Fix symmetrical case for hellinger distance. Fix #1854 (#1860)

* fix: fix bugs in hellinger distance computing

This changes fix the bugs that return different distance when we
call hellinger(x, y) and hellinger(y, x).
The cause of this bug is that we compute the distance based on one
distribution's index previously, but we should iterate all the
index appears in two probability distributions.

* rename variable + fix union indices error in python3

* fix and add tests for hellinger distance

* fix the currrent test for different length BOW inputs
* add a test for symmetrical inputs

gensim/matutils.py

@@ -897,10 +897,9 @@ def hellinger(vec1, vec2):
     if isbow(vec1) and isbow(vec2):
         # if it is a BoW format, instead of converting to dense we use dictionaries to calculate appropriate distance
         vec1, vec2 = dict(vec1), dict(vec2)
-        if len(vec2) < len(vec1):
-            vec1, vec2 = vec2, vec1  # swap references so that we iterate over the shorter vector
+        indices = set(list(vec1.keys()) + list(vec2.keys()))
         sim = np.sqrt(
-            0.5 * sum((np.sqrt(value) - np.sqrt(vec2.get(index, 0.0)))**2 for index, value in iteritems(vec1))
+            0.5 * sum((np.sqrt(vec1.get(index, 0.0)) - np.sqrt(vec2.get(index, 0.0)))**2 for index in indices)
         )
         return sim
     else:

gensim/test/test_similarity_metrics.py

@@ -105,12 +105,21 @@ def test_inputs(self):
 
     def test_distributions(self):
 
-        # checking bag of words as inputs
+        # checking different length bag of words as inputs
         vec_1 = [(2, 0.1), (3, 0.4), (4, 0.1), (5, 0.1), (1, 0.1), (7, 0.2)]
         vec_2 = [(1, 0.1), (3, 0.8), (4, 0.1)]
         result = matutils.hellinger(vec_1, vec_2)
-        expected = 0.185241936534
+        expected = 0.484060507634
+        self.assertAlmostEqual(expected, result)
+
+        # checking symmetrical bag of words inputs return same distance
+        vec_1 = [(2, 0.1), (3, 0.4), (4, 0.1), (5, 0.1), (1, 0.1), (7, 0.2)]
+        vec_2 = [(1, 0.1), (3, 0.8), (4, 0.1), (8, 0.1), (10, 0.8), (9, 0.1)]
+        result = matutils.hellinger(vec_1, vec_2)
+        result_symmetric = matutils.hellinger(vec_2, vec_1)
+        expected = 0.856921568786
         self.assertAlmostEqual(expected, result)
+        self.assertAlmostEqual(expected, result_symmetric)
 
         # checking ndarray, csr_matrix as inputs
         vec_1 = np.array([[1, 0.3], [0, 0.4], [2, 0.3]])