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melpca.cc 16.08 KiB 
/*  MELODIC - Multivariate exploratory linear optimized decomposition into 
              independent components
    
    melpca.cc - PCA and whitening 

    Christian F. Beckmann, FMRIB Image Analysis Group
    
    Copyright (C) 1999-200 University of Oxford */

/*  CCOPYRIGHT  */

#include "newimage/newimageall.h"
#include "utils/log.h"
#include "meloptions.h"
#include "meldata.h"
#include "melodic.h"
#include "newmat/newmatap.h"
#include "newmat/newmatio.h"
#include "melpca.h"
#include "libprob/libprob.h"

using namespace Utilities;
using namespace NEWIMAGE;

namespace Melodic{

   void MelodicPCA::perf_pca(const Matrix &Data)
   {    
     message("Starting PCA  ... ");

     SymmetricMatrix Corr;

     if(opts.segment.value().length()>0){
       Matrix Res;
       Res = ones(Data.Nrows(),1)*melodat.get_RXweight();
       Res = SP(melodat.get_Data(),Res);
       Corr = cov(Res.t());
     }
     else{
       Corr = cov(melodat.get_Data().t());
     }

     Matrix tmpE;
     DiagonalMatrix tmpD;
 
     EigenValues(Corr,tmpD,tmpE);

     if(opts.tsmooth.value()){
       message(" temporal smoothing of Eigenvectors " << endl);
       tmpE=melodat.smoothColumns(tmpE);
     }
  
     melodat.set_pcaE(tmpE);
     melodat.set_pcaD(tmpD);
     
     RowVector AdjEV;
     AdjEV = tmpD.AsRow().Reverse();
     SortDescending(AdjEV);
  
     RowVector PercEV(AdjEV);     
     PercEV = cumsum(AdjEV / sum(AdjEV,2).AsScalar());
     write_ascii_matrix(logger.appendDir("eigenvalues_percent"),PercEV);
     melodat.set_EVP(PercEV);
     AdjEV = (AdjEV - min(AdjEV).AsScalar())/(max(AdjEV).AsScalar() - min(AdjEV).AsScalar());
     melodat.set_EV((AdjEV));
     message("done" << endl);
   }
  
  void MelodicPCA::perf_white(const Matrix &Data)
  {
    Matrix RE;
    DiagonalMatrix RD;
    Matrix tmpWhite;
    Matrix tmpDeWhite;

    int N = melodat.get_pcaE().Ncols();    
    if(opts.pca_dim.value() > N){
      message("dimensionality too large - using -dim " << N << 
              " instead " << endl);
      opts.pca_dim.set_T(N);
    }
    if(opts.pca_dim.value() < 0){
      if(opts.remove_meanvol.value()){
	opts.pca_dim.set_T(N-2);
      }else{
	opts.pca_dim.set_T(N-1);
      }
    }
    if(opts.pca_dim.value() ==0){
      opts.pca_dim.set_T(pcadim());
      if(melodat.get_Data().Nrows()<20){
	opts.pca_dim.set_T(N-2);
	message("too few data points for full estimation, using "
		<< opts.pca_dim.value() << " instead"<< endl);
      }
    }
    if(opts.approach.value()==string("jade") && opts.pca_dim.value() > 30){
      message("dimensionality too large for jade estimation - using --dim 30 instead" << endl);
      opts.pca_dim.set_T(30);
    }
    message("Start whitening using  "<< opts.pca_dim.value()<<" dimensions ... " << endl);
    RowVector tmpEVP;
    tmpEVP << melodat.get_EVP();
    float varp = 1.0;
    if(opts.pca_dim.value() <= tmpEVP.Ncols()){
      varp = tmpEVP(opts.pca_dim.value());
    }
    message("  retaining "<< varp*100 <<" percent of the variability " << endl);

