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/*******************************************************************************
** MutualInformation.cpp
** Part of the mutual information toolbox
**
** Contains functions to calculate the mutual information of
** two variables X and Y, I(X;Y), to calculate the joint mutual information
** of two variables X & Z on the variable Y, I(XZ;Y), and the conditional
** mutual information I(x;Y|Z)
**
** Author: Adam Pocock
** Created 19/2/2010
**
** Copyright 2010 Adam Pocock, The University Of Manchester
** www.cs.manchester.ac.uk
**
** This file is part of MIToolbox.
**
** MIToolbox is free software: you can redistribute it and/or modify
** it under the terms of the GNU Lesser General Public License as published by
** the Free Software Foundation, either version 3 of the License, or
** (at your option) any later version.
**
** MIToolbox is distributed in the hope that it will be useful,
** but WITHOUT ANY WARRANTY; without even the implied warranty of
** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
** GNU Lesser General Public License for more details.
**
** You should have received a copy of the GNU Lesser General Public License
** along with MIToolbox. If not, see <http://www.gnu.org/licenses/>.
**
*******************************************************************************/
#include "MIToolbox.h"
#include "ArrayOperations.h"
#include "CalculateProbability.h"
#include "Entropy.h"
#include "MutualInformation.h"
#include "util.h"
double calculateMutualInformation(double *dataVector, double *targetVector, int vectorLength)
{
double mutualInformation = 0.0;
int firstIndex,secondIndex;
int i;
JointProbabilityState state = calculateJointProbability(dataVector,targetVector,vectorLength);
/*
** I(X;Y) = sum sum p(xy) * log (p(xy)/p(x)p(y))
*/
for (i = 0; i < state.numJointStates; i++)
{
firstIndex = i % state.numFirstStates;
secondIndex = i / state.numFirstStates;
if ((state.jointProbabilityVector[i] > 0) && (state.firstProbabilityVector[firstIndex] > 0) && (state.secondProbabilityVector[secondIndex] > 0))
{
/*double division is probably more stable than multiplying two small numbers together
** mutualInformation += state.jointProbabilityVector[i] * log(state.jointProbabilityVector[i] / (state.firstProbabilityVector[firstIndex] * state.secondProbabilityVector[secondIndex]));
*/
mutualInformation += state.jointProbabilityVector[i] * log(state.jointProbabilityVector[i] / state.firstProbabilityVector[firstIndex] / state.secondProbabilityVector[secondIndex]);
}
}
mutualInformation /= log(2.0);
FREE_FUNC(state.firstProbabilityVector);
state.firstProbabilityVector = NULL;
FREE_FUNC(state.secondProbabilityVector);
state.secondProbabilityVector = NULL;
FREE_FUNC(state.jointProbabilityVector);
state.jointProbabilityVector = NULL;
return mutualInformation;
}/*calculateMutualInformation(double *,double *,int)*/
double calculateConditionalMutualInformation(double *dataVector, double *targetVector, double *conditionVector, int vectorLength)
{
double mutualInformation = 0.0;
double firstCondition, secondCondition;
double *mergedVector = safe_calloc(vectorLength,sizeof(double));
mergeArrays(targetVector,conditionVector,mergedVector,vectorLength);
/* I(X;Y|Z) = H(X|Z) - H(X|YZ) */
/* double calculateConditionalEntropy(double *dataVector, double *conditionVector, int vectorLength); */
firstCondition = calculateConditionalEntropy(dataVector,conditionVector,vectorLength);
secondCondition = calculateConditionalEntropy(dataVector,mergedVector,vectorLength);
mutualInformation = firstCondition - secondCondition;
FREE_FUNC(mergedVector);
mergedVector = NULL;
return mutualInformation;
}/*calculateConditionalMutualInformation(double *,double *,double *,int)*/
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