matlab实现mmd距离计算
时间: 2023-11-13 20:58:39 浏览: 110
MMD(Maximum Mean Discrepancy)是一种度量两个概率分布之间距离的方法,可以用于非参数统计学习中的核方法。在Matlab中,可以使用以下步骤实现MMD距离计算:
1. 定义核函数,例如高斯核函数:K(x,y) = exp(-||x-y||^2/(2*sigma^2))。
2. 计算两个样本集的核矩阵,例如X和Y:K_xx = K(X,X),K_yy = K(Y,Y),K_xy = K(X,Y)。
3. 计算MMD距离:MMD^2 = ||1/n_x * sum(K_xx) - 1/n_xn_y * sum(K_xy) + 1/n_y * sum(K_yy)||^2,其中n_x和n_y分别为X和Y的样本数,n_xn_y = n_x * n_y。
以下是一个Matlab代码示例:
```
% 定义高斯核函数
function K = gaussian_kernel(X,Y,sigma)
n_x = size(X,1);
n_y = size(Y,);
XX = sum(X.^2,2);
YY = sum(Y.^2,2);
XY = X*Y';
dist = repmat(XX,1,n_y) + repmat(YY',n_x,1) - 2*XY;
K = exp(-dist/(2*sigma^2));
end
% 计算MMD距离
function MMD = mmd_distance(X,,sigma)
K_xx = gaussian_kernel(X,X,sigma);
K_yy = gaussian_kernel(Y,Y,sigma);
K_xy = gaussian_kernel(X,Y,sigma);
n_x = size(X,1);
n_y = size(Y,1);
MMD = norm(mean(K_xx,2)-1/n_x*sum(K_xx,'all')/n_x+1/n_xn_y*sum(K_xy,'all')-mean(K_yy,2)+1/n_y*sum(K_yy,'all')/n_y)^2;
end
% 示例
X = randn(100,10);
Y = randn(100,10);
sigma = 1;
MMD = mmd_distance(X,Y,sigma);
disp(['MMD distance between X and Y is ',num2str(MMD)]);
```