    RE = melodat.get_pcaE().Columns(N-opts.pca_dim.value()+1,N);
    RD << abs(melodat.get_pcaD().SymSubMatrix(N-opts.pca_dim.value()+1,N));    

    tmpWhite = sqrt(abs(RD.i()))*RE.t();
    tmpDeWhite = RE*sqrt(RD);
    melodat.set_white(tmpWhite);
    melodat.set_dewhite(tmpDeWhite);
    message(" ... done"<< endl << endl);
   }

  int MelodicPCA::pcadim()
  { 
    message("Estimating the number of sources from the data (PPCA) ..." << endl);

    //First, estimate the smoothness of the data;
    //   set up all strings

    string SM_path = opts.binpath + "smoothest";
    string Mask_fname = logger.appendDir("mask");

    if(opts.segment.value().length()>0){
      Mask_fname =  opts.segment.value();
    } 

    // Setup external call to smoothest:
    char callSMOOTHESTstr[1000];
    ostrstream osc(callSMOOTHESTstr,1000);
    osc  << SM_path << " -d " << melodat.data_dim()
    	 << " -r " << opts.inputfname.value() << " -m " 
    	 << Mask_fname << " > " << logger.appendDir("smoothest") << '\0';
    
    message("  Calling Smoothest: " << callSMOOTHESTstr << endl);
    system(callSMOOTHESTstr);

    //read back the results
    ifstream in;
    string str;
    float Resel = 1.0;

    in.open(logger.appendDir("smoothest").c_str(), ios::in);
    if(in>0){
      for(int ctr=1; ctr<7; ctr++){ in >> str;}
      in.close();
      if(str!="nan"){
	Resel = atof(str.c_str());
      }
    }

    //cerr << "  Resels : " << Resel << endl << endl;
    
    melodat.set_resels(Resel);
    
    Matrix PPCAest;
  
    //   if(!opts.varnorm.value()){
    SymmetricMatrix Corr;
    if(opts.segment.value().length()>0){
      Matrix Res;
      Res = ones(melodat.get_DataVN().Nrows(),1)*melodat.get_RXweight();
      Res = SP(melodat.get_DataVN(),Res);
      Corr = cov(Res.t());
     }
    else{
      Corr = cov(melodat.get_DataVN().t());
    }
    DiagonalMatrix tmpD;
    Matrix tmpE;
    EigenValues(Corr,tmpD,tmpE);
    // }

    RowVector AdjEV;
    AdjEV << tmpD.AsRow();
    AdjEV = AdjEV.Columns(3,AdjEV.Ncols());
    AdjEV = AdjEV.Reverse();

    RowVector CircleLaw;
    int NumVox = (int) floor(melodat.data_samples()/(2.5*Resel));


    CircleLaw = Feta(int(AdjEV.Ncols()), NumVox);

    for(int ctr=1;ctr<=CircleLaw.Ncols(); ctr++){
      if(CircleLaw(ctr)<5*10e-10){CircleLaw(ctr) = 5*10e-10;}
    } 

    //write_ascii_matrix(logger.appendDir("tmpA1"),AdjEV);
    //AdjEV = AdjEV.Columns(2,AdjEV.Ncols());
    //write_ascii_matrix(logger.appendDir("tmpA2"),AdjEV);

    //cerr<< AdjEV.Nrows() << " x " << AdjEV.Ncols() << endl;
    
    //cerr<< CircleLaw.Nrows() << " x " << CircleLaw.Ncols() << endl;

    float slope;
    slope = CircleLaw.Columns(int(AdjEV.Ncols()/4),AdjEV.Ncols() - 
			      int(AdjEV.Ncols()/4)).Sum() /  
      AdjEV.Columns(int(AdjEV.Ncols()/4),AdjEV.Ncols() - 
		    int(AdjEV.Ncols()/4)).Sum();

    //CircleLaw = slope * (CircleLaw-1) + 1;

    //    write_ascii_matrix(logger.appendDir("claw"),CircleLaw.Columns(1,AdjEV.Ncols()));

