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correlation.hpp
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correlation.hpp
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#include <math.h>
#include <vector>
#include <algorithm>
template <class PAIR_CONTAINER>
float pearson_correlation(const PAIR_CONTAINER &m_data)
{
if( m_data.empty() ){
throw __FILE__ ":pearson_correlation: No data found!";
}
const size_t len = m_data.size();
// Accumulate in double
double ave_x = 0.0;
double ave_y = 0.0;
for(typename PAIR_CONTAINER::const_iterator i = m_data.begin();i != m_data.end();++i){
ave_x += i->first;
ave_y += i->second;
}
ave_x /= len;
ave_y /= len;
// Accumulate in double
double xx = 0.0;
double yy = 0.0;
double xy = 0.0;
for(typename PAIR_CONTAINER::const_iterator i = m_data.begin();i != m_data.end();++i){
const float dx = (i->first - ave_x);
const float dy = (i->second - ave_y);
xy += dx*dy;
xx += dx*dx;
yy += dy*dy;
}
if(xy == 0.0){
return 0.0f;
}
// DEBUG -- testing the effects of normalizing the variance using (n - 1) instead of (n).
// Has a small effect ...
//xy /= len;
//xx /= (len - 1);
//yy /= (len - 1);
const float r = xy/sqrt( fabs(xx*yy) );
if( isnan(r) || isinf(r) ){
//cerr << "Invalid pearson correlation r = " << r << endl;
//cerr << "len = " << len << endl;
//cerr << "xx = " << xx << endl;
//cerr << "yy = " << yy << endl;
//cerr << "xy = " << xy << endl;
//for(typename PAIR_CONTAINER::const_iterator i = m_data.begin();i != m_data.end();++i){
// cerr << i->first << '\t' << i->second << endl;
//}
throw __FILE__ ":pearson_correlation: Error computing pearson correlation coefficient";
}
return r;
}
template <class PAIR_CONTAINER>
float spearman_correlation(const PAIR_CONTAINER &m_data)
{
const unsigned int len = m_data.size();
std::vector< std::pair<float, unsigned int> > local_rank(len);
std::vector< std::pair<float, float> > final_rank(len);
for(unsigned int i = 0;i < len;++i){
local_rank[i] = std::make_pair(m_data[i].first, i);
}
std::sort( local_rank.begin(), local_rank.end() );
// Allow for ties in the data
unsigned int index = 0;
while(index < len){
const unsigned int start = index;
do{
++index;
}
while( (index < len) && (local_rank[index].first == local_rank[start].first) );
const float ave_rank = start + 0.5f*( (index - start) - 1 );
for(unsigned int i = start;i < index;++i){
final_rank[local_rank[i].second].first = ave_rank;
}
}
//////////////////////////////////////////////////////////////////////
for(unsigned int i = 0;i < len;++i){
local_rank[i] = std::make_pair(m_data[i].second, i);
}
std::sort( local_rank.begin(), local_rank.end() );
// Allow for ties in the data
index = 0;
while(index < len){
const unsigned int start = index;
do{
++index;
}
while( (index < len) && (local_rank[index].first == local_rank[start].first) );
const float ave_rank = start + 0.5f*( (index - start) - 1 );
for(unsigned int i = start;i < index;++i){
final_rank[local_rank[i].second].second = ave_rank;
}
}
return pearson_correlation< std::vector< std::pair<float, float> > >(final_rank);
// The old version below is about two times *slower* that the new version above
#ifdef OLD_VERSION
const size_t len = m_data.size();
std::deque< std::pair<float, size_t> > rank_a;
std::deque< std::pair<float, size_t> > rank_b;
for(size_t i = 0;i < len;++i){
rank_a.push_back( std::make_pair(m_data[i].first, i) );
rank_b.push_back( std::make_pair(m_data[i].second, i) );
}
std::sort( rank_a.begin(), rank_a.end() );
std::sort( rank_b.begin(), rank_b.end() );
// Allow for ties in the data
std::unordered_map<float, size_t> total_rank_a;
std::unordered_map<float, size_t> norm_rank_a;
std::unordered_map<float, size_t> total_rank_b;
std::unordered_map<float, size_t> norm_rank_b;
for(size_t i = 0;i < len;++i){
total_rank_a[rank_a[i].first] += i;
++norm_rank_a[rank_a[i].first];
total_rank_b[rank_b[i].first] += i;
++norm_rank_b[rank_b[i].first];
}
std::deque< std::pair<float, float> > rank(len);
for(size_t i = 0;i < len;++i){
rank[rank_a[i].second].first = total_rank_a[rank_a[i].first]/norm_rank_a[rank_a[i].first];
rank[rank_b[i].second].second = total_rank_b[rank_b[i].first]/norm_rank_b[rank_b[i].first];
}
return pearson_correlation< std::deque< std::pair<float,float> > >(rank);
#endif // OLD_VERSION
}