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import torch
import random
# 参考
# 最大化均值差异MMD与Numpy/Tensorflow/Pytorch各类代码实现 - 小蔡叔叔开方舟的文章 - 知乎
# https://zhuanlan.zhihu.com/p/461656480
def guassian_kernel(source, target, kernel_mul=2.0, kernel_num=5, fix_sigma=None):
'''
将源域数据和目标域数据转化为核矩阵,即上文中的K
Params:
source: 源域数据(n * len(x))
target: 目标域数据(m * len(y))
kernel_mul:
kernel_num: 取不同高斯核的数量
fix_sigma: 不同高斯核的sigma值
Return:
sum(kernel_val): 多个核矩阵之和
'''
n_samples = int(source.size()[0])+int(target.size()[0])# 求矩阵的行数,一般source和target的尺度是一样的,这样便于计算
total = torch.cat([source, target], dim=0) #将source,target按列方向合并
#将total复制(n+m)份
total0 = total.unsqueeze(0).expand(int(total.size(0)), int(total.size(0)), int(total.size(1)))
#将total的每一行都复制成(n+m)行,即每个数据都扩展成(n+m)份
total1 = total.unsqueeze(1).expand(int(total.size(0)), int(total.size(0)), int(total.size(1)))
#求任意两个数据之间的和,得到的矩阵中坐标(i,j)代表total中第i行数据和第j行数据之间的l2 distance(i==j时为0)
L2_distance = ((total0-total1)**2).sum(2)
#调整高斯核函数的sigma值
if fix_sigma:
bandwidth = fix_sigma
else:
bandwidth = torch.sum(L2_distance.data) / (n_samples**2-n_samples)
#以fix_sigma为中值,以kernel_mul为倍数取kernel_num个bandwidth值(比如fix_sigma为1时,得到[0.25,0.5,1,2,4]
bandwidth /= kernel_mul ** (kernel_num // 2)
bandwidth_list = [bandwidth * (kernel_mul**i) for i in range(kernel_num)]
#高斯核函数的数学表达式
kernel_val = [torch.exp(-L2_distance / bandwidth_temp) for bandwidth_temp in bandwidth_list]
#得到最终的核矩阵
return sum(kernel_val)#/len(kernel_val)
def mmd_rbf(source, target, kernel_mul=2.0, kernel_num=5, fix_sigma=None):
'''
计算源域数据和目标域数据的MMD距离
Params:
source: 源域数据(n * len(x))
target: 目标域数据(m * len(y))
kernel_mul:
kernel_num: 取不同高斯核的数量
fix_sigma: 不同高斯核的sigma值
Return:
loss: MMD loss
'''
batch_size = int(source.size()[0])#一般默认为源域和目标域的batchsize相同
kernels = guassian_kernel(source, target,
kernel_mul=kernel_mul, kernel_num=kernel_num, fix_sigma=fix_sigma)
#根据式(3)将核矩阵分成4部分
XX = kernels[:batch_size, :batch_size]
YY = kernels[batch_size:, batch_size:]
XY = kernels[:batch_size, batch_size:]
YX = kernels[batch_size:, :batch_size]
loss = torch.mean(XX + YY - XY -YX)
return loss#因为一般都是n==m,所以L矩阵一般不加入计算