# Natural Language Toolkit: Spearman Rank Correlation
#
# Copyright (C) 2001-2015 NLTK Project
# Author: Joel Nothman <jnothman@student.usyd.edu.au>
# URL: <http://nltk.org>
# For license information, see LICENSE.TXT
from __future__ import division
"""
Tools for comparing ranked lists.
"""
def _rank_dists(ranks1, ranks2):
"""Finds the difference between the values in ranks1 and ranks2 for keys
present in both dicts. If the arguments are not dicts, they are converted
from (key, rank) sequences.
"""
ranks1 = dict(ranks1)
ranks2 = dict(ranks2)
for k in ranks1:
try:
yield k, ranks1[k] - ranks2[k]
except KeyError:
pass
[docs]def spearman_correlation(ranks1, ranks2):
"""Returns the Spearman correlation coefficient for two rankings, which
should be dicts or sequences of (key, rank). The coefficient ranges from
-1.0 (ranks are opposite) to 1.0 (ranks are identical), and is only
calculated for keys in both rankings (for meaningful results, remove keys
present in only one list before ranking)."""
n = 0
res = 0
for k, d in _rank_dists(ranks1, ranks2):
res += d * d
n += 1
try:
return 1 - (6 * res / (n * (n*n - 1)))
except ZeroDivisionError:
# Result is undefined if only one item is ranked
return 0.0
[docs]def ranks_from_sequence(seq):
"""Given a sequence, yields each element with an increasing rank, suitable
for use as an argument to ``spearman_correlation``.
"""
return ((k, i) for i, k in enumerate(seq))
[docs]def ranks_from_scores(scores, rank_gap=1e-15):
"""Given a sequence of (key, score) tuples, yields each key with an
increasing rank, tying with previous key's rank if the difference between
their scores is less than rank_gap. Suitable for use as an argument to
``spearman_correlation``.
"""
prev_score = None
rank = 0
for i, (key, score) in enumerate(scores):
try:
if abs(score - prev_score) > rank_gap:
rank = i
except TypeError:
pass
yield key, rank
prev_score = score