    RowVector PercEV(AdjEV);
    PercEV = cumsum(AdjEV / sum(AdjEV,2).AsScalar());

    //    write_ascii_matrix(logger.appendDir("ev"),AdjEV);

    //cerr << int(AdjEV.Ncols()) << "   " << NumVox << "   " << slope << endl;
    AdjEV << SP(AdjEV,pow(CircleLaw.Columns(1,AdjEV.Ncols()),-1));
    //  cerr << "recalculated" << endl;

    SortDescending(AdjEV);
    int maxEV = 1;
    float threshold = 0.98;
    for(int ctr_i = 1; ctr_i < PercEV.Ncols(); ctr_i++){ 
      if((PercEV(ctr_i)<threshold)&&(PercEV(ctr_i+1)>=threshold)){maxEV=ctr_i;}
    }

    if(maxEV<3){maxEV=PercEV.Ncols()/2;}
    RowVector NewEV;
    Matrix temp1;
    temp1 = abs(AdjEV);
    NewEV << temp1.SubMatrix(1,1,1,maxEV);
    PPCAest = ppca_est(NewEV, NumVox);
    RowVector estimators(5);
    estimators = 1.0;
    
    Matrix PPCA2(PPCAest);
    
    for(int ctr=1; ctr<=PPCA2.Ncols(); ctr++){
      PPCA2.Column(ctr) = (PPCA2.Column(ctr) - 
			   min(PPCA2.Column(ctr)).AsScalar()) / 
	( max(PPCA2.Column(ctr)).AsScalar() - 
	  min(PPCA2.Column(ctr)).AsScalar());
    }
    
    int ctr_i = 1;
    while((ctr_i< PPCAest.Nrows()-1)&&
	  (PPCAest(ctr_i,2) < PPCAest(ctr_i+1,2))&&(ctr_i<maxEV))
      {estimators(1)=ctr_i+1;ctr_i++;}
    ctr_i = 1;
    while((ctr_i< PPCAest.Nrows()-1)&&
	  (PPCAest(ctr_i,3) < PPCAest(ctr_i+1,3))&&(ctr_i<maxEV))
      {estimators(2)=ctr_i+1;ctr_i++;}
    ctr_i = 1;
    while((ctr_i< PPCAest.Nrows()-1)&&
	  (PPCAest(ctr_i,4) < PPCAest(ctr_i+1,4))&&(ctr_i<maxEV))
      {estimators(3)=ctr_i+1;ctr_i++;}
    ctr_i = 1;
    while((ctr_i< PPCAest.Nrows()-1)&&
	  (PPCAest(ctr_i,5) < PPCAest(ctr_i+1,5))&&(ctr_i<maxEV))
      {estimators(4)=ctr_i+1;ctr_i++;}
    ctr_i = 1;
    while((ctr_i< PPCAest.Nrows()-1)&&
	  (PPCAest(ctr_i,6) < PPCAest(ctr_i+1,6))&&(ctr_i<maxEV))
      {estimators(5)=ctr_i+1;ctr_i++;}

    int res = 0;
    ColumnVector PPCA;

    if(opts.pca_est.value() == string("lap")){
      res = int(estimators(1));
      PPCA << PPCA2.Column(2);
    }

    if(opts.pca_est.value() == string("bic")){
      res = int(estimators(2));
      PPCA << PPCA2.Column(2);
    }
    if(opts.pca_est.value() == string("mdl")){
      res = int(estimators(3));
      PPCA << PPCA2.Column(4);
    }
    if(opts.pca_est.value() == string("aic")){
      res = int(estimators(5));
      PPCA << PPCA2.Column(6);
    }
    if(res==0){//median estimator
      PPCA = PPCA2.Column(2);

      for(int ctr=1; ctr<=PPCA2.Nrows(); ctr++){ 
	RowVector tmp = PPCA2.SubMatrix(ctr,ctr,2,6);
// 	SortAscending(tmp);
// 	float themean = float(tmp.Sum()/5);
// 	if(std::abs(int(tmp(2)-themean)) < std::abs(int(tmp(3)-themean)))
// 	  PPCA(ctr) = tmp(2);
// 	else
// 	  PPCA(ctr) = tmp(3);

