Interpreting negative Word2Vec similarity from gensim

Question

E.g. we train a word2vec model using gensim:

from gensim import corpora, models, similarities
from gensim.models.word2vec import Word2Vec

documents = ["Human machine interface for lab abc computer applications",
              "A survey of user opinion of computer system response time",
              "The EPS user interface management system",
              "System and human system engineering testing of EPS",
              "Relation of user perceived response time to error measurement",
              "The generation of random binary unordered trees",
              "The intersection graph of paths in trees",
              "Graph minors IV Widths of trees and well quasi ordering",
              "Graph minors A survey"]

texts = [[word for word in document.lower().split()] for document in documents]
w2v_model = Word2Vec(texts, size=500, window=5, min_count=1)

And when we query the similarity between words, we find negative similarity scores:

>>> w2v_model.similarity('graph', 'computer')
0.046929569156789336
>>> w2v_model.similarity('graph', 'system')
0.063683518562347399
>>> w2v_model.similarity('survey', 'generation')
-0.040026775040430063
>>> w2v_model.similarity('graph', 'trees')
-0.0072684112978664561

How do we interpret the negative scores?

If it's a cosine similarity shouldn't the range be [0,1]?

What is the upper bound and lower bound of the Word2Vec.similarity(x,y) function? There isn't much written in the docs: https://radimrehurek.com/gensim/models/word2vec.html#gensim.models.word2vec.Word2Vec.similarity =(

Looking at the Python wrapper code, there isn't much too: https://github.com/RaRe-Technologies/gensim/blob/develop/gensim/models/word2vec.py#L1165

(If possible, please do point me to the .pyx code of where the similarity function is implemented.)

Answer 1

Cosine similarity ranges from -1 to 1, same as a regular cosine wave.

As for the source:

https://github.com/RaRe-Technologies/gensim/blob/ba1ce894a5192fc493a865c535202695bb3c0424/gensim/models/word2vec.py#L1511

def similarity(self, w1, w2):
    """
    Compute cosine similarity between two words.
    Example::
      >>> trained_model.similarity('woman', 'man')
      0.73723527
      >>> trained_model.similarity('woman', 'woman')
      1.0
    """
    return dot(matutils.unitvec(self[w1]), matutils.unitvec(self[w2])

Answer 2

As others have said, the cosine similarity can range from -1 to 1 based on the angle between the two vectors being compared. The exact implementation in gensim is a simple dot product of the normalized vectors.

https://github.com/RaRe-Technologies/gensim/blob/4f0e2ae0531d67cee8d3e06636e82298cb554b04/gensim/models/keyedvectors.py#L581

def similarity(self, w1, w2):
        """
        Compute cosine similarity between two words.
        Example::
          >>> trained_model.similarity('woman', 'man')
          0.73723527
          >>> trained_model.similarity('woman', 'woman')
          1.0
        """
        return dot(matutils.unitvec(self[w1]), matutils.unitvec(self[w2]))

In terms of interpretation, you can think of these values like you might think of correlation coefficients. A value of 1 is a perfect relationship between word vectors (e.g., "woman" compared with "woman"), a value of 0 represents no relationship between words, and a value of -1 represents a perfect opposite relationship between words.