MATLAB最大均值差異(Maximum Mean Discrepancy)

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注：X與Y數(shù)據(jù)維度必須一致！

1. MMD介紹

2. MATLAB程序

數(shù)據(jù)

注：數(shù)據(jù)集僅供參考，并不能真正用于研究中。

源域：

2.17891.78115.0794.9312

0.86212.12874.98252.3388

2.63471.95634.53924.8442

2.71792.90014.90274.8582

2.66861.67994.37924.6411

1.67362.30814.83843.2979

1.56662.64675.05044.459

-0.56112.23654.39255.1316

5.66931.73554.53354.6407

3.20322.1034.19485.2605

3.35252.83014.63835.6972

-1.04073.51984.71064.9243

3.92292.11614.56661.772

2.56073.8024.26814.6322

3.30722.50834.60952.2236

2.71212.43384.1362.2348

5.35472.10884.4024.9884

1.83021.49214.62163.5862

2.88912.12864.64193.8606

-0.08962.68943.68436.6392

3.14041.94614.26045.9859

2.34063.19885.08724.7518

2.50672.97044.27494.3441

8.21531.75925.24093.8201

0.30272.75893.98264.8484

4.02231.75664.62194.92

6.13672.10984.78325.4567

4.97952.4184.77263.1959

-1.07462.43114.76834.5599

5.49392.60464.46635.1159

4.57091.98384.95964.9317

1.37462.68455.19213.2068

1.71780.79764.69483.7012

目標域：

1.95842.02424.75942.587

-2.83423.45944.43715.2375

1.62512.77375.01456.3262

0.70162.52654.88813.2105

3.55792.57734.8564.283

4.32822.75814.70956.715

3.16192.54274.13235.5883

4.99332.29853.84553.8381

3.22142.64784.32762.5246

-0.28482.58534.64813.4857

2.8761.50963.99212.4505

0.85592.56335.4833.0589

4.21492.66184.20173.3713

MMD

function mmd_XY=my_mmd(X, Y, sigma)

%Author：kailugaji

%Maximum Mean Discrepancy 最大均值差異 越小說明X與Y越相似

%X與Y數(shù)據(jù)維度必須一致, X, Y為無標簽數(shù)據(jù)，源域數(shù)據(jù)，目標域數(shù)據(jù)

%mmd_XY=my_mmd(X, Y, 4)

%sigma is kernel size, 高斯核的sigma

[N_X, ~]=size(X);

[N_Y, ~]=size(Y);

K = rbf_dot(X,X,sigma); %N_X*N_X

L = rbf_dot(Y,Y,sigma); %N_Y*N_Y

KL = rbf_dot(X,Y,sigma); %N_X*N_Y

c_K=1/(N_X^2);

c_L=1/(N_Y^2);

c_KL=2/(N_X*N_Y);

mmd_XY=sum(sum(c_K.*K))+sum(sum(c_L.*L))-sum(sum(c_KL.*KL));

mmd_XY=sqrt(mmd_XY);

Guassian Kernel

function H=rbf_dot(X,Y,deg)

%Author：kailugaji

%高斯核函數(shù)/徑向基函數(shù) K(x, y)=exp(-d^2/sigma), d=(x-y)^2, 假設X與Y維度一樣

%Deg is kernel size,高斯核的sigma

[N_X,~]=size(X);

[N_Y,~]=size(Y);

G = sum((X.*X),2);

H = sum((Y.*Y),2);

Q = repmat(G,1,N_Y(1));

R = repmat(H',N_X(1),1);

H = Q + R - 2*X*Y';

H=exp(-H/2/deg^2); %N_X*N_Y

結果

>> mmd_XY=my_mmd(x, y, 4)

mmd_XY =

0.1230

3. 參考文獻

Gretton, A., K. Borgwardt, M. Rasch, B. Schoelkopf and A. Smola:?A Kernel Two-Sample Test. JMLR 2012.

Gretton, A., B. Sriperumbudur, D. Sejdinovic, H, Strathmann, S. Balakrishnan, M. Pontil, K. Fukumizu: Optimal kernel choice for large-scale two-sample tests. NIPS 2012.

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