slight cleanup, seems to work well.

examples/bigrams.py

@@ -10,8 +10,15 @@ The ``from_frequencies`` method allows generating wordclouds from a list or
 array of ``(word, frequency)`` tuples, where ``word`` can be any string, and
 ``frequency`` can be any int or float.
 
+
+We are using the likelihood ratio score developed by Dunning to find "collocations",
+which are phrases made up of two or more words (we only consider two here).
+If the chance that a bigram is a collocation is high, we discount the appearances
+of the single words -- otherwise they would always be at least as big as the bigram.
+
 """
 
+
 import numpy as np
 from PIL import Image
 from os import path
@@ -20,10 +27,31 @@ import random
 from itertools import tee
 from collections import defaultdict
 import re
+from math import log
 
 from wordcloud import WordCloud, STOPWORDS
 
 
+# dunning's likelihood ratio with notation from
+# http://nlp.stanford.edu/fsnlp/promo/colloc.pdf
+
+
+def l(k, n, x):
+    return log(max(x, 1e-10)) * k + log(max(1 - x, 1e-10)) * (n - k)
+
+
+def score(bigram, counts, n_words):
+    N = n_words
+    c12 = counts[bigram]
+    c1 = counts[bigram[0]]
+    c2 = counts[bigram[1]]
+    p = c2 / N
+    p1 = c12 / c1
+    p2 = (c2 - c12) / (N - c1)
+    score = l(c12, c1, p) + l(c2 - c12, N - c1, p) - l(c12, c1, p1) - l(c2 - c12, N - c1, p2)
+    return -2 * score
+
+
 def grey_color_func(word, font_size, position, orientation, random_state=None, **kwargs):
     return "hsl(0, 0%%, %d%%)" % random.randint(60, 100)
 
@@ -35,6 +63,7 @@ def pairwise(iterable):
     next(b, None)
     return zip(a, b)
 
+
 def unigrams_and_bigrams(text, stopwords=None):
     stopwords = [s.lower() for s in stopwords] if stopwords is not None else []
     words = re.findall(r"\w[\w']+", text)
@@ -54,19 +83,19 @@ def unigrams_and_bigrams(text, stopwords=None):
     for bigram in bigrams:
         # join tuples by a space
         counts_bigrams[bigram] += 1
-        
+
     counts_all = {}
     counts_all.update(counts_unigrams)
-    counts_all.update(counts_bigrams)    
-    
+    counts_all.update(counts_bigrams)
+
     # decount words inside bigrams
-    for bigram in counts_bigrams().keys():
+    for bigram in counts_bigrams.keys():
         # collocation detection (30 is arbitrary):
         if score(bigram, counts_all, n_words) > 30:
             counts_unigrams[bigram[0]] -= counts_bigrams[bigram]
             counts_unigrams[bigram[1]] -= counts_bigrams[bigram]
         # add joined bigram into unigrams
-        counts_unigrams[' '.join(bigram)] = counts_bigram[bigram]
+        counts_unigrams[' '.join(bigram)] = counts_bigrams[bigram]
     return counts_unigrams
 
 
@@ -91,6 +120,6 @@ wc = WordCloud(max_words=1000, mask=mask, margin=10,
 # from_freqencies ignores "stopwords" so we have to do it ourselves
 wc.generate_from_frequencies(unigrams_and_bigrams(text, STOPWORDS).items())
 plt.imshow(wc)
-wc.to_file("a_new_hope.png")
+wc.to_file("a_new_hope_bigrams.png")
 plt.axis("off")
 plt.show()