GiniIndex.cxx

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// @(#)root/tmva $Id$ 
// Author: Andreas Hoecker, Joerg Stelzer, Helge Voss, Kai Voss 

/**********************************************************************************
 * Project: TMVA - a Root-integrated toolkit for multivariate data analysis       *
 * Package: TMVA                                                                  *
 * Class  : TMVA::GiniIndex                                                       *
 * Web    : http://tmva.sourceforge.net                                           *
 *                                                                                *
 * Description: Implementation of the GiniIndex as separation criterion           *
 *              Large Gini Indices (maximum 0.5) mean , that the sample is well   *
 *              mixed (same amount of signal and bkg)                             *
 *              bkg. Small Indices mean, well separated.                          *
 *              general defniniton:                                               *     
 *              Gini(Sample M) = 1 - (c(1)/N)^2 - (c(2)/N)^2 .... - (c(k)/N)^2    * 
 *              Where: M is a smaple of whatever N elements (events)              *
 *                     that belong to K different classes                         *
 *                     c(k) is the number of elements that belong to class k      *
 *              for just Signal and Background classes this boils down to:        *
 *              Gini(Sample) = 2s*b/(s+b)^2                                       *
 *                                                                                *
 * Authors (alphabetical):                                                        *
 *      Andreas Hoecker <Andreas.Hocker@cern.ch> - CERN, Switzerland              *
 *      Helge Voss      <Helge.Voss@cern.ch>     - MPI-K Heidelberg, Germany      *
 *      Kai Voss        <Kai.Voss@cern.ch>       - U. of Victoria, Canada         *
 *                                                                                *
 * Copyright (c) 2005:                                                            *
 *      CERN, Switzerland                                                         * 
 *      U. of Victoria, Canada                                                    * 
 *      Heidelberg U., Germany                                                    * 
 *                                                                                *
 * Redistribution and use in source and binary forms, with or without             *
 * modification, are permitted according to the terms listed in LICENSE           *
 * (http://tmva.sourceforge.net/LICENSE)                                          *
 **********************************************************************************/

//_______________________________________________________________________
//                                                                      
// Implementation of the GiniIndex as separation criterion              
//                                                                      
//_______________________________________________________________________

#include "TMVA/GiniIndex.h"

ClassImp(TMVA::GiniIndex)

////////////////////////////////////////////////////////////////////////////////
///     Gini(Sample M) = 1 - (c(1)/N)^2 - (c(2)/N)^2 .... - (c(k)/N)^2    
///     Where: M is a smaple of whatever N elements (events)             
///            that belong to K different classes                        
///            c(k) is the number of elements that belong to class k     
///     for just Signal and Background classes this boils down to:       
///     Gini(Sample) = 2s*b/(s+b)^2    ( = 2 * purity * (1-purity) )                                     
///   
/// !! what we use here is 2*Gini.. as for the later use the factor
///    2 is irrelevant and hence I'd like to save this calculation

Double_t TMVA::GiniIndex::GetSeparationIndex( const Double_t &s, const Double_t &b )
{
   if (s+b <= 0)      return 0;
   if (s<=0 || b <=0) return 0;
   //   else               return s*b/(s+b)/(s+b); 
   else               return 2*s*b/(s+b)/(s+b); 
}