void SmoTutor::sequentialMinimalOptimisation()
{
int numberChanged;
int examineAll = 0;
int epoch = 1;
do
{
numberChanged = 0;
if (examineAll == 1)
{
for (int i = 0; i < ntp; i++)
{
numberChanged += examineExample(i);
}
examineAll = 0;
}
else
{
for (int i = 0; i < ntp; i++)
{
if (alpha[i] > 0 && alpha[i] < C[i])
{
numberChanged += examineExample(i);
}
}
if (numberChanged == 0)
{
examineAll = 1;
}
}
/*
mexPrintf("epoch %d number of changes %d/%d\n",
epoch++,
numberChanged,
nonZeroLagrangeMultipliers());
*/
}
while (numberChanged > 0 || examineAll);
}
// Calls the same method of the superclass.
bool svm::genericTrain(const dmatrix& input, const ivector& ids) {
char buffer[80];
if (validProgressObject()) {
getProgressObject().reset();
getProgressObject().setTitle("SVM: Training");
getProgressObject().setMaxSteps(nClasses);
}
bias.resize(nClasses,getParameters().bias,false,true);
trainData=new dmatrix(input);
alpha.resize(nClasses,input.rows(),0,false,true);
makeTargets(ids);
errorCache.resize(input.rows());
const parameters& param=getParameters();
C=param.C;
tolerance=param.tolerance;
epsilon=param.epsilon;
bool abort=false;
// train one SVM for each class
for (int cid=0; cid<nClasses && !abort; cid++) {
int numChanged=0;
bool examineAll=true;
currentTarget=&target->getRow(cid);
currentClass=cid;
currentAlpha=&alpha.getRow(cid);
_lti_debug("Training class " << cid << "\n");
fillErrorCache();
while ((numChanged > 0 || examineAll) && !abort) {
numChanged=0;
if (examineAll) {
// iterate over all alphas
for (int i=0; i<trainData->rows(); i++) {
if (examineExample(i)) {
numChanged++;
}
}
// next turn, look only at non-bound alphas
examineAll=false;
} else {
// iterate over all non-0 and non-C alphas
int *tmpAlpha=new int[alpha.getRow(cid).size()];
int j=0,i=0;
for (i=0; i<alpha.getRow(cid).size(); i++) {
if (alpha.getRow(cid).at(i) != 0.0 &&
alpha.getRow(cid).at(i) != C) {
tmpAlpha[j++]=i;
}
}
delete[] tmpAlpha;
for (i=0; i<j; i++) {
if (examineExample(i)) {
numChanged++;
}
}
// next turn, examine all if we did not succeed this time
if (numChanged == 0) {
examineAll=true;
}
}
}
// update progress info object
if (validProgressObject()) {
sprintf(buffer,"numChanged=%d, error=%f",numChanged,errorSum);
getProgressObject().step(buffer);
abort=abort || getProgressObject().breakRequested();
}
// now limit the number of support vectors
// does not work yet, so disable it
if (0) {
int supnum=0;
ivector index(currentAlpha->size());
ivector newindex(currentAlpha->size());
dvector newkey(currentAlpha->size());
for (int i=0; i<currentAlpha->size(); i++) {
if (currentAlpha->at(i) > 0) {
supnum++;
}
index[i]=i;
}
if (supnum > param.nSupport && param.nSupport > 0) {
lti::sort2<double> sorter;
sorter.apply(*currentAlpha,index,newkey,newindex);
int i;
for (i=0; i<newkey.size() &&
lti::abs(newkey[i]) > std::numeric_limits<double>::epsilon(); i++) {
}
for (int j=i; j<currentAlpha->size()-param.nSupport; j++) {
currentAlpha->at(newindex[j])=0;
}
_lti_debug("Final alpha: " << *currentAlpha << std::endl);
}
}
}
defineOutputTemplate();
_lti_debug("alpha:\n" << alpha << "\n");
// make sure that all lagrange multipliers are larger than
// zero, otherwise we might get into trouble later
alpha.apply(rectify);
if (abort) {
setStatusString("Training aborted by user!");
}
return !abort;
}
static int compute_svm_adaboost(ESupportVectorMachine *esvm,int n,int d,
double *x[],int y[],int nmodels,int kernel,
double kp,double C,double tol,double eps,
int maxloops,int verbose)
{
int i,b;
int *samples;