	PPCA(ctr) = float(tmp.Sum()/5);
      }

      ctr_i = 1; 
      while((PPCA(ctr_i) < PPCA(ctr_i+1))&&(ctr_i<maxEV)){
	res=ctr_i+1;ctr_i++;
      }
    }

    //    cerr << estimators << "   "  << res << endl;
			       
    //write_ascii_matrix(logger.appendDir("PPCA2"),PPCA2);
    AdjEV = (AdjEV - min(AdjEV).AsScalar())/(max(AdjEV).AsScalar() - min(AdjEV).AsScalar());


    write_ascii_matrix(logger.appendDir("PPCA"),PPCA);			      
    write_ascii_matrix(logger.appendDir("eigenvalues_adjusted"),AdjEV.t());
    write_ascii_matrix(logger.appendDir("eigenvalues_percent"),PercEV.t());

    melodat.set_EVP(PercEV);
    melodat.set_EV(AdjEV);
    melodat.set_PPCA(PPCA);

    //PPCA << sum(PPCAest.Columns(2,6),2);
    
    //ctr_i = 1;
    
    //while((PPCA(ctr_i) < PPCA(ctr_i+1))&&(ctr_i<maxEV)){
    //  res=ctr_i+1;ctr_i++;
    //} 
    
    //res = int(sum(estimators,2).AsScalar()/5);
    
    // res = int(estimators(1)); // Laplace approximation
    //     SortAscending(estimators);
    //     if(std::abs(int(estimators(2))-res) < std::abs(int(estimators(3))-res))
    //       res = int(estimators(2));
    //     else
    //       res = int(estimators(3));
    
    
    //write_ascii_matrix(logger.appendDir("PPCA"),PPCAest);
    //write_ascii_matrix(logger.appendDir("dimest"),estimators);
    
    return res;
  }

RowVector MelodicPCA::Feta(int n1, int n2)
  {
    float nu = (float) n1/n2; 
    float bm = pow((1-sqrt(nu)),2.0);
    float bp = pow((1+sqrt(nu)),2.0);

    //cerr << "nu, bm, bp " << nu << " " <<bm << " " << bp << endl;

    float lrange = 0.9*bm;
    float urange = 1.1*bp;

    // int dummy;
   
    RowVector eta(30*n1);
    float rangestepsize = (urange - lrange) / eta.Ncols(); 
    for(int ctr_i = 0; ctr_i < eta.Ncols(); ctr_i++){ 
      eta(ctr_i+1) = lrange + rangestepsize * (ctr_i);
    }

    RowVector teta(10*n1);
    teta = 0;
    float stepsize = (bp - bm) / teta.Ncols();
    for(int ctr_i = 0; ctr_i < teta.Ncols(); ctr_i++){ 
      teta(ctr_i+1) = stepsize*(ctr_i);
    }  
    
    //cerr << teta(1)+bm << " " << teta(1000)+bm << endl;
    //cerr << eta(1)<< " " << eta(eta.Ncols())<< endl;
    
    //cerr << "BP1" << endl;
 
    //write_ascii_matrix(logger.appendDir("teta"),teta.t());


    //  RowVector tmp1(teta);
    //     tmp1 = teta + bm;
    
    //     cerr << "tmp1" << endl;
    //     tmp1 =  pow(2*M_PI*nu*(tmp1),-1);
    //     cerr << "tmp1" << endl;
    
    //     RowVector tmp2(teta); 
    //     cerr << "tmp2" << endl;
    //     tmp2 = SP(teta, bp-bm-teta);
    //     cerr << "tmp2" << endl;
    //     tmp2=abs(tmp2);
    //     cerr << "tmp2" << endl;


