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/* MELODIC - Multivariate exploratory linear optimized decomposition into
independent components
melica.cc - ICA estimation
Christian F. Beckmann, FMRIB Image Analysis Group
Copyright (C) 1999-2002 University of Oxford */
/* CCOPYRIGHT */
#include "newimage/newimageall.h"
#include "utils/log.h"
#include "meloptions.h"
#include "meldata.h"
#include "melodic.h"
#include "newmatap.h"
#include "newmatio.h"
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using namespace Utilities;
using namespace NEWIMAGE;
namespace Melodic{
void MelodicICA::ica_fastica_symm(const Matrix &Data)
{
// based on Aapo Hyvrinen's fastica method
// see www.cis.hut.fi/projects/ica/fastica/
//initialize matrices
Matrix redUMM_old;
Matrix tmpU;
//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;
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);
//termination condition : angle between old and new < epsilon
minAbsSin = 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_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);
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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;
}
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//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)
{
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// based on Aapo Hyvrinen'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 = Identity(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;
}
// redUMM = redUMM + ( tmpU *tmpU.t()) * 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);}
}
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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 = Identity(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 = Identity(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::sort()
{
int numComp = melodat.get_mix().Ncols();
Matrix tmpIC = melodat.get_IC();
Matrix tmpA = melodat.get_mix();
for(int ctr_i = 1; ctr_i <= numComp; ctr_i++){
if(tmpIC.Row(ctr_i).Sum()>0){
tmpIC.Row(ctr_i) = -tmpIC.Row(ctr_i);
tmpA.Column(ctr_i) = -tmpA.Column(ctr_i);
};
}
melodat.set_mix(tmpA);
melodat.set_IC(tmpIC);
Matrix tmpW = pinv(tmpA);
melodat.set_unmix(tmpW);
}
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
// cout << endl << "Dim = " << dim << endl << "Samples = " << samples << endl;
if(opts.approach.value()==string("symm")){
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());
melodat.set_IC(temp);
sort();
}
}
}