double **trx;
int *try;
double *prob;
double *prob_copy;
double sumalpha;
double epsilon;
int *pred;
double *margin;
double sumprob;
int nclasses;
int *classes;
if(nmodels<1){
fprintf(stderr,"compute_svm_adaboost: nmodels must be greater than 0\n");
return 1;
}
if(C<=0){
fprintf(stderr,"compute_svm_adaboost: regularization parameter C must be > 0\n");
return 1;
}
if(eps<=0){
fprintf(stderr,"compute_svm_adaboost: parameter eps must be > 0\n");
return 1;
}
if(tol<=0){
fprintf(stderr,"compute_svm_adaboost: parameter tol must be > 0\n");
return 1;
}
if(maxloops<=0){
fprintf(stderr,"compute_svm_adaboost: parameter maxloops must be > 0\n");
return 1;
}
switch(kernel){
case SVM_KERNEL_LINEAR:
break;
case SVM_KERNEL_GAUSSIAN:
if(kp <=0){
fprintf(stderr,"compute_svm_adaboost: parameter kp must be > 0\n");
return 1;
}
break;
case SVM_KERNEL_POLINOMIAL:
if(kp <=0){
fprintf(stderr,"compute_svm_adaboost: parameter kp must be > 0\n");
return 1;
}
break;
default:
fprintf(stderr,"compute_svm_adaboost: kernel not recognized\n");
return 1;
}
nclasses=iunique(y,n, &classes);
if(nclasses<=0){
fprintf(stderr,"compute_svm_adaboost: iunique error\n");
return 1;
}
if(nclasses==1){
fprintf(stderr,"compute_svm_adaboost: only 1 class recognized\n");
return 1;
}
if(nclasses==2)
if(classes[0] != -1 || classes[1] != 1){
fprintf(stderr,"compute_svm_adaboost: for binary classification classes must be -1,1\n");
return 1;
}
if(nclasses>2){
fprintf(stderr,"compute_svm_adaboost: multiclass classification not allowed\n");
return 1;
}
if(!(esvm->svm=(SupportVectorMachine *)
calloc(nmodels,sizeof(SupportVectorMachine)))){
fprintf(stderr,"compute_svm_adaboost: out of memory\n");
return 1;
}
if(!(esvm->weights=dvector(nmodels))){
fprintf(stderr,"compute_svm_adaboost: out of memory\n");
return 1;
}
if(!(trx=(double **)calloc(n,sizeof(double*)))){
fprintf(stderr,"compute_svm_adaboost: out of memory\n");
return 1;
}
if(!(try=ivector(n))){
fprintf(stderr,"compute_svm_adaboost: out of memory\n");
return 1;
}
if(!(prob_copy=dvector(n))){
fprintf(stderr,"compute_svm_adaboost: out of memory\n");
return 1;
}
if(!(prob=dvector(n))){
fprintf(stderr,"compute_svm_adaboost: out of memory\n");
return 1;
}
if(!(pred=ivector(n))){
fprintf(stderr,"compute_svm_adaboost: out of memory\n");
return 1;
}
for(i =0;i<n;i++)
prob[i]=1.0/(double)n;
esvm->nmodels=nmodels;
sumalpha=0.0;
for(b=0;b<nmodels;b++){
for(i =0;i<n;i++)
prob_copy[i]=prob[i];
if(sample(n, prob_copy, n, &samples, TRUE,b)!=0){
fprintf(stderr,"compute_svm_adaboost: sample error\n");
return 1;
}
for(i =0;i<n;i++){
trx[i] = x[samples[i]];
try[i] = y[samples[i]];
}
if(compute_svm(&(esvm->svm[b]),n,d,trx,try,kernel,kp,C,
tol,eps,maxloops,verbose,NULL)!=0){
fprintf(stderr,"compute_svm_adaboost: compute_svm error\n");
return 1;
}
free_ivector(samples);
epsilon=0.0;
for(i=0;i<n;i++){
pred[i]=predict_svm(&(esvm->svm[b]),x[i],&margin);
if(pred[i] < -1 ){
fprintf(stderr,"compute_svm_adaboost: predict_svm error\n");
return 1;
}
if(pred[i]==0 || pred[i] != y[i])
epsilon += prob[i];
free_dvector(margin);
}
if(epsilon > 0 && epsilon < 0.5){
esvm->weights[b]=0.5 *log((1.0-epsilon)/epsilon);
sumalpha+=esvm->weights[b];
}else{
esvm->nmodels=b;
break;
}
sumprob=0.0;
for(i=0;i<n;i++){
prob[i]=prob[i]*exp(-esvm->weights[b]*y[i]*pred[i]);
sumprob+=prob[i];
}
if(sumprob <=0){
fprintf(stderr,"compute_svm_adaboost: sumprob = 0\n");
return 1;
}
for(i=0;i<n;i++)
prob[i] /= sumprob;
}
if(esvm->nmodels<=0){
fprintf(stderr,"compute_svm_adaboost: no models produced\n");
return 1;
}
