001*opts.epsilon.value())&&(itt_ctr>10) || (norm2(w+w_old) < 0.001*opts.epsilon.value())&&(itt_ctr>10)){ break; } //cout << norm2(w-w_old) << " " << norm2(w+w_old) << endl; itt_ctr++; } while(itt_ctr <= opts.maxNumItt.value()); if(itt_ctr<opts.maxNumItt.value()){ redUMM.Column(ctrIC) = w; message(" estimated using " << itt_ctr << " iterations " << endl); ctrIC++; numRestart = 0; } else{ if(numRestart > opts.maxRestart.value()){ message(endl << " Estimation failed after " << numRestart << " attempts " << " giving up " << endl); break; }else{ numRestart++; message(endl <<" Estimation failed - restart " << numRestart << endl); } } } if(numRestart < opts.maxRestart.value()){ no_convergence = false; {Matrix temp(melodat.get_dewhite() * redUMM); melodat.set_mix(temp);} {Matrix temp(redUMM.t()*melodat.get_white()); melodat.set_unmix(temp);} } } } void MelodicICA::ica_maxent(const Matrix &Data){ // based on Aapo Hyv�rinen's fastica method // see www.cis.hut.fi/projects/ica/fastica/ message(" MAXENT " << endl); //initialize matrices Matrix redUMM_old; Matrix tmpU; Matrix gtmpU; double lambda = 0.015/std::log((double)melodat.get_white().Ncols()); //srand((unsigned int)timer(NULL)); redUMM = melodat.get_white()* unifrnd(melodat.get_white().Ncols(),dim); // got to start somewhere if(opts.guessfname.value().size()>1){ message(" Use columns in " << opts.guessfname.value() << " as initial values for the mixing matrix " <<endl); Matrix guess ; guess = melodat.get_white()*read_ascii_matrix(opts.guessfname.value()); redUMM.Columns(1,guess.Ncols()) = guess; } // symm_orth(redUMM); int itt_ctr=1; double minAbsSin = 1.0; Matrix Id; Id = IdentityMatrix(redUMM.Ncols()); //cerr << " nonlinearity : " << opts.nonlinearity.value() << endl; do{ // da loop!!! redUMM_old = redUMM; //calculate IC estimates tmpU = Data.t() * redUMM; if(opts.nonlinearity.value()=="tanh"){ //Matrix hyptanh; //hyptanh = tanh(opts.nlconst1.value()*tmpU); //redUMM = (Data * hyptanh - opts.nlconst1.value()*SP(ones(dim,1)* //sum(1-pow(hyptanh,2),1),redUMM))/samples; gtmpU = tanh(opts.nlconst1.value()*tmpU); redUMM = redUMM + lambda*(Id+(1-2*gtmpU.t()*tmpU))*redUMM; } if(opts.nonlinearity.value()=="gauss"){ gtmpU = pow(1+exp(-(opts.nlconst2.value()/2) * tmpU),-1); redUMM = redUMM + lambda*(Id - (gtmpU.t()-tmpU.t())*tmpU)*redUMM; } //termination condition : angle between old and new < epsilon minAbsSin = abs(1 - diag(abs(redUMM.t()*redUMM_old)).Minimum()); message(" Step no. " << itt_ctr << " change : " << minAbsSin << endl); if(abs(minAbsSin) < opts.epsilon.value()){ break;} itt_ctr++; } while(itt_ctr < opts.maxNumItt.value()); if(itt_ctr>=opts.maxNumItt.value()){ cerr << " No convergence after " << itt_ctr <<" steps "<<endl; } else { message(" Convergence after " << itt_ctr <<" steps " << endl << endl); no_convergence = false; {Matrix temp(melodat.get_dewhite() * redUMM); melodat.set_mix(temp);} {Matrix temp(redUMM.t()*melodat.get_white()); melodat.set_unmix(temp);} } } void MelodicICA::ica_jade(const Matrix &Data){ int dim_sym = (int) (dim*(dim+1))/2; int num_CM = dim_sym; Matrix CM; Matrix R; R = IdentityMatrix(dim); Matrix Qij; Qij = zeros(dim); Matrix Xim; Matrix Xjm; Matrix scale; scale = ones(dim,1)/samples; for (int im =1; im <= dim; im++){ Xim = Data.Row(im); write_ascii_matrix("Xim",Data.Row(1)); //Qij = SP((scale * pow(Xim,2)),Data) * Data.t();//- R - 2*R.Column(im)*R.Column(im).t(); Qij = (pow(Xim,2)) * Data.t();//- R - 2*R.Column(im)*R.Column(im).t(); if(im==1){CM = Qij; write_ascii_matrix("CM",CM);exit(2);}else{CM |= Qij;} for (int jm = 1; jm < im; jm++){ Xjm = Data.Row(jm); Qij = (SP((scale * SP(Xim,Xjm)),Data) * Data.t() - R.Column(im)*R.Column(jm).t() - R.Column(jm)*R.Column(im).t()); Qij *= sqrt(2); CM |= Qij; } } write_ascii_matrix("CM",CM); Matrix