    RowVector feta(teta);
    feta = SP(pow(2*M_PI*nu*(teta + bm),-1), pow(SP(teta, bp-bm-teta),0.5));
   
    //Matrix location;
    teta = teta + bm;

    //cerr << "teta : " << teta.Nrows() << " x " << teta.Ncols() << endl;
    //cerr << "eta : " << eta.Nrows() << " x " << eta.Ncols() << endl;
    //cerr << "feta : " << feta.Nrows() << " x " << feta.Ncols() << endl;
    //c/err << "vor location (input)" << endl;
    //cin >> dummy;
    //location = SP(teta.t()*ones(1,eta.Ncols()),pow(ones(teta.Ncols(),1)*eta,-1));
    //cerr << "nach location (input)" << endl;
    //cin >> dummy;
    //cerr << " weiter " << endl;

    //for(int ctr_i = 1; ctr_i <= location.Ncols(); ctr_i++){
    //  for(int ctr_j = 1; ctr_j <= location.Nrows(); ctr_j++){
    //	if(location(ctr_j,ctr_i)<1){location(ctr_j,ctr_i)=1;}
    //	else {location(ctr_j,ctr_i)=0;}
    //  }
    // } 
    //write_ascii_matrix(logger.appendDir("location"),location);
    // write_ascii_matrix(logger.appendDir("teta"),teta);
    //write_ascii_matrix(logger.appendDir("eta"),eta);
    //write_ascii_matrix(logger.appendDir("feta"),feta);
 
  
    //RowVector claw; 
    //  claw = n1*(1-sum(SP(stepsize*feta.t()*ones(1,eta.Ncols()),location),1).AsRow());

    RowVector claw(eta);
    claw = 0;
    for(int ctr_i = 1; ctr_i <= eta.Ncols(); ctr_i++){
      double tmpval = 0.0;
      for(int ctr_j = 1; ctr_j <= teta.Ncols(); ctr_j++){
	if(( double(teta(ctr_j))/double(eta(ctr_i)) )<1)
	  tmpval += feta(ctr_j);
      }
      claw(ctr_i) = n1*(1-stepsize*tmpval);
    }
    
    //write_ascii_matrix(logger.appendDir("claw"),claw);
    //cerr << "BP1" << endl;
    RowVector Res(n1); //invert the CDF
    //cerr << "n1=" << n1 << endl;
    for(int ctr_i = 1; ctr_i < eta.Ncols(); ctr_i++){
      if(floor(claw(ctr_i))>floor(claw(ctr_i+1))){
	//	cerr << int(floor(claw(ctr_i))) << " ";
	Res(int(floor(claw(ctr_i)))) = eta(ctr_i);
      }
    }
 
    //cerr << endl;
    //    cerr << " Done with loop " << int(floor(tmp4b(ctr_i))) << endl; 
    //write_ascii_matrix(logger.appendDir("claw-dstn"),Res);
    return Res;
  }


  RowVector MelodicPCA::cumsum(const RowVector& Inp)
  {
    UpperTriangularMatrix UT(Inp.Ncols());
    UT=1.0;
    RowVector Res;
    Res = Inp * UT;
    return Res;
  }


  Matrix MelodicPCA::ppca_est(const RowVector& eigenvalues, const int N)
  {
    RowVector logLambda(eigenvalues);
    logLambda = log(eigenvalues);

    int d = logLambda.Ncols();

    RowVector k(d);
    for(int ctr_i = 1; ctr_i <=d; ctr_i++){
      k(ctr_i)=ctr_i;
    }
   
    RowVector m(d);
    m=d*k-0.5*SP(k,k+1); 

    RowVector loggam(d);
    loggam = 0.5*k.Reverse();
    for(int ctr_i = 1; ctr_i <=d; ctr_i++){
      loggam(ctr_i)=lgam(loggam(ctr_i));
    }
    loggam = cumsum(loggam); 

    RowVector l_probU(d);
    l_probU = -log(2)*k + loggam - cumsum(0.5*log(M_PI)*k.Reverse());