if(sumalpha <=0){
fprintf(stderr,"compute_svm_adaboost: sumalpha = 0\n");
return 1;
}
for(b=0;b<esvm->nmodels;b++)
esvm->weights[b] /= sumalpha;
free(trx);
free_ivector(classes);
free_ivector(try);
free_ivector(pred);
free_dvector(prob);
free_dvector(prob_copy);
return 0;
}
static void svm_smo(SupportVectorMachine *svm)
{
int i,k;
int numChanged;
int examineAll;
int nloops=0;
svm->end_support_i=svm->n;
if(svm->kernel_type==SVM_KERNEL_LINEAR){
svm->kernel_func=dot_product_func;
svm->learned_func=learned_func_linear;
}
if(svm->kernel_type==SVM_KERNEL_POLINOMIAL){
svm->kernel_func=polinomial_kernel;
svm->learned_func=learned_func_nonlinear;
}
if(svm->kernel_type==SVM_KERNEL_GAUSSIAN){
/*
svm->precomputed_self_dot_product=(double *)calloc(svm->n,sizeof(double));
*/
for(i=0;i<svm->n;i++)
svm->precomputed_self_dot_product[i] = dot_product_func(i,i,svm);
svm->kernel_func=rbf_kernel;
svm->learned_func=learned_func_nonlinear;
}
numChanged=0;
examineAll=1;
svm->convergence=1;
while(svm->convergence==1 &&(numChanged>0 || examineAll)){
numChanged=0;
if(examineAll){
for(k=0;k<svm->n;k++)
numChanged += examineExample(k,svm);
}else{
for(k=0;k<svm->n;k++)
if(svm->alph[k] > 0 && svm->alph[k] < svm->Cw[k])
numChanged += examineExample(k,svm);
}
if(examineAll==1)
examineAll=0;
else if(numChanged==0)
examineAll=1;
nloops+=1;
if(nloops==svm->maxloops)
svm->convergence=0;
if(svm->verbose==1)
fprintf(stdout,"%6d\b\b\b\b\b\b\b",nloops);
}
}
alphaRet* getAlphaFromTrainSet(int N, F2D* trn1, F2D* trn2, int iterations)
{
float tolerance, C, eps, *b;
F2D *a_result, *b_result;
int NumChanged, r, ExamineAll, cnt, d, dim, ret, iter, i;
F2D *X, *Y;
F2D *a, *e;
b = malloc(sizeof(float));
alphaRet* alpha;
alpha = (alphaRet*)malloc(sizeof(alphaRet));
tolerance = 0.001;
C = 0.05;
d = -1;
dim = 256;
eps = 0.001;
a_result = fSetArray(iterations, N, 0);
b_result = fSetArray(iterations, 1, 0);
ret = 0;
X = usps_read_partial( trn1, trn2, 0, 1, (N/iterations), iterations);
for(iter=0; iter<iterations; iter++)
{
Y = usps_read_partial( trn1, trn2, iter, 0, N/iterations, iterations);
a = fSetArray(N, 1, 0);
arrayref(b,0) = 0; /** check if ptr **/
e = fSetArray(N, 1, 0);
ExamineAll = 1;
cnt = 0;
NumChanged = 0;
while(NumChanged>0 || ExamineAll == 1)
{
cnt = cnt + 1;
NumChanged = 0;
if(ExamineAll == 1)
{
for(i=0; i<N; i++)
{
ret = examineExample(i, a, b, C, e, X, Y, tolerance, N, eps, dim);
NumChanged = NumChanged + ret;
}
}
else
{
for(i=0; i<N; i++)
{
if( asubsref(a,i) > 0 && asubsref(a,i) <C )
{
ret = examineExample(i, a, b, C, e, X, Y, tolerance, N, eps, dim);
NumChanged = NumChanged + ret;
}
}
}
if(ExamineAll == 1)
ExamineAll = 0;
else if(NumChanged == 0)
ExamineAll = 1;
}
for(r=0; r<N; r++)
subsref(a_result,iter,r) = asubsref(a,r); /** a_result has size iteration,N .. Check **/
asubsref(b_result,iter) = arrayref(b,0);
fFreeHandle(Y);
fFreeHandle(e);
fFreeHandle(a);
}
alpha->C = C;
alpha->d = d;
alpha->dim = dim;
alpha->eps = eps;
alpha->a_result = a_result;
alpha->b_result = b_result;
alpha->a = a;
alpha->b = arrayref(b,0);
alpha->X = X;
alpha->tolerance = tolerance;
alpha->ret;
free(b);
return alpha;
}
svmModel SMO::train()
{
int passes = 0;
int maxPasses = 25;
int numChanged = 0;
int examineAll = 1;
alpha.resize(points.size(), 0);
errorCache.resize(points.size(), 0);
w.resize(points.size(), 0);
threshold = 0;
// Normalize the input points
normalizeFeatures();
// SMO outer loop:
// Every iteration altranates between sweep through all points examineAll = 1 and sweep through non-boundary points examineAll = 0.
