Collocations

1   Overview

Collocations are expressions of multiple words which commonly co-occur. For example, the top ten bigram collocations in Genesis are listed below, as measured using Pointwise Mutual Information.

 
>>> import nltk
>>> from nltk.collocations import *
>>> bigram_measures = nltk.collocations.BigramAssocMeasures()
>>> trigram_measures = nltk.collocations.TrigramAssocMeasures()
>>> finder = BigramCollocationFinder.from_words(
...     nltk.corpus.genesis.words('english-web.txt'))
>>> finder.nbest(bigram_measures.pmi, 10)  
[('cutting', 'instrument'), ('sewed', 'fig'), ('sweet', 'savor'),
 ('Ben', 'Ammi'), ('appoint', 'overseers'), ('olive', 'leaf'),
 ('months', 'later'), ('remaining', 'silent'), ('seek', 'occasion'),
 ('leaf', 'plucked')]

While these words are highly collocated, the expressions are also very infrequent. Therefore it is useful to apply filters, such as ignoring all bigrams which occur less than three times in the corpus:

 
>>> finder.apply_freq_filter(3)
>>> finder.nbest(bigram_measures.pmi, 10)  
[('Lahai', 'Roi'), ('gray', 'hairs'), ('Beer', 'Lahai'), ('Most', 'High'),
 ('ewe', 'lambs'), ('many', 'colors'), ('burnt', 'offering'),
 ('Paddan', 'Aram'), ('east', 'wind'), ('living', 'creature')]

We may similarly find collocations among tagged words:

 
>>> finder = BigramCollocationFinder.from_words(
...     nltk.corpus.brown.tagged_words('ca01', simplify_tags=True))
>>> finder.nbest(bigram_measures.pmi, 5)  
[(('weekend', 'N'), ('duty', 'N')),
 (('top', 'ADJ'), ('official', 'N')),
 (('George', 'NP'), ('P.', 'NP')),
 (('medical', 'ADJ'), ('intern', 'N')),
 (('1962', 'NUM'), ("governor's", 'N'))]

Or tags alone:

 
>>> finder = BigramCollocationFinder.from_words(t for w, t in
...     nltk.corpus.brown.tagged_words('ca01', simplify_tags=True))
>>> finder.nbest(bigram_measures.pmi, 10)  
[(':', '('), ('(', 'NUM'), ('NUM', ')'), (':', 'NUM'), (')', 'NUM'),
 ('-', 'WH'), ('VN', ':'), ('``', 'EX'), ('EX', 'MOD'), ('WH', 'VBZ')]

Or spanning intervening words:

 
>>> finder = BigramCollocationFinder.from_words(
...     nltk.corpus.genesis.words('english-web.txt'),
...     window_size = 20)
>>> finder.apply_freq_filter(2)
>>> ignored_words = nltk.corpus.stopwords.words('english')
>>> finder.apply_word_filter(lambda w: len(w) < 3 or w.lower() in ignored_words)
>>> finder.nbest(bigram_measures.likelihood_ratio, 10) 
[('chief', 'chief'), ('hundred', 'years'), ('father', 'father'), ('lived', 'years'),
('years', 'father'), ('lived', 'father'), ('land', 'Egypt'), ('land', 'Canaan'),
('lived', 'hundred'), ('land', 'land')]

2   Finders

The collocations package provides collocation finders which by default consider all ngrams in a text as candidate collocations:

 
>>> text = "I do not like green eggs and ham, I do not like them Sam I am!"
>>> tokens = nltk.wordpunct_tokenize(text)
>>> finder = BigramCollocationFinder.from_words(tokens)
>>> scored = finder.score_ngrams(bigram_measures.raw_freq)
>>> sorted(bigram for bigram, score in scored)  
[(',', 'I'), ('I', 'am'), ('I', 'do'), ('Sam', 'I'), ('am', '!'),
 ('and', 'ham'), ('do', 'not'), ('eggs', 'and'), ('green', 'eggs'),
 ('ham', ','), ('like', 'green'), ('like', 'them'), ('not', 'like'),
 ('them', 'Sam')]

We could otherwise construct the collocation finder from manually-derived FreqDists:

 
>>> word_fd = nltk.FreqDist(tokens)
>>> bigram_fd = nltk.FreqDist(nltk.bigrams(tokens))
>>> finder = BigramCollocationFinder(word_fd, bigram_fd)
>>> scored == finder.score_ngrams(bigram_measures.raw_freq)
True

A similar interface is provided for trigrams:

 
>>> finder = TrigramCollocationFinder.from_words(tokens)
>>> scored = finder.score_ngrams(trigram_measures.raw_freq)
>>> set(trigram for trigram, score in scored) == set(nltk.trigrams(tokens))
True

We may want to select only the top n results:

 
>>> sorted(finder.nbest(trigram_measures.raw_freq, 2))
[('I', 'do', 'not'), ('do', 'not', 'like')]

Alternatively, we can select those above a minimum score value:

 
>>> sorted(finder.above_score(trigram_measures.raw_freq,
...                           1.0 / len(nltk.trigrams(tokens))))
[('I', 'do', 'not'), ('do', 'not', 'like')]

3   Filtering candidates

All the ngrams in a text are often too many to be useful when finding collocations. It is generally useful to remove some words or punctuation, and to require a minimum frequency for candidate collocations.

