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information.py
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information.py
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# This file is part of pyConnectivity
#
# pyConnectivity is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 2 of the License, or
# (at your option) any later version.
#
# pyConnectivity 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 General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with pyConnectivity. If not, see <http://www.gnu.org/licenses/>.
#
# Copyright 2014 Carlo Nicolini <carlo.nicolini@iit.it>
#
# Further informations and API are available at
# http://perso.crans.org/aynaud/communities/api.html
"""
This module implements variation of information.
"""
__author__ = "Carlo Nicolini <carlo.nicolini@iit.it>"
__all__ = ["confusion_matrix", "normalized_mutual_information",
"variation_of_information", "adjusted_rand_index"]
from pyconnectivity import nx, np, copy, logging, statistic, community
# http://thirdorderscientist.org/homoclinic-orbit/2013/9/5/how-to-compare-communities-using-variation-of-information
import math
import string
import sys
import fileinput
import numpy as np
import copy
# http://thirdorderscientist.org/homoclinic-orbit/2013/9/5/how-to-compare-communities-using-variation-of-information
def confusion_matrix(partA, partB):
if len(partA) != len(partB):
raise Exception("Incompatible partitions!")
N = len(partA)
Ca = len(np.unique(partA.values()))
Cb = len(np.unique(partB.values()))
# important to bring all the symbol to the same meaning, renumbering is
# important
partitionA = community.__renumber(copy.copy(partA))
partitionB = community.__renumber(copy.copy(partB))
Ca, Cb = {}, {}
for c in partitionA.values():
Ca[c] = []
for c in partitionB.values():
Cb[c] = []
for n, c in partitionA.iteritems():
Ca[c].append(n)
for n, c in partitionB.iteritems():
Cb[c].append(n)
C = np.zeros([len(Ca), len(Cb)])
for i in range(0, len(Ca.keys())):
for j in range(0, len(Cb.keys())):
C[i][j] = len(set(Ca[i]).intersection(set(Cb[j])))
return C
def informations(C, N):
"""
Compute the normalized mutual information
"""
# Compute Ni,Nj
Ni = C.sum(1)
Nj = C.sum(0)
# Compute numerator of mutual information
num = 0.0
for i in range(0, C.shape[0]):
for j in range(0, C.shape[1]):
if C[i][j] == 0.0:
num += 0.0
else:
num += C[i][j] * np.log((C[i][j] * float(N)) / (Ni[i] * Nj[j]))
# Compute denominator of mutual information
Ha, Hb = 0.0, 0.0
d1 = (Ni * (np.log(Ni) - np.log(N))).sum()
d2 = (Nj * (np.log(Nj) - np.log(N))).sum()
# Normalized mutual information
nmi = -2.0 * num / (d1 + d2)
# Compute entropy of first and second set
Ha = -(Ni / N * (np.log(Ni) - np.log(N))).sum()
Hb = -(Nj / N * (np.log(Nj) - np.log(N))).sum()
return nmi, Ha, Hb
def variation_of_information(partitionA, partitionB):
C = confusion_matrix(partitionA, partitionB)
nmi, Ha, Hb = informations(C, len(partitionA))
# In case both partitions are composed of only one community
if C.shape == (1, 1):
vi = 0.0
nmi = 1.0
return vi
# Compute variation of information as H(X)+H(y)-2I(X|Y)
vi = (1.0 - nmi) * (Ha + Hb)
return vi
def normalized_mutual_information(partitionA, partitionB):
C = confusion_matrix(partitionA, partitionB)
nmi, Ha, Hb = informations(C, len(partitionA))
return nmi
def normalized_variation_of_information(partitionA, partitionB):
vi = variation_of_information(partitionA, partitionB)
return vi / np.log2(len(partitionA))
def adjusted_rand_index(partitionA, partitionB):
C = confusion_matrix(partitionA, partitionB)
numRows, numCols = C.shape
rowChoiceSum = 0
columnChoiceSum = 0
totalChoiceSum = 0
total = 0
def pairs(x):
return x * (x - 1 ) / 2
for i in range(0,numRows):
rowSum = 0
for j in range(0, numCols):
rowSum += C[i, j]
totalChoiceSum += pairs(C[i, j])
total += rowSum
rowChoiceSum += pairs(rowSum)
for j in range(0,numCols):
columnSum = 0
for i in range(0, numRows):
columnSum += C[i, j]
columnChoiceSum += pairs(columnSum)
rowColumnChoiceSumDivTotal = rowChoiceSum * columnChoiceSum / pairs(total);
return (totalChoiceSum - rowColumnChoiceSumDivTotal) / ((rowChoiceSum + columnChoiceSum) / 2 - rowColumnChoiceSumDivTotal)
class PartitionInformation:
def __init__(self, partA, partB):
if len(partA) != len(partB):
raise Exception("Incompatible partitions!")
N = len(partA)
Ca = len(np.unique(partA.values()))
Cb = len(np.unique(partB.values()))
# important to bring all the symbol to the same meaning, renumbering is
# important
partitionA = self.renumber(partA)
partitionB = self.renumber(partB)
Ca, Cb = {}, {}
for c in partitionA.values():
Ca[c] = []
for c in partitionB.values():
Cb[c] = []
for n, c in partitionA.iteritems():
Ca[c].append(n)
for n, c in partitionB.iteritems():
Cb[c].append(n)
C = np.zeros([len(Ca), len(Cb)])
for i in range(0, len(Ca.keys())):
for j in range(0, len(Cb.keys())):
C[i][j] = len(set(Ca[i]).intersection(set(Cb[j])))
self.confusion_matrix = copy.copy(C)
# Compute Ni,Nj
Ni = C.sum(1)
Nj = C.sum(0)
# Compute numerator of mutual information
num = 0.0
for i in range(0, C.shape[0]):
for j in range(0, C.shape[1]):
if C[i][j] == 0.0:
num += 0.0
else:
num += C[i][j] * \
np.log((C[i][j] * float(N)) / (Ni[i] * Nj[j]))
# Compute denominator of mutual information
Ha, Hb = 0.0, 0.0
d1 = (Ni * (np.log(Ni) - np.log(N))).sum()
d2 = (Nj * (np.log(Nj) - np.log(N))).sum()
# Normalized mutual information
self.nmi = -2.0 * num / (d1 + d2)
# Compute entropy of first and second set
self.Ha = -(Ni / N * (np.log(Ni) - np.log(N))).sum()
self.Hb = -(Nj / N * (np.log(Nj) - np.log(N))).sum()
if C.shape == (1, 1):
self.vi = 0.0
self.nmi = 1.0
else:
# Compute variation of information as H(X)+H(y)-2I(X|Y)
self.vi = (1.0 - self.nmi) * (self.Ha + self.Hb)
self.nvi = self.vi / np.log2(len(partitionA))
def renumber(self, partition):
count = 0
ret = partition.copy()
new_values = dict([])
for key in partition.keys():
value = partition[key]
new_value = new_values.get(value, -1)
if new_value == -1:
new_values[value] = count
new_value = count
count += 1
ret[key] = new_value
return ret