def v_measure(self, beta=1):
"""Computes Rosenberg and Hirschberg's V-measure (EMNLP '07),
which ranges between 0 and 1 (1 is best). The beta parameter
can be used to weigh homogeneity or completeness; the default
is balanced harmonic mean, beta > 1 favors homogeneity."""
h_c = entropy_of_multinomial(self.gold_sizes.values())
h_k = entropy_of_multinomial(
[sum(table.values()) for table in self.by_test.values()])
if h_c == 0:
h**o = 1
else:
h_c_given_k = self.conditional_entropy_gold_given_test()
h**o = 1 - h_c_given_k / h_c
if h_k == 0:
comp = 1
else:
h_k_given_c = conditional_entropy_Y_Given_X(
dict(self.as_confusion_items()))
comp = 1 - h_k_given_c / h_k
return fscore(h**o, comp, beta) #computes the harmonic mean
def normalized_vi(self):
"""Calculates NVI (Reichart and Rappoport '09), which is
VI/H(C), variation of information normalized by the entropy of
the true clustering. This metric has value 0 for perfect
clusterings and 1 for the single-cluster clustering;
'reasonable' clusterings have scores in between."""
hc = entropy_of_multinomial(self.gold_sizes.values())
if hc == 0:
return 0
return self.variation_of_information() / hc
def normalized_mutual_information(self):
"""Normalized mutual information (Strehl and Ghosh JMLR '02
"Cluster Ensembles"), eq 2: mutual information normalized by
the square root of the product of entropies. The value is
between 0 and 1, and is 1 for identical clusterings."""
denom = (sqrt(
entropy_of_multinomial(self.gold_sizes.values()) *
entropy_of_multinomial([sum(table.values())
for table in self.by_test.values()])))
if denom == 0:
if entropy_of_multinomial(self.gold_sizes.values()) == 0:
#gold clustering is entirely uninformative
#so anything we do is good
return 1
else:
#induced clustering is entirely uninformative
return 0
return self.mutual_information() / denom
def entropy(self):
from Probably import entropy_of_multinomial
return entropy_of_multinomial(self.values())