Implementation of the GiniIndex With Laplace correction 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 definition:

\[ Gini(Sample M) = 1 - (\frac{c(1)}{N})^2 - (\frac{c(2)}{N})^2 .... - (\frac{c(k)}{N})^2 \]

Where:

\( M \) is a sample 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:

The Laplace's correction to the probability distribution would turn the \( \frac{c(1)}{N} \) into \( \frac{(c(1)+1)}{(N+2)} \) using this the simple Gini Index for two classes

\[ Gini(Sample) = \frac{2sb}{(s+b)^2} \]

turns into

\[ GiniLaplace(Sample) = \frac{2(sb+s+b+1)}{(s+b+2)^2} \]

Definition at line 59 of file GiniIndexWithLaplace.h.

Public Member Functions
	GiniIndexWithLaplace ()

	GiniIndexWithLaplace (const GiniIndexWithLaplace &g)

virtual	~GiniIndexWithLaplace ()

virtual Double_t	GetSeparationIndex (const Double_t s, const Double_t b)

Public Member Functions inherited from TMVA::SeparationBase
	SeparationBase ()
	Constructor.

	SeparationBase (const SeparationBase &s)
	Copy constructor.

virtual	~SeparationBase ()

const TString &	GetName ()

virtual Double_t	GetSeparationGain (const Double_t nSelS, const Double_t nSelB, const Double_t nTotS, const Double_t nTotB)
	Separation Gain: the measure of how the quality of separation of the sample increases by splitting the sample e.g.