Aligning words in 2 sentences using a numpy 2d array - numpy

Question

Given 2 sentences, I need to align the words in those sentences based on the best similarity match between the words in these sentences.
For instance, consider 2 sentences:
sent1 = "John saw Mary" # 3 tokens
sent2 = "All the are grown by farmers" # 6 tokens
Here, for each token in sent1, I need to find the most similar token in sent2. Further, if a token in sent2 is already matched with a token in sent1, then it cannot be matched with another token in sent1.
For the purpose, I use a similarity matrix between the tokens in a sentence, as given below
cosMat = (array([[0.1656948 , 0.16653526, 0.13380264, 0.09286133, 0.16262592,
0.14392284],
[0.40876892, 0.46331584, 0.28574535, 0.34924293, 0.2480594 ,
0.25846344],
[0.15394737, 0.10269377, 0.12189645, 0.09426117, 0.09631223,
0.10549664]], dtype=float32)
cosMat is a 2d ndarray of size (3,6) which contain the cosine similarity scores of the tokens in both the sentences.
np.argmax would provide the following array as output
np.argmax(cosMat,axis=1)
array([1, 1, 0]))
However this is not a valid solution, as the first and second tokens of sent1 aligns with second token of sent2.
Instead I chose to do the following:
sortArr = np.dstack(np.unravel_index(np.argsort(-cosMat.ravel()), cosMat.shape))
rowSet = set()
colSet = set()
matches = list()
for item in sortArr[0]:
if item[1] not in colSet:
if item[0] not in rowSet:
matches.append((item[0],item[1],cosMat[item[0],item[1]]))
colSet.add(item[1])
rowSet.add(item[0])
matches
This gives the following output, which is the desirable output:
[(1, 1, 0.46331584), (0, 0, 0.1656948), (2, 2, 0.121896446)]
My question is, is there a more efficient way to achieve, for what I have done using the code above?

Answer 1

Here's an alternative, it requires you to copy the initial similarity matrix. Everytime you find the best match, you discard the two tokens from the pair by replacing the correspond row and column in the copied matrix by 0. This ensures you do not find the same token in multiple pairs.
res = []
mat = np.copy(cosMat)
for _ in range(mat.shape[0]):
i, j = np.unravel_index(mat.argmax(), mat.shape)
res.append((i, j, mat[i, j]))
mat[i,:], mat[:,j] = 0, 0
Will return:
[(1, 1, 0.46331584), (0, 0, 0.1656948), (2, 2, 0.12189645)]
However, considering you only using np.argsort once. Yours will, most probably, be faster.
Otherwise, I would rewrite your version, for conciseness, as:
sortArr = zip(*np.unravel_index(np.argsort(-cosMat.ravel()), cosMat.shape))
matches = []
rows, cols = set(), set()
for x, y in sortArr:
if x not in cols and y not in rows:
matches.append((x, y, cosMat[x, y]))
cols.add(x)
rows.add(y)
You could use a single set instead of two, by using some kind of prefix for the indices in order to distinguish rows from columns. Here again I'm not sure there's much gain in doing so:
matches = []
matched = set()
for x, y in sortArr:
if 'i%i'%x not in matched and 'j%i'%y not in matched:
matches.append((x, y, cosMat[x, y]))
matched.update(['i%s'%x, 'j%s'%y])