MATLAB高斯混合数据的生成

作者:凯鲁嘎吉 - 博客园 http://www.cnblogs.com/kailugaji/

高斯混合模型的基本原理:聚类——GMM,MATLAB中GMM聚类算法:MATLAB中“fitgmdist”的用法及其GMM聚类算法。本文主要讨论如何用MATLAB人工生成符合高斯混合模型的数据,文中给出生成二维数据与三维数据的案例。

1. 二维数据生成

1.1. 程序

function data=generate_GMM()
%前两列是数据,最后一列是类标签
%数据规模
N=300;
%数据维度
dim=2;
%%
%混合比例
para_pi=[0.4 0.15 0.15 0.15 0.15];
%第一类数据
mul=[0 0]; % 均值
S1=[1 0;0 1]; % 协方差
data1=mvnrnd(mul, S1, para_pi(1)*N); % 产生高斯分布数据
%第二类数据
mu2=[4 4];
S2=[2 -1;-1 2];
data2=mvnrnd(mu2,S2,para_pi(2)*N);
%第三类数据
mu3=[-4 4];
S3=[2 1;1 2];
data3=mvnrnd(mu3,S3,para_pi(3)*N);
%第四类数据
mu4=[-4 -4];
S4=[2 -1;-1 2];
data4=mvnrnd(mu4,S4,para_pi(4)*N);
%第五类数据
mu5=[4 -4];
S5=[2 1;1 2];
data5=mvnrnd(mu5,S5,para_pi(5)*N);
%显示数据
plot(data1(:,1),data1(:, 2),'bo');
hold on;
plot(data2(:,1),data2(:,2),'ro');
plot(data3(:,1),data3(:,2),'go');
plot(data4(:,1),data4(:,2),'ko');
plot(data5(:,1),data5(:,2),'mo');
data = [data1, ones(para_pi(1)*N,1); data2, 2*ones(para_pi(2)*N,1); data3, 3*ones(para_pi(3)*N,1); data4, 4*ones(para_pi(4)*N,1); data5, 5*ones(para_pi(5)*N,1)];
%%
%将数据集存入文件
fid1=fopen('gauss_data.txt','w');
for i=1:N
for d=1:dim+1
fprintf(fid1, '%.4f ', data(i, d));
end
fprintf(fid1, '\n');
end
fclose(fid1);

