Given a sparse matrix listing, what’s the best way to calculate the cosine similarity between each of the columns (or rows) in the matrix? I would rather not iterate n-choose-two times.
Say the input matrix is:
A= [0 1 0 0 1 0 0 1 1 1 1 1 0 1 0]
The sparse representation is:
A = 0, 1 0, 4 1, 2 1, 3 1, 4 2, 0 2, 1 2, 3
In Python, it’s straightforward to work with the matrix-input format:
import numpy as np from sklearn.metrics import pairwise_distances from scipy.spatial.distance import cosine A = np.array( [[0, 1, 0, 0, 1], [0, 0, 1, 1, 1], [1, 1, 0, 1, 0]]) dist_out = 1-pairwise_distances(A, metric="cosine") dist_out
Gives:
array([[ 1. , 0.40824829, 0.40824829],
[ 0.40824829, 1. , 0.33333333],
[ 0.40824829, 0.33333333, 1. ]])
That’s fine for a full-matrix input, but I really want to start with the sparse representation (due to the size and sparsity of my matrix). Any ideas about how this could best be accomplished?
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Answer
You can compute pairwise cosine similarity on the rows of a sparse matrix directly using sklearn. As of version 0.17 it also supports sparse output:
from sklearn.metrics.pairwise import cosine_similarity
from scipy import sparse
A = np.array([[0, 1, 0, 0, 1], [0, 0, 1, 1, 1],[1, 1, 0, 1, 0]])
A_sparse = sparse.csr_matrix(A)
similarities = cosine_similarity(A_sparse)
print('pairwise dense output:n {}n'.format(similarities))
#also can output sparse matrices
similarities_sparse = cosine_similarity(A_sparse,dense_output=False)
print('pairwise sparse output:n {}n'.format(similarities_sparse))
Results:
pairwise dense output: [[ 1. 0.40824829 0.40824829] [ 0.40824829 1. 0.33333333] [ 0.40824829 0.33333333 1. ]] pairwise sparse output: (0, 1) 0.408248290464 (0, 2) 0.408248290464 (0, 0) 1.0 (1, 0) 0.408248290464 (1, 2) 0.333333333333 (1, 1) 1.0 (2, 1) 0.333333333333 (2, 0) 0.408248290464 (2, 2) 1.0
If you want column-wise cosine similarities simply transpose your input matrix beforehand:
A_sparse.transpose()