a = torch.tensor([[ [1, 2], [3, 4] ], [ [5, 6], [7, 8] ] ], dtype=torch.float)
print(a.shape)
"""
[
    [
        [1, 2],
        [3, 4]
    ],
    [
        [5, 6],
        [7, 8]
    ]
]
"""

假設(shè)有2個矩陣：[[1, 2], [3, 4]] 和 [[5, 6], [7, 8]], 求2者的余弦相似。

按照dim=0求余弦相似：

import torch.nn.functional as F
input1 = torch.tensor([[1, 2], [3, 4]], dtype=torch.float)
input2 = torch.tensor([[5, 6], [7, 8]], dtype=torch.float)
output = F.cosine_similarity(input1, input2, dim=0)
print(output)

結(jié)果如下：

tensor([0.9558, 0.9839])

那么，這個數(shù)值是怎么得來的？是按照

具體求解如下：

print(F.cosine_similarity(torch.tensor([1,3], dtype=torch.float) , torch.tensor([5,7], dtype=torch.float), dim=0))
print(F.cosine_similarity(torch.tensor([2,4], dtype=torch.float) , torch.tensor([6,8], dtype=torch.float), dim=0))

運行結(jié)果如下:

tensor(0.9558)tensor(0.9839)

可以用scipy.spatial進一步佐證:

from scipy import spatial

dataSetI = [1,3]
dataSetII = [5,7]
result = 1 - spatial.distance.cosine(dataSetI, dataSetII)
print(result)

運行結(jié)果如下:

0.95577900872195

同理：

dataSetI = [2,4]
dataSetII = [6,8]
result = 1 - spatial.distance.cosine(dataSetI, dataSetII)
print(result)

運行結(jié)果如下:

0.9838699100999074

按照dim=1求余弦相似:

output = F.cosine_similarity(input1, input2, dim=1)
print(output)

運行結(jié)果如下：

tensor([0.9734, 0.9972])

同理，用用scipy.spatial進一步佐證:

dataSetI = [1,2]
dataSetII = [5,6]
result = 1 - spatial.distance.cosine(dataSetI, dataSetII)
print(result)

運行結(jié)果：0.973417168333576

dataSetI = [3,4]
dataSetII = [7,8]
result = 1 - spatial.distance.cosine(dataSetI, dataSetII)
print(result)

運行結(jié)果：

0.9971641204866132

結(jié)果與F.cosine_similarity相符合。

補充：給定一個張量，計算多個張量與它的余弦相似度，并將計算得到的余弦相似度標準化。

import torch
def get_att_dis(target, behaviored):
    attention_distribution = []
    for i in range(behaviored.size(0)):
        attention_score = torch.cosine_similarity(target, behaviored[i].view(1, -1))  # 計算每一個元素與給定元素的余弦相似度
        attention_distribution.append(attention_score)
    attention_distribution = torch.Tensor(attention_distribution)
 
    return attention_distribution / torch.sum(attention_distribution, 0)        # 標準化
 
a = torch.FloatTensor(torch.rand(1, 10))
print('a', a)
b = torch.FloatTensor(torch.rand(3, 10))
print('b', b)
 
similarity = get_att_dis(target=a, behaviored=b)
print('similarity', similarity)

a tensor([[0.9255, 0.2194, 0.8370, 0.5346, 0.5152, 0.4645, 0.4926, 0.9882, 0.2783,
0.9258]])
b tensor([[0.6874, 0.4054, 0.5739, 0.8017, 0.9861, 0.0154, 0.8513, 0.8427, 0.6669,
0.0694],
[0.1720, 0.6793, 0.7764, 0.4583, 0.8167, 0.2718, 0.9686, 0.9301, 0.2421,
0.0811],
[0.2336, 0.4783, 0.5576, 0.6518, 0.9943, 0.6766, 0.0044, 0.7935, 0.2098,
0.0719]])
similarity tensor([0.3448, 0.3318, 0.3234])

總結(jié)

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