while ((numChanged > 0 || examineAll) && (passes < maxPasses)) {
numChanged = 0;
if (examineAll) {
for (unsigned int i = 0; i < points.size(); i++)
{
if (plugin->isAborted() == true)
{
plugin->progress.report("User Aborted", 0, ABORT, true);
return svmModel();
}
plugin->progress.report("Training SVM for class " + className, passes*100/maxPasses + (i+1)*100/maxPasses/points.size(), NORMAL);
numChanged += examineExample (i);
}
}
else {
for (unsigned int i = 0; i < points.size(); i++)
if (alpha[i] != 0 && alpha[i] != C)
{
if (plugin->isAborted() == true)
{
plugin->progress.report("User Aborted", 0, ABORT, true);
return svmModel();
}
plugin->progress.report("Training SVM for class " + className, passes*100/maxPasses + (i+1)*100/maxPasses/points.size(), NORMAL);
numChanged += examineExample (i);
}
}
if (examineAll == 1)
examineAll = 0;
else if (numChanged == 0)
examineAll = 1;
/*
double s = 0.0;
for (unsigned int i=0; i<points.size(); i++)
s += alpha[i];
double t = 0.;
for (unsigned int i=0; i<points.size(); i++)
for (unsigned int j=0; j<points.size(); j++)
t += alpha[i]*alpha[j]*target[i]*target[j]*kernel(points[i],points[j]);
double objFunc = (s - t/2.0);
plugin->progress.report(QString("The value of objective function should increase with each iteration.\n The value of objective function = %1").arg(objFunc).toStdString(), (passes*100)/maxPasses, NORMAL);
*/
passes++;
}
plugin->progress.report("Finished training SVM for class " + className, 100, NORMAL, true);
// Get the model for this class
vector<double> m_alpha;
vector<int> m_target;
int numberOfsupportVectors = 0;
vector<point> supportVectors;
int attributes = points[0].size();
for (unsigned int i = 0; i < alpha.size() ; i++)
{
if (alpha[i] > 0)
{
m_alpha.push_back(alpha[i]);
}
}
for (unsigned int i = 0; i < alpha.size(); i++)
{
if (alpha[i] > 0)
{
numberOfsupportVectors++;
supportVectors.push_back(points[i]);
m_target.push_back(target[i]);
}
}
svmModel model = svmModel(className, kernelType, threshold, attributes, w, sigma, numberOfsupportVectors, m_alpha, supportVectors, m_target, mu, stdv);
// Compute the error rates.
