Compute cosine similarity between samples in X and Y.

Cosine similarity, or the cosine kernel, computes similarity as the normalized dot product of X and Y:

Input data.

Input data. If None , the output will be the pairwise similarities between all samples in X .

Whether to return dense output even when the input is sparse. If False , the output is sparse if both input arrays are sparse.

Added in version 0.17: parameter dense_output for dense output.

Examples

>>> from sklearn.metrics.pairwise import cosine_similarity
>>> X = [[0, 0, 0], [1, 1, 1]]
>>> Y = [[1, 0, 0], [1, 1, 0]]
>>> cosine_similarity(X, Y)
array([[0.     , 0.     ],
       [0.57..., 0.81...]])