redUMM; redUMM = IdentityMatrix(dim); bool exitloop = false; int ctr_itt = 0; int ctr_updates = 0; Matrix Givens; Givens = zeros(2,num_CM); Matrix Givens_ip; Givens_ip = zeros(2); Matrix Givens_ro; Givens_ro = zeros(2); double det_on, det_off; double cos_theta, sin_theta, theta; while(!exitloop && ctr_itt <= opts.maxNumItt.value()){ ctr_itt++; cout << "loop" <<endl; for(int ctr_p = 1; ctr_p < dim; ctr_p++){ for(int ctr_q = ctr_p+1; ctr_q <= dim; ctr_q++){ for(int ctr_i = 0; ctr_i < num_CM; ctr_i++){ int Ip = ctr_p + ctr_i * dim; int Iq = ctr_q + ctr_i * dim; Givens(1,ctr_i + 1) = CM(ctr_p,Ip) - CM(ctr_q,Iq); Givens(2,ctr_i + 1) = CM(ctr_p,Iq) - CM(ctr_q,Ip); } Givens_ip = Givens * Givens.t(); det_on = Givens_ip(1,1) - Givens_ip(2,2); det_off = Givens_ip(1,2) + Givens_ip(2,1); theta = 0.5 * atan2(det_off, det_on + sqrt(det_on*det_on + det_off*det_off)); cout << theta << endl; if(abs(theta) > opts.epsilon.value()){ ctr_updates++; message(" Step No. "<< ctr_itt << " change : " << theta << endl); //create Givens rotation matrix cos_theta = cos(theta); sin_theta = sin(theta); Givens_ro(1,1) = cos_theta; Givens_ro(1,2) = -sin_theta; Givens_ro(2,1) = sin_theta; Givens_ro(2,2) = cos_theta; //update 2 entries of redUMM {Matrix tmp_redUMM; tmp_redUMM = redUMM.Column(ctr_p); tmp_redUMM |= redUMM.Column(ctr_q); tmp_redUMM *= Givens_ro; redUMM.Column(ctr_p) = tmp_redUMM.Column(1); redUMM.Column(ctr_q) = tmp_redUMM.Column(2);} //update Cumulant matrix {Matrix tmp_CM; tmp_CM = CM.Row(ctr_p); tmp_CM &= CM.Row(ctr_q); tmp_CM = Givens_ro.t() * tmp_CM; CM.Row(ctr_p) = tmp_CM.Row(1); CM.Row(ctr_q) = tmp_CM.Row(2);} //update Cumulant matrices for(int ctr_i = 0; ctr_i < num_CM; ctr_i++){ int Ip = ctr_p + ctr_i * dim; int Iq = ctr_q + ctr_i * dim; CM.Column(Ip) = cos_theta*CM.Column(Ip)+sin_theta*CM.Column(Iq); CM.Column(Iq) = cos_theta*CM.Column(Iq)-sin_theta*CM.Column(Ip); } }else{ exitloop = true; } } } }//while loop if(ctr_itt > opts.maxNumItt.value()){ cerr << " No convergence after " << ctr_itt <<" steps "<<endl; } else { message(" Convergence after " << ctr_itt <<" steps " << endl << endl); no_convergence = false; {Matrix temp(melodat.get_dewhite() * redUMM); melodat.set_mix(temp);} {Matrix temp(redUMM.t()*melodat.get_white()); melodat.set_unmix(temp);} } } Matrix MelodicICA::sign(const Matrix &Inp){ Matrix Res = Inp; Res = 1; for(int ctr_i = 1; ctr_i <= Inp.Ncols(); ctr_i++){ for(int ctr_j = 1; ctr_j <= Inp.Nrows(); ctr_j++){ if(Inp(ctr_j,ctr_i)<0){Res(ctr_j,ctr_i)=-1;} } } return Res; } void MelodicICA::perf_ica(const Matrix &Data){ message("Starting ICA estimation using " << opts.approach.value() << endl << endl); dim = Data.Nrows(); samples = Data.Ncols(); no_convergence = true; //switch to the chosen method if(opts.approach.value()==string("symm") || opts.approach.value()==string("tica") || opts.approach.value()==string("parafac") || opts.approach.value()==string("concat")) ica_fastica_symm(Data); if(opts.approach.value()==string("defl")) ica_fastica_defl(Data); if(opts.approach.value()==string("jade")) ica_jade(Data); if(opts.approach.value()==string("maxent")) ica_maxent(Data); if(!no_convergence){//calculate the IC Matrix temp(melodat.get_unmix()*melodat.get_Data()); // Add the mean time course again // temp += melodat.get_unmix()*melodat.get_meanC()*ones(1,temp.Ncols()); //re-normalise the decomposition to std(mix)=1 Matrix scales; scales = stdev(melodat.get_mix()); //cerr << " SCALES 1 " << scales << endl; Matrix tmp, tmp2; tmp = SP(melodat.get_mix(),ones(melodat.get_mix().Nrows(),1)*pow(scales,-1)); temp = SP(temp,scales.t()*ones(1,temp.Ncols())); scales = scales.t(); melodat.set_mix(tmp); melodat.set_IC(temp); melodat.set_ICstats(scales); melodat.sort(); message("Calculating T- and S-modes " << endl); melodat.set_TSmode(); } } }