plugin->progress.report("Computing Error Rates using the model for class " + className, 0, NORMAL, true);
double trainErrorRate = 0;
double testErrorRate = 0;
double crossValidationErrorRate = 0;
for (unsigned int i = 0; i < points.size(); i++)
{
plugin->progress.report("Comuting Error Rates using the model for class " + className, (i+1)*60.0/points.size(), NORMAL, true);
if (model.predict(points[i]) > 0 != target[i] > 0)
trainErrorRate++;
}
trainErrorRate = trainErrorRate*100/points.size();
for (unsigned int i = 0; i < testSet.size(); i++)
{
plugin->progress.report("Comuting Error Rates using the model for class " + className, 60 + (i+1)*20.0/testSet.size(), NORMAL, true);
if (model.predict(testSet[i]) > 0 != yTest[i] > 0)
testErrorRate++;
}
testErrorRate = testErrorRate*100/points.size();
for (unsigned int i = 0; i < crossValidationSet.size(); i++)
{
plugin->progress.report("Comuting Error Rates using the model for class " + className, 80 + (i+1)*20/crossValidationSet.size(), NORMAL, true);
if (model.predict(crossValidationSet[i]) > 0 != yCV[i] > 0)
crossValidationErrorRate++;
}
crossValidationErrorRate = crossValidationErrorRate*100/crossValidationSet.size();
if (testSet.size() && crossValidationSet.size())
plugin->progress.report(QString("%1\nTrain error = %2\nCrossValidation error = %3\nTest error = %4\n").arg(className.c_str()).arg(trainErrorRate).arg(crossValidationErrorRate).arg(testErrorRate).toStdString(), 100, WARNING, true);
else
plugin->progress.report(QString("%1\nTrain error = %2").arg(className.c_str()).arg(trainErrorRate).toStdString(), 100, WARNING, true);
return model;
}
/* --------------------------------------------------------------
Finds the second Lagrange multiplayer to be optimize.
-------------------------------------------------------------- */
long examineExample( long i1 )
{
double y1, alpha1, E1, r1;
double tmax;
double E2, temp;
long k, i2;
long k0;
y1 = target[i1];
alpha1 = alpha[i1];
if( alpha1 > 0 && alpha1 < C(i1) )
E1 = error_cache[i1];
else
E1 = learned_func(i1) - y1;
r1 = y1 * E1;
if(( r1 < -tolerance && alpha1 < C(i1) )
|| (r1 > tolerance && alpha1 > 0)) {
/* Try i2 by three ways; if successful, then immediately return 1; */
for( i2 = (-1), tmax = 0, k = 0; k < N; k++ ) {
if( alpha[k] > 0 && alpha[k] < C(k) ) {
E2 = error_cache[k];
temp = fabs(E1 - E2);
if( temp > tmax ) {
tmax = temp;
i2 = k;
}
}
}
if( i2 >= 0 ) {
if( takeStep(i1,i2) )
return( 1 );
}
#ifdef RANDOM
for( k0 = rand(), k = k0; k < N + k0; k++ ) {
i2 = k % N;
#else
for( k = 0; k < N; k++) {
i2 = k;
#endif
if( alpha[i2] > 0 && alpha[i2] < C(i2) ) {
if( takeStep(i1,i2) )
return( 1 );
}
}
#ifdef RANDOM
for( k0 = rand(), k = k0; k < N + k0; k++ ) {
i2 = k % N;
#else
for( k = 0; k < N; k++) {
i2 = k;
#endif
if( takeStep(i1,i2) )
return( 1 );
}
} /* if( ... ) */
return( 0 );
}
/* --------------------------------------------------------------
Main SMO optimization cycle.
-------------------------------------------------------------- */
void runSMO( void )
{
long numChanged = 0;
long examineAll = 1;
long k;
while( numChanged > 0 || examineAll ) {
numChanged = 0;
if( examineAll ) {
for( k = 0; k < N; k++ ) {
numChanged += examineExample( k );
}
}
else {
for( k = 0; k < N; k++ ) {
if( alpha[k] != 0 && alpha[k] != C(k) )
numChanged += examineExample( k );
}
}
if( examineAll == 1 )
examineAll = 0;
else if( numChanged == 0 )
examineAll = 1;
}
}
/* ==============================================================
Main MEX function - interface to Matlab.
