Why there is no cos similarity metric?

[LiNaihan]

Hi, @Cysu ! I think your work is wonderful, and this repository really helps a lot in person reid! But I have a few question. First, I think all your metric is based on Euclidean distance, which is obvious in the function "pairwise_distance" in .reid.evaluator. But as far as I know, cos similarity is also a popular metric.

Second, I noticed that your feature extracted by resnet is the logit calculated by Resnet.classifier, which confused me a lot since I think the feature should be the output of the avgpool layer, which I think is consistent with other author's work. By the way, I noticed the "cut_at_pooling" option in Resnet, which I think is the solution to this problem but should be after x = F.avg_pool2d(x, x.size()[2:]) x = x.view(x.size(0), -1) instead of before them. I'm really interested in your work, hoping your reply!

[zydou]

If you want cos similarity, you can ref to this to write a cos similarity function:

def cosine_similarity(x1, x2, dim=1, eps=1e-8):
    r"""Returns cosine similarity between x1 and x2, computed along dim.

    .. math ::
        \text{similarity} = \dfrac{x_1 \cdot x_2}{\max(\Vert x_1 \Vert _2 \cdot \Vert x_2 \Vert _2, \epsilon)}

    Args:
        x1 (Variable): First input.
        x2 (Variable): Second input (of size matching x1).
        dim (int, optional): Dimension of vectors. Default: 1
        eps (float, optional): Small value to avoid division by zero.
            Default: 1e-8

    Shape:
        - Input: :math:`(\ast_1, D, \ast_2)` where D is at position `dim`.
        - Output: :math:`(\ast_1, \ast_2)` where 1 is at position `dim`.

    >>> input1 = autograd.Variable(torch.randn(100, 128))
    >>> input2 = autograd.Variable(torch.randn(100, 128))
    >>> output = F.cosine_similarity(input1, input2)
    >>> print(output)
    """
    w12 = torch.sum(x1 * x2, dim)
    w1 = torch.norm(x1, 2, dim)
    w2 = torch.norm(x2, 2, dim)
    return (w12 / (w1 * w2).clamp(min=eps)).squeeze()

Copied from http://pytorch.org/docs/0.2.0/_modules/torch/nn/functional.html#cosine_similarity

[Cysu]

@zydou Thanks a lot!

@ElijhaLee L2-Normalized features + Euclidean distance is equivalent to cosine similarity. Using classification scores rather than pooled features slightly improves performance in my experiments. Not much difference though.