Make termsim matrix positive definite even with negative similarities (#2397)

* Make termsim matrix positive definite even with negative similarities

* Test that termsim matrix with negative similarities is positive definite

* Use `or` instead of `{...}` for documenting a union of types

Author: Witiko

gensim/similarities/termsim.py

@@ -168,7 +168,7 @@ class SparseTermSimilarityMatrix(SaveLoad):
         strict column diagonal dominance. Positive definiteness is a necessary precondition if you
         later wish to derive a change-of-basis matrix from the term similarity matrix using Cholesky
         factorization.
-    nonzero_limit : {int, None}, optional
+    nonzero_limit : int or None, optional
         The maximum number of non-zero elements outside the diagonal in a single column of the
         sparse term similarity matrix. If None, then no limit will be imposed.
     dtype : numpy.dtype, optional
@@ -242,11 +242,11 @@ def __init__(self, source, dictionary=None, tfidf=None, symmetric=True, positive
                     key=lambda x: (lambda term_index, _: (tfidf.idfs[term_index], -term_index))(*x), reverse=True)
 
             for row_number, (t2_index, similarity) in zip(range(num_rows), rows):
-                if positive_definite and column_sum[t1_index] + similarity >= 1.0:
+                if positive_definite and column_sum[t1_index] + abs(similarity) >= 1.0:
                     break
                 if symmetric:
                     if column_nonzero[t2_index] <= nonzero_limit \
-                            and (not positive_definite or column_sum[t2_index] + similarity < 1.0) \
+                            and (not positive_definite or column_sum[t2_index] + abs(similarity) < 1.0) \
                             and not (t1_index, t2_index) in matrix:
                         matrix[t1_index, t2_index] = similarity
                         column_nonzero[t1_index] += 1

gensim/test/test_similarities.py

@@ -800,21 +800,22 @@ def test_symmetric(self):
 
     def test_positive_definite(self):
         """Test the positive_definite parameter of the matrix constructor."""
+        negative_index = UniformTermSimilarityIndex(self.dictionary, term_similarity=-0.5)
         matrix = SparseTermSimilarityMatrix(
-            self.index, self.dictionary, nonzero_limit=2).matrix.todense()
+            negative_index, self.dictionary, nonzero_limit=2).matrix.todense()
         expected_matrix = numpy.array([
-            [1.0, 0.5, 0.5, 0.0, 0.0],
-            [0.5, 1.0, 0.0, 0.5, 0.0],
-            [0.5, 0.0, 1.0, 0.0, 0.0],
-            [0.0, 0.5, 0.0, 1.0, 0.0],
+            [1.0, -.5, -.5, 0.0, 0.0],
+            [-.5, 1.0, 0.0, -.5, 0.0],
+            [-.5, 0.0, 1.0, 0.0, 0.0],
+            [0.0, -.5, 0.0, 1.0, 0.0],
             [0.0, 0.0, 0.0, 0.0, 1.0]])
         self.assertTrue(numpy.all(expected_matrix == matrix))
 
         matrix = SparseTermSimilarityMatrix(
-            self.index, self.dictionary, nonzero_limit=2, positive_definite=True).matrix.todense()
+            negative_index, self.dictionary, nonzero_limit=2, positive_definite=True).matrix.todense()
         expected_matrix = numpy.array([
-            [1.0, 0.5, 0.0, 0.0, 0.0],
-            [0.5, 1.0, 0.0, 0.0, 0.0],
+            [1.0, -.5, 0.0, 0.0, 0.0],
+            [-.5, 1.0, 0.0, 0.0, 0.0],
             [0.0, 0.0, 1.0, 0.0, 0.0],
             [0.0, 0.0, 0.0, 1.0, 0.0],
             [0.0, 0.0, 0.0, 0.0, 1.0]])