============================================================== */
void mexFunction( int nlhs, mxArray *plhs[],
int nrhs, const mxArray*prhs[] )
{
long i,j ;
double *labels12, *initAlpha, *nsv, *tmp, *trn_err, *margin;
double nerr;
double C1, C2;
/* ---- get input arguments ----------------------- */
if(nrhs < 5)
mexErrMsgTxt("Not enough input arguments.");
/* data matrix [dim x N ] */
if( !mxIsNumeric(prhs[0]) || !mxIsDouble(prhs[0]) ||
mxIsEmpty(prhs[0]) || mxIsComplex(prhs[0]) )
mexErrMsgTxt("Input X must be a real matrix.");
/* vector of labels (1,2) */
if( !mxIsNumeric(prhs[1]) || !mxIsDouble(prhs[1]) ||
mxIsEmpty(prhs[1]) || mxIsComplex(prhs[1]) ||
(mxGetN(prhs[1]) != 1 && mxGetM(prhs[1]) != 1))
mexErrMsgTxt("Input I must be a real vector.");
labels12 = mxGetPr(prhs[1]); /* labels (1,2) */
dataA = mxGetPr(prhs[0]); /* pointer at patterns */
dataB = dataA;
dim = mxGetM(prhs[0]); /* data dimension */
N = mxGetN(prhs[0]); /* number of data */
/* kernel identifier */
ker = kernel_id( prhs[2] );
if( ker == -1 )
mexErrMsgTxt("Improper kernel identifier.");
/* get pointer to arguments */
arg1 = mxGetPr(prhs[3]);
/* one or two real trade-off constant(s) */
if( !mxIsNumeric(prhs[4]) || !mxIsDouble(prhs[4]) ||
mxIsEmpty(prhs[4]) || mxIsComplex(prhs[4]) ||
(mxGetN(prhs[4]) != 1 && mxGetM(prhs[4]) != 1 ))
mexErrMsgTxt("Improper input argument C.");
else {
/* allocate memory for constant C */
if( (const_C = mxCalloc(N, sizeof(double) )) == NULL) {
mexErrMsgTxt("Not enough memory.");
}
if( MAX( mxGetN(prhs[4]), mxGetM(prhs[4])) == 1 ) {
C1 = mxGetScalar(prhs[4]);
for( i=0; i < N; i++ ) const_C[i] = C1;
} else
if( MAX( mxGetN(prhs[4]), mxGetM(prhs[4])) == 2 ) {
tmp = mxGetPr(prhs[4]);
C1 = tmp[0];
C2 = tmp[1];
for( i=0; i < N; i++ ) {
if( labels12[i]==1) const_C[i] = C1; else const_C[i] = C2;
}
} else
if( MAX( mxGetN(prhs[4]), mxGetM(prhs[4])) == N ) {
tmp = mxGetPr(prhs[4]);
for( i=0; i < N; i++ ) const_C[i] = tmp[i];
} else {
mexErrMsgTxt("Improper argument C.");
}
}
/* real parameter eps */
if( nrhs >= 6 ) {
if( !mxIsNumeric(prhs[5]) || !mxIsDouble(prhs[5]) ||
mxIsEmpty(prhs[5]) || mxIsComplex(prhs[5]) ||
mxGetN(prhs[5]) != 1 || mxGetM(prhs[5]) != 1 )
mexErrMsgTxt("Input eps must be a scalar.");
else
eps = mxGetScalar(prhs[5]); /* take eps argument */
}
/* real parameter tol */
if(nrhs >= 7) {
if( !mxIsNumeric(prhs[6]) || !mxIsDouble(prhs[6]) ||
mxIsEmpty(prhs[6]) || mxIsComplex(prhs[6]) ||
mxGetN(prhs[6]) != 1 || mxGetM(prhs[6]) != 1 )
mexErrMsgTxt("Input tol must be a scalar.");
else
tolerance = mxGetScalar(prhs[6]); /* take tolerance argument */
}
/* real vector of Lagrangeian multipliers */
if(nrhs >= 8) {
if( !mxIsNumeric(prhs[7]) || !mxIsDouble(prhs[7]) ||
mxIsEmpty(prhs[7]) || mxIsComplex(prhs[7]) ||
(mxGetN(prhs[7]) != 1 && mxGetM(prhs[7]) != 1 ))
mexErrMsgTxt("Input Alpha must be a vector.");
}
/* real scalar - bias */
if( nrhs >= 9 ) {
if( !mxIsNumeric(prhs[8]) || !mxIsDouble(prhs[8]) ||
mxIsEmpty(prhs[8]) || mxIsComplex(prhs[8]) ||
mxGetN(prhs[8]) != 1 || mxGetM(prhs[8]) != 1 )
mexErrMsgTxt("Input bias must be a scalar.");
}
/* ---- init variables ------------------------------- */
ker_cnt = 0;
/* allocate memory for targets (labels) (1,-1) */
if( (target = mxCalloc(N, sizeof(double) )) == NULL) {
mexErrMsgTxt("Not enough memory.");
}
/* transform labels12 (1,2) from to targets (1,-1) */