Given our sample text above, if we remove all trigrams containing personal pronouns from candidature, score_ngrams should return 6 less results, and 'do not like' will be the only candidate which occurs more than once:

 
>>> len(finder.score_ngrams(trigram_measures.raw_freq))
14
>>> finder.apply_word_filter(lambda w: w in ('I', 'me'))
>>> len(finder.score_ngrams(trigram_measures.raw_freq))
8
>>> sorted(finder.above_score(trigram_measures.raw_freq,
...                           1.0 / len(nltk.trigrams(tokens))))
[('do', 'not', 'like')]

Sometimes a filter is a function on the whole ngram, rather than each word, such as if we may permit 'and' to appear in the middle of a trigram, but not on either edge:

 
>>> finder.apply_ngram_filter(lambda w1, w2, w3: 'and' in (w1, w3))
>>> len(finder.score_ngrams(trigram_measures.raw_freq))
6

Finally, it is often important to remove low frequency candidates, as we lack sufficient evidence about their significance as collocations:

 
>>> finder.apply_freq_filter(2)
>>> len(finder.score_ngrams(trigram_measures.raw_freq))
1

4   Association measures

A number of measures are available to score collocations or other associations. The arguments to measure functions are marginals of a contingency table, in the bigram case (n_ii, (n_ix, n_xi), n_xx):

        w1    ~w1
     ------ ------
 w2 | n_ii | n_oi | = n_xi
     ------ ------
~w2 | n_io | n_oo |
     ------ ------
     = n_ix        TOTAL = n_xx

We test their calculation using some known values presented in Manning and Schutze's text and other papers.

Student's t: examples from Manning and Schutze 5.3.2

 
>>> print '%0.4f' % bigram_measures.student_t(8, (15828, 4675), 14307668)
0.9999
>>> print '%0.4f' % bigram_measures.student_t(20, (42, 20), 14307668)
4.4721

Chi-square: examples from Manning and Schutze 5.3.3

 
>>> print '%0.2f' % bigram_measures.chi_sq(8, (15828, 4675), 14307668)
1.55
>>> print '%0.0f' % bigram_measures.chi_sq(59, (67, 65), 571007)
456400

Likelihood ratios: examples from Dunning, CL, 1993

 
>>> print '%0.2f' % bigram_measures.likelihood_ratio(110, (2552, 221), 31777)
270.72
>>> print '%0.2f' % bigram_measures.likelihood_ratio(8, (13, 32), 31777)
95.29

Pointwise Mutual Information: examples from Manning and Schutze 5.4

 
>>> print '%0.2f' % bigram_measures.pmi(20, (42, 20), 14307668)
18.38
>>> print '%0.2f' % bigram_measures.pmi(20, (15019, 15629), 14307668)
0.29

TODO: Find authoritative results for trigrams.

5   Using contingency table values

While frequency counts make marginals readily available for collocation finding, it is common to find published contingency table values. The collocations package therefore provides a wrapper, ContingencyMeasures, which wraps an association measures class, providing association measures which take contingency values as arguments, (n_ii, n_io, n_oi, n_oo) in the bigram case.

 
>>> from nltk.metrics import ContingencyMeasures
>>> cont_bigram_measures = ContingencyMeasures(bigram_measures)
>>> print '%0.2f' % cont_bigram_measures.likelihood_ratio(8, 5, 24, 31740)
95.29
>>> print '%0.2f' % cont_bigram_measures.chi_sq(8, 15820, 4667, 14287173)
1.55

6   Ranking and correlation

It is useful to consider the results of finding collocations as a ranking, and the rankings output using different association measures can be compared using the Spearman correlation coefficient.

Ranks can be assigned to a sorted list of results trivially by assigning strictly increasing ranks to each result:

 
>>> from nltk.metrics.spearman import *
>>> results_list = ['item1', 'item2', 'item3', 'item4', 'item5']
>>> print list(ranks_from_sequence(results_list))
[('item1', 0), ('item2', 1), ('item3', 2), ('item4', 3), ('item5', 4)]

If scores are available for each result, we may allow sufficiently similar results (differing by no more than rank_gap) to be assigned the same rank:

 
>>> results_scored = [('item1', 50.0), ('item2', 40.0), ('item3', 38.0),
...                   ('item4', 35.0), ('item5', 14.0)]
>>> print list(ranks_from_scores(results_scored, rank_gap=5))
[('item1', 0), ('item2', 1), ('item3', 1), ('item4', 1), ('item5', 4)]

The Spearman correlation coefficient gives a number from -1.0 to 1.0 comparing two rankings. A coefficient of 1.0 indicates identical rankings; -1.0 indicates exact opposite rankings.

 
>>> print '%0.1f' % spearman_correlation(
...         ranks_from_sequence(results_list),
...         ranks_from_sequence(results_list))
1.0
>>> print '%0.1f' % spearman_correlation(
...         ranks_from_sequence(reversed(results_list)),
...         ranks_from_sequence(results_list))
-1.0
>>> results_list2 = ['item2', 'item3', 'item1', 'item5', 'item4']
>>> print '%0.1f' % spearman_correlation(
...        ranks_from_sequence(results_list),
...        ranks_from_sequence(results_list2))
0.6
>>> print '%0.1f' % spearman_correlation(
...        ranks_from_sequence(reversed(results_list)),
...        ranks_from_sequence(results_list2))
-0.6