    RowVector tmp1;
    tmp1 = -cumsum(eigenvalues).Reverse()+sum(eigenvalues,2).AsScalar();
    tmp1(1) = 0.95*tmp1(2);
    tmp1=tmp1.Reverse();

    RowVector tmp2;
    tmp2 = -cumsum(logLambda).Reverse()+sum(logLambda,2).AsScalar();
    tmp2(1)=tmp2(2);
    tmp2=tmp2.Reverse();

    RowVector tmp3;
    tmp3 = d-k;
    tmp3(d) = 1.0;

    RowVector tmp4;
    tmp4 = SP(tmp1,pow(tmp3,-1));    
    for(int ctr_i = 1; ctr_i <=d; ctr_i++){
      if(tmp4(ctr_i)<0.01){tmp4(ctr_i)=0.01;}
      if(tmp3(ctr_i)<0.01){tmp3(ctr_i)=0.01;}
      if(tmp1(ctr_i)<0.01){tmp1(ctr_i)=0.01;}
    }

    RowVector l_nu;
    l_nu = SP(-N/2*(d-k),log(tmp4));
    l_nu(d) = 0;

    RowVector l_lam;
    l_lam = -(N/2)*cumsum(logLambda);

    RowVector l_lhood;
    l_lhood = SP(pow(tmp3,-1),tmp2)-log(SP(pow(tmp3,-1),tmp1));

    Matrix t1,t2, t3;
    UpperTriangularMatrix triu(d);
    triu = 1.0;
    for(int ctr_i = 1; ctr_i <= triu.Ncols(); ctr_i++){
      triu(ctr_i,ctr_i)=0.0;
    }
    t1 = (ones(d,1) * eigenvalues);
    t1 = SP(triu,t1.t() - t1);
    t2 = pow(tmp4,-1).t()*ones(1,d);
    t3 = ones(d,1)*pow(eigenvalues,-1);
    t2 = SP(triu, t2.t()-t3.t());
    for(int ctr_i = 1; ctr_i <= t1.Ncols(); ctr_i++){
      for(int ctr_j = 1; ctr_j <= t1.Nrows(); ctr_j++){
	if(t1(ctr_j,ctr_i)<=0){t1(ctr_j,ctr_i)=1;}
      } 
    }
    for(int ctr_i = 1; ctr_i <= t2.Ncols(); ctr_i++){
      for(int ctr_j = 1; ctr_j <= t2.Nrows(); ctr_j++){
	if(t2(ctr_j,ctr_i)<=0){t2(ctr_j,ctr_i)=1;}
      }
    } 
    t1 = cumsum(sum(log(t1),2).AsRow());
    t2 = cumsum(sum(log(t2),2).AsRow());

    RowVector l_Az(d);
    l_Az << (t1+t2);

    RowVector l_lap;
    l_lap = l_probU + l_nu +l_Az + l_lam + 0.5*log(2*M_PI)*(m+k)-0.5*log(N)*k;
 
    RowVector l_BIC;
    l_BIC = l_lam + l_nu - 0.5*log(N)*(m+k);

    RowVector l_RRN;
    l_RRN = -0.5*N*SP(k,log(SP(cumsum(eigenvalues),pow(k,-1))))+l_nu;

    RowVector l_AIC;
    l_AIC = -2*N*SP(tmp3,l_lhood)+ 2*(1+d*k+0.5*(k-1));
    l_AIC = -l_AIC;

    RowVector l_MDL;
    l_MDL = -N*SP(tmp3,l_lhood)+ 0.5*(1+d*k+0.5*(k-1))*log(N);
    l_MDL = -l_MDL;

    Matrix Res;

    Res = eigenvalues.t();
    Res |= l_lap.t();
    Res |= l_BIC.t();
    Res |= l_MDL.t();
    Res |= l_RRN.t();
    Res |= l_AIC.t();
    
   
    return Res;

  }




}