for( i = 0; i < N; i++ ) {
target[i] = - labels12[i]*2 + 3;
}
/* create output variable for bias */
plhs[1] = mxCreateDoubleMatrix(1,1,mxREAL);
b = mxGetPr(plhs[1]);
/* take init value of bias if given */
if( nrhs >= 9 ) {
*b = -mxGetScalar(prhs[8]);
}
/* allocate memory for error_cache */
if( (error_cache = mxCalloc(N, sizeof(double) )) == NULL) {
mexErrMsgTxt("Not enough memory for error cache.");
}
/* create vector for Lagrangeians */
plhs[0] = mxCreateDoubleMatrix(N,1,mxREAL);
alpha = mxGetPr(plhs[0]);
/* if Lagrangeians given then use them as initial values */
if( nrhs >= 8 ) {
initAlpha = mxGetPr(prhs[7]);
for( i = 0; i < N; i++ ) {
alpha[i] = initAlpha[i];
}
/* Init error cache for non-bound multipliers. */
for( i = 0; i < N; i++ ) {
if( alpha[i] != 0 && alpha[i] != C(i) ) {
error_cache[i] = learned_func(i) - target[i];
}
}
}
/* ---- run SMO ------------------------------------------- */
runSMO();
/* ---- outputs --------------------------------- */
if( nlhs >= 3 ) {
/* count number of support vectors */
plhs[2] = mxCreateDoubleMatrix(1,1,mxREAL);
nsv = mxGetPr(plhs[2]);
*nsv = 0;
for( i = 0; i < N; i++ ) {
if( alpha[i] > ZERO_LIM ) (*nsv)++; else alpha[i] = 0;
}
}
if( nlhs >= 4 ) {
plhs[3] = mxCreateDoubleMatrix(1,1,mxREAL);
(*mxGetPr(plhs[3])) = (double)ker_cnt;
}
if( nlhs >= 5) {
/* evaluates classification error on traning patterns */
plhs[4] = mxCreateDoubleMatrix(1,1,mxREAL);
trn_err = mxGetPr(plhs[4]);
nerr = 0;
for( i = 0; i < N; i++ ) {
if( target[i] == 1 ) {
if( learned_func(i) < 0 ) nerr++;
}
else
if( learned_func(i) >= 0 ) nerr++;
}
*trn_err = nerr/N;
}
if( nlhs >= 6) {
/* compute margin */
plhs[5] = mxCreateDoubleMatrix(1,1,mxREAL);
margin = mxGetPr(plhs[5]);
*margin = 0;
for( i = 0; i < N; i++ ) {
for( j = 0; j < N; j++ ) {
if( alpha[i] > 0 && alpha[j] > 0 )
*margin += alpha[i]*alpha[j]*target[i]*target[j]*kernel(i,j);
}
}
*margin = 1/sqrt(*margin);
}
/* decision function of type <w,x>+b is used */
*b = -*b;
/* ----- free memory --------------------------------------- */
mxFree( error_cache );
mxFree( target );
}
/* --------------------------------------------------------------
Finds the second Lagrange multiplayer to be optimize.
-------------------------------------------------------------- */
long examineExample( long i1 )
{
double y1, alpha1, E1, r1;
double tmax;
double E2, temp;
long k, i2;
long k0;
y1 = target[i1];
alpha1 = alpha[i1];
E1 = w*data[i1] - *b - y1;
r1 = y1 * E1;
if(( r1 < -tolerance && alpha1 < C )
|| (r1 > tolerance && alpha1 > 0)) {
/* Try i2 by three ways; if successful, then immediately return 1; */
for( i2 = (-1), tmax = 0, k = 0; k < num_data; k++ ) {
if( alpha[k] > 0 && alpha[k] < C ) {
E2 = w*data[k] - *b - target[k];
temp = fabs(E1 - E2);
if( temp > tmax ) {
tmax = temp;
i2 = k;
}
}
}
if( i2 >= 0 ) {
if( takeStep(i1,i2) )
return( 1 );
}
#ifdef RANDOM
for( k0 = rand(), k = k0; k < num_data + k0; k++ ) {
i2 = k % num_data;
#else
for( k = 0; k < num_data; k++) {
i2 = k;
#endif
if( alpha[i2] > 0 && alpha[i2] < C ) {
if( takeStep(i1,i2) )
return( 1 );
}
}
#ifdef RANDOM
for( k0 = rand(), k = k0; k < num_data + k0; k++ ) {
i2 = k % num_data;
#else
for( k = 0; k < num_data; k++) {
i2 = k;
#endif
if( takeStep(i1,i2) )
return( 1 );
}
} /* if( ... ) */
return( 0 );
}
/* --------------------------------------------------------------
Main SMO optimization cycle.
