double kl_distance(const histogram<double>& sample1,const histogram<double>& sample2)
{
//let's include the whole range
double _min=std::min(sample1.min(),sample2.min());
double _max=std::max(sample1.max(),sample2.max());
double _range=_max-_min;
//now we are going to iterate through samples
double distance=0.0;
int _size=std::max(sample1.size(),sample2.size());
double _bin=_range/_size;
double v=_min+_bin/2.0;
for(int i=0;i<_size;i++,v+=_bin)
{
double _P=0.0;
if(v>=sample1.min() && v<=sample1.max()) _P=sample1[v];
double _Q=0.0;
if(v>=sample2.min() && v<=sample2.max()) _Q=sample2[v];
if(_P>0.0 && _Q>0.0)//TODO: epsilon?
distance+=_P*log(_P/_Q);
}
return distance;
}
//! apply k-means classify to histogram
void apply_k_means_classify(const histogram<double>& input,
const std::vector<double>& mu,
std::vector<int>& cls )
{
int number_of_classes=mu.size();
int i,j,k;
//calculate all the classes
for(j=0;j<input.size();j++)
{
int best_k=0;
double best_dist=0;
for(k=0;k<number_of_classes;k++)
{
double dist=fabs(input.value(j)-mu[k]);
if(dist<best_dist|| best_k==0)
{
best_dist=dist;
best_k=k+1;
}
}
cls[j]=best_k;
}
}
void simple_k_means( histogram<double>& hist, std::vector<double>& mu,int k_means,int maxiter)
{
std::vector<int> cls(hist.size(),0);
if(mu.size()!=k_means)
{
mu.resize(k_means);
//initializing k-means using uniform distribution
double vol_min=hist.find_percentile(0.001);
double vol_max=hist.find_percentile(0.999);
for(int j=0;j<k_means;j++)
mu[j]= vol_min+(vol_max-vol_min)*j/(double)(k_means-1);
}
for(int iter=0;iter<maxiter;iter++)
{
apply_k_means_classify(hist,mu,cls);
estimate_mu(hist,cls,mu);
}
}