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# Natural Language Toolkit: Spearman Rank Correlation
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#
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# Copyright (C) 2001-2020 NLTK Project
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# Author: Joel Nothman <jnothman@student.usyd.edu.au>
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# URL: <http://nltk.org>
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# For license information, see LICENSE.TXT
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"""
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Tools for comparing ranked lists.
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"""
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def _rank_dists(ranks1, ranks2):
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"""Finds the difference between the values in ranks1 and ranks2 for keys
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present in both dicts. If the arguments are not dicts, they are converted
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from (key, rank) sequences.
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"""
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ranks1 = dict(ranks1)
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ranks2 = dict(ranks2)
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for k in ranks1:
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try:
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yield k, ranks1[k] - ranks2[k]
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except KeyError:
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pass
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def spearman_correlation(ranks1, ranks2):
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"""Returns the Spearman correlation coefficient for two rankings, which
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should be dicts or sequences of (key, rank). The coefficient ranges from
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-1.0 (ranks are opposite) to 1.0 (ranks are identical), and is only
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calculated for keys in both rankings (for meaningful results, remove keys
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present in only one list before ranking)."""
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n = 0
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res = 0
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for k, d in _rank_dists(ranks1, ranks2):
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res += d * d
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n += 1
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try:
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return 1 - (6 * res / (n * (n * n - 1)))
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except ZeroDivisionError:
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# Result is undefined if only one item is ranked
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return 0.0
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def ranks_from_sequence(seq):
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"""Given a sequence, yields each element with an increasing rank, suitable
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for use as an argument to ``spearman_correlation``.
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"""
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return ((k, i) for i, k in enumerate(seq))
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def ranks_from_scores(scores, rank_gap=1e-15):
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"""Given a sequence of (key, score) tuples, yields each key with an
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increasing rank, tying with previous key's rank if the difference between
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their scores is less than rank_gap. Suitable for use as an argument to
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``spearman_correlation``.
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"""
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prev_score = None
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rank = 0
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for i, (key, score) in enumerate(scores):
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try:
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if abs(score - prev_score) > rank_gap:
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rank = i
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except TypeError:
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pass
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yield key, rank
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prev_score = score
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