关于

MMD （maximum mean discrepancy）是用来衡量两组数据分布之间相似度的度量。一般地，如果两组数据分布相似，那么MMD 损失就相对较小，说明两组数据/特征处于相似的特征空间中。基于这个想法，对于源域和目标域数据，在使用深度学习进行特征提取中，使用MMD损失，可以让模型提取两个域的共有特征/空间，从而实现源域到目标域的迁移。

参考论文：https://arxiv.org/abs/1409.6041

工具

Python

 

方法实现

定义mmd函数

#!/usr/bin/env python
# encoding: utf-8

import torch

# Consider linear time MMD with a linear kernel:
# K(f(x), f(y)) = f(x)^Tf(y)
# h(z_i, z_j) = k(x_i, x_j) + k(y_i, y_j) - k(x_i, y_j) - k(x_j, y_i)
#             = [f(x_i) - f(y_i)]^T[f(x_j) - f(y_j)]
#
# f_of_X: batch_size * k
# f_of_Y: batch_size * k
def mmd_linear(f_of_X, f_of_Y):
    delta = f_of_X - f_of_Y
    loss = torch.mean(torch.mm(delta, torch.transpose(delta, 0, 1)))
    return loss

def guassian_kernel(source, target, kernel_mul=2.0, kernel_num=5, fix_sigma=None):
    n_samples = int(source.size()[0])+int(target.size()[0])
    total = torch.cat([source, target], dim=0)
    total0 = total.unsqueeze(0).expand(int(total.size(0)), int(total.size(0)), int(total.size(1)))
    total1 = total.unsqueeze(1).expand(int(total.size(0)), int(total.size(0)), int(total.size(1)))
    L2_distance = ((total0-total1)**2).sum(2)
    if fix_sigma:
        bandwidth = fix_sigma
    else:
        bandwidth = torch.sum(L2_distance.data) / (n_samples**2-n_samples)
    bandwidth /= kernel_mul ** (kernel_num // 2)
    bandwidth_list = [bandwidth * (kernel_mul**i) for i in range(kernel_num)]
    kernel_val = [torch.exp(-L2_distance / bandwidth_temp) for bandwidth_temp in bandwidth_list]
    return sum(kernel_val)#/len(kernel_val)


def mmd_rbf_accelerate(source, target, kernel_mul=2.0, kernel_num=5, fix_sigma=None):
    batch_size = int(source.size()[0])
    kernels = guassian_kernel(source, target,
        kernel_mul=kernel_mul, kernel_num=kernel_num, fix_sigma=fix_sigma)
    loss = 0
    for i in range(batch_size):
        s1, s2 = i, (i+1)%batch_size
        t1, t2 = s1+batch_size, s2+batch_size
        loss += kernels[s1, s2] + kernels[t1, t2]
        loss -= kernels[s1, t2] + kernels[s2, t1]
    return loss / float(batch_size)

def mmd_rbf_noaccelerate(source, target, kernel_mul=2.0, kernel_num=5, fix_sigma=None):
    batch_size = int(source.size()[0])
    kernels = guassian_kernel(source, target,
                              kernel_mul=kernel_mul, kernel_num=kernel_num, fix_sigma=fix_sigma)
    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

定义基于mmd特征对齐CNN模型

# encoding=utf-8

import torch.nn as nn
import torch.nn.functional as F


class Network(nn.Module):
    def __init__(self):
        super(Network, self).__init__()
        self.conv1 = nn.Sequential(
            nn.Conv2d(in_channels=3, out_channels=64, kernel_size=(1, 3)),
            nn.ReLU()
        )
        self.conv2 = nn.Sequential(
            nn.Conv2d(in_channels=64, out_channels=64, kernel_size=(1, 3)),
            nn.ReLU(),
            nn.Dropout(0.4),
            nn.MaxPool2d(kernel_size=(1, 2), stride=2)
        )
        self.fc1 = nn.Sequential(
            nn.Linear(in_features=64 * 98, out_features=100),
            nn.ReLU()
        )
        self.fc2 = nn.Sequential(
            nn.Linear(in_features=100, out_features=2)
        )

    def forward(self, src, tar):
        x_src = self.conv1(src)
        x_tar = self.conv1(tar)
        
        x_src = self.conv2(x_src)
        x_tar = self.conv2(x_tar)
        #print(x_src.shape)
        x_src = x_src.reshape(-1, 64 * 98)
        x_tar = x_tar.reshape(-1, 64 * 98)
        
        x_src_mmd = self.fc1(x_src)
        x_tar_mmd = self.fc1(x_tar)
        
        #x_src = self.fc1(x_src)
        #x_tar = self.fc1(x_tar)
        
        #x_src_mmd = self.fc2(x_src)
        #x_tar_mmd = self.fc2(x_tar)
        
        y_src = self.fc2(x_src_mmd)
        
        return y_src, x_src_mmd, x_tar_mmd
    

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