MATLAB最大均值差異(Maximum Mean Discrepancy)

作者：凱魯嘎吉 - 博客園 http://www.cnblogs.com/kailugaji/

更多內容，請看標簽：MATLAB、聚類

注：X與Y數據維度必須一致！

1. MMD介紹

2. MATLAB程序

數據

注：數據集僅供參考，並不能真正用於研究中。

源域：
2.1789	1.7811	5.079	4.9312
0.8621	2.1287	4.9825	2.3388
2.6347	1.9563	4.5392	4.8442
2.7179	2.9001	4.9027	4.8582
2.6686	1.6799	4.3792	4.6411
1.6736	2.3081	4.8384	3.2979
1.5666	2.6467	5.0504	4.459
-0.5611	2.2365	4.3925	5.1316
5.6693	1.7355	4.5335	4.6407
3.2032	2.103	4.1948	5.2605
3.3525	2.8301	4.6383	5.6972
-1.0407	3.5198	4.7106	4.9243
3.9229	2.1161	4.5666	1.772
2.5607	3.802	4.2681	4.6322
3.3072	2.5083	4.6095	2.2236
2.7121	2.4338	4.136	2.2348
5.3547	2.1088	4.402	4.9884
1.8302	1.4921	4.6216	3.5862
2.8891	2.1286	4.6419	3.8606
-0.0896	2.6894	3.6843	6.6392
3.1404	1.9461	4.2604	5.9859
2.3406	3.1988	5.0872	4.7518
2.5067	2.9704	4.2749	4.3441
8.2153	1.7592	5.2409	3.8201
0.3027	2.7589	3.9826	4.8484
4.0223	1.7566	4.6219	4.92
6.1367	2.1098	4.7832	5.4567
4.9795	2.418	4.7726	3.1959
-1.0746	2.4311	4.7683	4.5599
5.4939	2.6046	4.4663	5.1159
4.5709	1.9838	4.9596	4.9317
1.3746	2.6845	5.1921	3.2068
1.7178	0.7976	4.6948	3.7012
目標域：
1.9584	2.0242	4.7594	2.587
-2.8342	3.4594	4.4371	5.2375
1.6251	2.7737	5.0145	6.3262
0.7016	2.5265	4.8881	3.2105
3.5579	2.5773	4.856	4.283
4.3282	2.7581	4.7095	6.715
3.1619	2.5427	4.1323	5.5883
4.9933	2.2985	3.8455	3.8381
3.2214	2.6478	4.3276	2.5246
-0.2848	2.5853	4.6481	3.4857
2.876	1.5096	3.9921	2.4505
0.8559	2.5633	5.483	3.0589
4.2149	2.6618	4.2017	3.3713

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數據維度必須一致, X, Y為無標簽數據，源域數據，目標域數據
%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/徑向基函數 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.