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func.py
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import torch
import torch.nn.functional as F
import copy
import math
import random
from scipy.optimize import linear_sum_assignment
def compute_kernel(x, y, kernel_type='gaussian', kernel_param=1.0):
"""
计算核矩阵
Args:
x: 样本集合X，大小为 (batch_size, feature_dim)
y: 样本集合Y，大小为 (batch_size, feature_dim)
kernel_type: 核函数类型，可以是 'gaussian' 或 'linear'
kernel_param: 核函数参数，对于高斯核，表示高斯核的方差
Returns:
kernel_matrix: 核矩阵，大小为 (batch_size, batch_size)
"""
if kernel_type == 'gaussian':
x_norm = (x**2).sum(dim=-1, keepdim=True) # 计算 x 的范数的平方
y_norm = (y**2).sum(dim=-1, keepdim=True) # 计算 y 的范数的平方
xy = torch.matmul(x, y.t()) # 计算 x 和 y 的内积
pairwise_distance = x_norm + y_norm.t() - 2 * xy # 计算欧氏距离的平方
kernel_matrix = torch.exp(-pairwise_distance / (2 * kernel_param**2)) # 高斯核函数
elif kernel_type == 'linear':
kernel_matrix = torch.matmul(x, y.t()) # 线性核函数
else:
raise ValueError("Unsupported kernel type.")
return kernel_matrix
def mk_mmd_loss(x, y, kernel_types=['gaussian','gaussian','gaussian','gaussian','gaussian'], kernel_params=[0.1, 0.5, 1.0, 2.0, 5.0]):
"""
计算MK-MMD损失函数
Args:
x: 样本集合X，大小为 (batch_size, feature_dim)
y: 样本集合Y，大小为 (batch_size, feature_dim)
kernel_types: 核函数类型列表，例如 ['gaussian', 'linear']
kernel_params: 核函数参数列表，例如 [1.0, 0.5]
Returns:
mk_mmd: MK-MMD损失值
"""
batch_size = x.size(0)
n_kernels = len(kernel_types)
# 计算各个核矩阵
xx_kernels = [compute_kernel(x, x, kernel_type, kernel_param) for kernel_type, kernel_param in zip(kernel_types, kernel_params)]
yy_kernels = [compute_kernel(y, y, kernel_type, kernel_param) for kernel_type, kernel_param in zip(kernel_types, kernel_params)]
xy_kernels = [compute_kernel(x, y, kernel_type, kernel_param) for kernel_type, kernel_param in zip(kernel_types, kernel_params)]
# 计算MK-MMD值
mk_mmd = 0.0
for i in range(n_kernels):
xx = xx_kernels[i]
yy = yy_kernels[i]
xy = xy_kernels[i]
mmd = torch.mean(xx) - 2 * torch.mean(xy) + torch.mean(yy)
mk_mmd += torch.sqrt(torch.max(torch.tensor(0.0), mmd))
mk_mmd /= n_kernels
return mk_mmd
def mk_dis(x,y, kernel_types=['gaussian','gaussian','gaussian','gaussian','gaussian'], kernel_params=[0.1, 0.5, 1.0, 2.0, 5.0]):
n_kernels = len(kernel_types)
# 计算各个核矩阵
xx_kernels = [compute_kernel(x, x, kernel_type, kernel_param) for kernel_type, kernel_param in zip(kernel_types, kernel_params)]
yy_kernels = [compute_kernel(y, y, kernel_type, kernel_param) for kernel_type, kernel_param in zip(kernel_types, kernel_params)]
xy_kernels = [compute_kernel(x, y, kernel_type, kernel_param) for kernel_type, kernel_param in zip(kernel_types, kernel_params)]
total_dis=0
for i in range(n_kernels):
# xx = xx_kernels[i]
# yy = yy_kernels[i]
xy = xy_kernels[i]
# xx_dig=torch.diag(xx)
# yy_dig=torch.diag(yy)
# x2=xx_dig.unsqueeze(1).repeat(1,xy.shape[1])
# y2=yy_dig.unsqueeze(0).repeat(xy.shape[0],1)
# print(x2)
# print(y2)
x2,y2=1,1 # 高斯分布对角线为1
dis = x2 - 2 * xy + y2
dis = torch.sqrt(torch.max(torch.tensor(0.0), dis))
total_dis += dis
avg_dis = total_dis / n_kernels
return avg_dis
class KernelKMeans:
def __init__(self, n_clusters=3, gamma=1.0, max_iter=100, device=None, centers=None):
self.n_clusters = n_clusters
self.gamma = gamma
self.max_iter = max_iter
self.device = device
if self.device is None:
torch.device("cpu")
self.centers_=centers
def _kernel_function(self, X, Y):
pairwise_sq_dists = mk_dis(X,Y)
K = torch.exp(-self.gamma * pairwise_sq_dists)
return K
def fit(self, X):
n_samples = X.shape[0]
self.labels_ = torch.zeros(n_samples, dtype=torch.int64).to(self.device)
if self.centers_ is None:
self.centers_ = X[torch.randperm(n_samples)[:self.n_clusters]].to(self.device)
self.iterations_ = 0
for _ in range(self.max_iter):
self.iterations_ += 1
distances = mk_dis(X, self.centers_)
self.labels_ = torch.argmin(distances, dim=1).to(self.device)
prev_centers = self.centers_.clone().to(self.device)
for i in range(self.n_clusters):
cluster_points = X[self.labels_ == i].to(self.device)
self.centers_[i]= torch.mean(cluster_points,dim=0)
# weights = self._kernel_function(cluster_points, cluster_points).sum(dim=1)
# weighted_sum = torch.sum(cluster_points * weights.view(-1, 1), dim=0)
# total_weights = torch.sum(weights)
# self.centers_[i] = weighted_sum / total_weights
if torch.allclose(prev_centers, self.centers_):
break
self.inertia_ = torch.sum(torch.min(distances, dim=1).values)
def predict(self, X):
distances = mk_dis(X, self.centers_)
labels = torch.argmin(distances, dim=1).to(self.device)
return labels,distances
def find_min_distance(A, B):
# 构建距离矩阵
distances=mk_dis(A,B)
# print(distances)
# 使用线性分配问题求解最小匹配
row_indices, col_indices = linear_sum_assignment(distances)
# print(row_indices)
# print(col_indices)
#
# # 计算匹配的距离和
# min_distance = distances[row_indices, col_indices].sum()
return col_indices
if __name__ == '__main__':
# a=torch.rand([2,5])
# b=torch.rand([3,5])
# print(mk_mmd_loss(a,b))
# print(mk_dis(a,b))
# model = KernelKMeans()
# a = torch.rand([10, 5])
# model.fit(a)
# print(model.predict(a))
a = torch.rand([6, 64])
b = torch.rand([6, 64])
result = find_min_distance(a,b)
print(result)