>>> sorted(normalise({1: 1, 2: 2, 3: 1}).items())
[(1, 0.25), (2, 0.5), (3, 0.25)]
"""
- length = sum([f for f in frequencies.values()])
+ length = sum(f for f in frequencies.values())
return collections.defaultdict(int, ((k, v / length)
for (k, v) in frequencies.items()))
return len(frequencies1) / total
-def cosine_distance(frequencies1, frequencies2):
+def cosine_similarity(frequencies1, frequencies2):
"""Finds the distances between two frequency profiles, expressed as dictionaries.
Assumes every key in frequencies1 is also in frequencies2
- >>> cosine_distance({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
- -2.22044604...e-16
- >>> cosine_distance({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
- -2.22044604...e-16
- >>> cosine_distance({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
- 0.4226497308...
- >>> cosine_distance({'a':0, 'b':1}, {'a':1, 'b':1}) # doctest: +ELLIPSIS
- 0.29289321881...
+ >>> cosine_similarity({'a':1, 'b':1, 'c':1}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
+ 1.0000000000...
+ >>> cosine_similarity({'a':2, 'b':2, 'c':2}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
+ 1.0000000000...
+ >>> cosine_similarity({'a':0, 'b':2, 'c':0}, {'a':1, 'b':1, 'c':1}) # doctest: +ELLIPSIS
+ 0.5773502691...
+ >>> cosine_similarity({'a':0, 'b':1}, {'a':1, 'b':1}) # doctest: +ELLIPSIS
+ 0.7071067811...
"""
numerator = 0
length1 = 0
for k in frequencies1:
numerator += frequencies1[k] * frequencies2[k]
length1 += frequencies1[k]**2
- for k in frequencies2.keys():
- length2 += frequencies2[k]
- return 1 - (numerator / (length1 ** 0.5 * length2 ** 0.5))
+ for k in frequencies2:
+ length2 += frequencies2[k]**2
+ return numerator / (length1 ** 0.5 * length2 ** 0.5)
-def log_pl(frequencies1, frequencies2):
- return sum([frequencies2[l] * log10(frequencies1[l]) for l in frequencies1])
-
-def inverse_log_pl(frequencies1, frequencies2):
- return -log_pl(frequencies1, frequencies2)
-
-def index_of_coincidence(frequencies):
- """Finds the (expected) index of coincidence given a set of frequencies
- """
- return sum([f ** 2 for f in frequencies.values()]) * len(frequencies.keys())
-
if __name__ == "__main__":
import doctest