Cosine Similarity

Functional Interface

torchmetrics.functional.pairwise_cosine_similarity(x, y=None, reduction=None, zero_diagonal=None)[source]

Calculate pairwise cosine similarity.

s_{cos}(x,y) = \frac{<x,y>}{||x|| \cdot ||y||} = \frac{\sum_{d=1}^D x_d \cdot y_d }{\sqrt{\sum_{d=1}^D x_i^2} \cdot \sqrt{\sum_{d=1}^D y_i^2}}

If both $x$ and $y$ are passed in, the calculation will be performed pairwise between the rows of $x$ and $y$ . If only $x$ is passed in, the calculation will be performed between the rows of $x$ .

Parameters:

x (Tensor) – Tensor with shape [N, d]
y (Optional[Tensor]) – Tensor with shape [M, d], optional
reduction (Optional[Literal['mean', 'sum', 'none', None]]) – reduction to apply along the last dimension. Choose between ‘mean’, ‘sum’ (applied along column dimension) or ‘none’, None for no reduction
zero_diagonal (Optional[bool]) – if the diagonal of the distance matrix should be set to 0. If only $x$ is given this defaults to True else if $y$ is also given it defaults to False

Return type:

Tensor

Returns:

A [N,N] matrix of distances if only x is given, else a [N,M] matrix

Example

>>> import torch
>>> from torchmetrics.functional.pairwise import pairwise_cosine_similarity
>>> x = torch.tensor([[2, 3], [3, 5], [5, 8]], dtype=torch.float32)
>>> y = torch.tensor([[1, 0], [2, 1]], dtype=torch.float32)
>>> pairwise_cosine_similarity(x, y)
tensor([[0.5547, 0.8682],
        [0.5145, 0.8437],
        [0.5300, 0.8533]])
>>> pairwise_cosine_similarity(x)
tensor([[0.0000, 0.9989, 0.9996],
        [0.9989, 0.0000, 0.9998],
        [0.9996, 0.9998, 0.0000]])

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