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MMD：maximum mean discrepancy。最大平均差异, 用于判断两个分布p和q是否相同。它的基本假设是：如果对于所有以分布生成的样本空间为输入的函数f，如果两个分布生成的足够多的样本在f上的对应的像的均值都相等，那么那么可以认为这两个分布是同一个分布。现在一般用于度量两个分布之间的相似性。
Keras 2.2.4 tensorflow 1.9.0
import torch
import matplotlib
import os
import argparse
import numpy as np
from PIL import Image
from torch.autograd import Variable
from keras.applications.inception_v3 import InceptionV3
os.environ["TF_CPP_MIN_LOG_LEVEL"] = '3' # 只显示 Error
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
def data_list(dirPath):
# read img
generatedImgs = []
realImgs = []
for root, dirs, files in os.walk(dirPath):
for filename in sorted(files):
# 判断该文件是否是目标文件
if "generated" in filename:
generatedPath = root + '/' + filename
generatedImgs.append(readImg(generatedPath))
# 对比图片路径
realPath = root + '/' + filename.replace('generated', 'real')
realImgs.append(readImg(realPath))
return generatedImgs, realImgs
def readImg(imgPath):
img = Image.open(imgPath) # RGB
# img.show()
# PIL转numpy类型
img = np.array(img).astype(np.float)
return img/255
if __name__ == '__main__':
### 参数设定
parser = argparse.ArgumentParser()
parser.add_argument('--dataset_dir', type=str, default=r'D:\Project\pix2pix-master\results', help='results')
parser.add_argument('--name', type=str, default='faces', help='name of dataset')
opt = parser.parse_args()
# 数据集
dirPath = os.path.join(opt.dataset_dir, opt.name)
generatedImgs, realImgs = data_list(dirPath)
size = len(generatedImgs)
print("数据集：", size)
X = torch.Tensor(generatedImgs)
Y = torch.Tensor(realImgs)
print('shape: ', X.shape, Y.shape)
# prepare the inception v3 model
model = InceptionV3(include_top=False, pooling='avg')
X, Y = model.predict(X), model.predict(Y)
X, Y = Variable(torch.Tensor(X)), Variable(torch.Tensor(Y))
mmd = mmd_rbf(X, Y)
print("mmd: ", mmd)
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