-------------------------------------------------------------- */
void runSMO( void )
{
long numChanged = 0;
long examineAll = 1;
long k;
while( numChanged > 0 || examineAll ) {
numChanged = 0;
if( examineAll ) {
for( k = 0; k < num_data; k++ ) {
numChanged += examineExample( k );
}
}
else {
for( k = 0; k < num_data; k++ ) {
if( alpha[k] != 0 && alpha[k] != C )
numChanged += examineExample( k );
}
}
if( examineAll == 1 )
examineAll = 0;
else if( numChanged == 0 )
examineAll = 1;
}
}
/* ==============================================================
Main MEX function - interface to Matlab.
============================================================== */
void mexFunction( int nlhs, mxArray *plhs[],
int nrhs, const mxArray*prhs[] )
{
long i,j ;
double *labels12, *nsv, *trn_err, *margin;
double nerr;
/* ---- check number of input arguments ------------- */
if(nrhs != 5 )
mexErrMsgTxt("Incorrect number of input arguments.");
if(nlhs < 2)
mexErrMsgTxt("Not enough output arguments.");
/* ---- get input arguments ----------------------- */
labels12 = mxGetPr(prhs[1]); /* labels (1,2) */
data = mxGetPr(prhs[0]); /* pointer at data */
dim = mxGetM(prhs[0]); /* data dimension */
num_data = mxGetN(prhs[0]); /* number of data */
C = mxGetScalar( prhs[2] );
eps = mxGetScalar( prhs[3] );
tolerance = mxGetScalar( prhs[4] );
/* ---- init variables ------------------------------- */
ker_cnt=0; /* num of dot product evaluations */
/* allocate memory for targets (labels) (1,-1) */
if( (target = (double*)mxCalloc(num_data, sizeof(double) )) == NULL) {
mexErrMsgTxt("Not enough memory.");
}
/* transform labels12 (1,2) from to targets (1,-1) */
for( i = 0; i < num_data; i++ ) {
target[i] = - labels12[i]*2 + 3;
}
/* create output variable for bias */
plhs[1] = mxCreateDoubleMatrix(1,1,mxREAL);
b = mxGetPr(plhs[1]); *b= 0;
/* create vector for Lagrangeians */
plhs[0] = mxCreateDoubleMatrix(num_data,1,mxREAL);
alpha = mxGetPr(plhs[0]);
/* inicialize alpha */
for( i = 0; i < num_data; i++ ) {
alpha[i] = 0;
}
w=0;
/* ---- run SMO ------------------------------------------- */
runSMO();
/* ---- outputs ---------------------------------- */
if( nlhs >= 3 ) {
/* count number of support vectors */
plhs[2] = mxCreateDoubleMatrix(1,1,mxREAL);
nsv = mxGetPr(plhs[2]);
*nsv = 0;
for( i = 0; i < num_data; i++ ) {
if( alpha[i] > 0) (*nsv)++;
}
}
if( nlhs >= 4 ) {
/* number of used iterations */
plhs[3] = mxCreateDoubleMatrix(1,1,mxREAL);
(*mxGetPr(plhs[3])) = (double)ker_cnt;
}
if( nlhs >= 5) {
/* evaluates classification error on traning patterns */
plhs[4] = mxCreateDoubleMatrix(1,1,mxREAL);
trn_err = mxGetPr(plhs[4]);
*trn_err = 0;
for( i = 0; i < num_data; i++ ) {
if( target[i]*(w*data[i]-*b) < 0) (*trn_err)++;
}
*trn_err = (*trn_err)/(double)num_data;
}
if( nlhs >= 6) {
/* compute margin */
plhs[5] = mxCreateDoubleMatrix(1,1,mxREAL);
margin = mxGetPr(plhs[5]);
*margin = 1/sqrt(w*w);
}
/* decision function of type <w,x>+b is used */
*b = -*b;
/* ----- free memory --------------------------------------- */
mxFree( target );
}