1.2. 图像

1.3. 数据

-0.545510895080894	-0.376258667656416	1
0.374552558897674 0.507947640696775 1
-0.543488756435145 -1.37429164174078 1
1.81674776949293 0.137611179142222 1
-1.13998872085001 1.01039299620699 1
1.14786721735582 0.207004703224859 1
-1.70294252385711 -0.103099215770313 1
0.0412850370487988 -0.195177061697310 1
-0.0290779721068919 -0.135740617792583 1
1.20156687436050 0.785293100134734 1
-0.436725759877869 1.81621157992917 1
1.54564665100393 0.0521836769281596 1
-1.47074023395844 -1.03631822338874 1
-0.592323493112913 0.0368269076747419 1
-1.20464720277048 0.386236582716893 1
-0.0268027179877074 0.946328586724753 1
0.689163840469742 0.363460264428701 1
-1.22578553639022 1.45577857770520 1
1.98235629235162 1.23957524822078 1
0.722139387530663 0.135722562156936 1
0.426061788318672 -0.640173428232819 1
-1.06473611766422 -1.79093796498374 1
-0.0208890425378482 -1.78188146258966 1
-0.335868994910233 -1.22740346873807 1
-0.998438482903848 1.04283040882465 1
1.87048144588107 -0.00711709671883774 1
-1.09383228203225 -1.10301743848135 1
-1.20635174064544 1.04079783475122 1
-1.45468265207870 0.387024751709480 1
0.477438173899314 -1.56885894319954 1
0.395517166570296 1.63566457794523 1
0.0127565610991932 -1.31747151564540 1
0.588244305798010 -0.770606857586131 1
0.292251846731924 -1.56405947064427 1
0.728195887049746 0.637052412407101 1
0.916384718400930 -1.51351246140111 1
-1.29608649587100 0.169458582238240 1
2.20003870472710 0.0639531351969648 1
-0.601447112807249 0.640878604433810 1
0.961926051186633 1.52088956213435 1
0.730358994297656 1.98972700194211 1
-2.17215248555966 -1.09045030833633 1
-0.350959881900495 0.833789718172194 1
-0.349589841180652 -1.91963579276902 1
-1.06240791125327 1.43138152092021 1
0.304127023543034 1.17021454099990 1
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2.36570028887232 -1.09880959658705 1
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1.10550496182430 -1.15415172874195 1
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1.54448192457976 0.151875567931926 1
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1.35489766124073 2.34256831156063 1
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0.581096571550465 1.17453838970134 1
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0.917751266060919 -0.657506326182589 1
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1.26999492311366 0.810680984781717 1
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-1.52207229775273 0.749815780538519 1
0.0446125639186305 0.0299683762124543 1
0.987983190454411 -0.612913405189806 1
0.800503104827616 0.918230554969138 1
-1.08343410496977 -0.733932667894764 1
1.76914639732084 1.55116726073502 1
0.986959900933206 -0.663725674981786 1
-1.36104628754580 1.30619567448118 1
0.0550199981573708 0.331657475411092 1
0.338974101191037 -0.859239935132467 1
-1.14124191451059 0.0223083748809411 1
0.358376148834936 1.95334737608871 1
0.632621192872067 0.693497444406873 1
-0.330060047581271 0.347134256096482 1
0.0762545593670635 -1.26382021965231 1
0.432432069335672 0.780865579724367 1
-1.10984737506597 -0.226376879877599 1
0.973408237206523 -0.369816426260412 1
1.01178818947520 -0.185059622746829 1
0.450873476806951 -0.462633883999610 1
-0.868977983745262 1.33846758967167 1
0.857310060734281 -0.577977792199812 1
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0.624388816884225 2.03367134489104 1
-1.20705716828968 1.15343255555437 1
1.81335576028267 0.849682684264488 1
0.994905245705837 1.53886387077322 1
0.579005595985224 -1.58750073493957 1
1.20031539783778 0.479588829491639 1
2.15151625102986 1.11948856191139 1
1.38455526292789 -0.422564879467687 1
-0.965035030674835 0.213521202486582 1
1.72950610850028 -0.112681878056680 1
-0.0111424529195589 1.92758349368306 1
-0.608182225006691 -0.743062527373251 1
6.26191132851482 2.87420234778389 2
1.46708536828177 4.25933314661017 2
4.03512816519817 3.55838996904576 2
1.56291290267162 5.93213541837081 2
2.96236859827081 4.37151621826476 2
3.64143063677362 4.88689583161662 2
6.38266804240388 3.34558908666101 2
5.41309508707033 3.35837439232833 2
2.30763884124060 4.64357035916882 2
1.94146522926749 3.59676642990087 2
1.52805472175875 5.48742166863894 2
3.37947088416179 4.13546180253651 2
3.21758346388238 1.75465508363488 2
4.92098227770249 2.72247830961419 2
5.52880682285822 2.44875436837217 2
5.64261670568491 2.82376694427663 2
4.24043924394131 3.89438173035117 2
5.46466404478820 4.28382676990317 2
3.95567234720622 3.66422513585000 2
4.09085068078046 7.23388238849599 2
2.99902277594830 4.00041225146169 2
3.85403068887563 3.22625573591014 2
5.21472864087325 4.32253841766911 2
2.84692148498926 3.44846498856175 2
4.01186710155383 2.02718224126495 2
4.30344011638458 2.91792209130873 2
3.02572894146083 6.92568297671023 2
2.52390865374576 4.67273361504838 2
3.29669675181033 5.10650923628543 2
2.67404933672749 6.37163861175736 2
4.14608767191083 4.45153308892660 2
2.69680280080912 5.18811828663690 2
1.51437308217565 5.05846837008456 2
3.93462302848637 4.30358583470654 2
2.70493715992304 3.73426722910466 2
4.28769182326535 4.93248502602472 2
2.08595382511258 4.74263599702177 2
3.81219187638740 5.50053543094262 2
5.43715368098522 3.90844411861587 2
4.74483548517909 3.18409801820196 2
4.01495899961387 3.52442373699206 2
2.01031761274835 6.63092272795666 2
3.38200833205790 4.87869800104605 2
2.15486571629534 2.64912537458821 2
4.61913522058550 1.17807382732939 2
-2.41983520346350 6.85250494294405 3
-3.91895198693660 4.30466947036677 3
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-5.25130856752767 5.12603408807742 3
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-5.69301728266434 2.11993425665485 3
-5.58200771470702 0.879147529661482 3
-5.75547440020193 2.38389935224039 3
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-2.53442114176800 3.12820506221048 3
-5.48593353106808 1.05573675748163 3
-4.69694792261799 4.32324665818441 3
-4.53287897254505 4.31558634252341 3
-3.40824627224202 2.82618015057078 3
-4.54362215345362 1.90971151401584 3
-2.58926813815895 5.80021670830004 3
-3.84341520256589 4.88917870913694 3
-3.42204804497922 4.23019459522267 3
-4.13229646764044 2.97591908765228 3
-3.96744300534690 5.19020008301123 3
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-2.38177252199409 6.82035106813690 3
-4.88273180490767 5.20027313219846 3
-2.90011672474735 6.81908441253178 3
-5.59693327231870 6.34390256873062 3
-3.65555788343370 2.41110355975260 3
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-4.16788088460357 1.98016388606870 3
-7.13141235432678 2.50098865284353 3
-3.82942576858549 3.60639122698253 3
-2.78090623000099 4.93165228176749 3
-3.75308089259298 3.06115467845300 3
-4.40204438880523 4.14589819485963 3
-1.84084098927512 3.48444117374196 3
-1.70189927604420 6.06507753034884 3
-5.96158916139604 4.49241737024208 3
-5.04990024101003 3.65858083982453 3
-5.44605518486153 2.31171509463054 3
-2.62360844695056 1.35243403718315 3
-5.71885561684177 3.22238799248740 3
-5.15558931162033 -1.93151831428770 4
-3.13819376759068 -4.26842286451585 4
-4.65128978496079 -4.66813132800655 4
-6.55160390643011 -1.63312515289099 4
-3.19554916278024 -4.59379356680950 4
-3.66227304508280 -4.12082943673340 4
-4.49289926473170 -3.14984190235144 4
-4.55548884160883 -4.95301034623535 4
-3.70812542145989 -6.51356102416401 4
-1.71989911425951 -6.01173781843615 4
-0.539004834471935 -7.14448691144402 4
-1.91587781399240 -6.80703912184080 4
-6.87395794730588 -3.56173142735883 4
-4.75364662811086 -1.77970472900929 4
-4.38871174218452 -5.70642976639587 4
-3.87755277810941 -5.78917234218382 4
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-2.18647469486795 -3.74929421191038 4
-5.07228681009131 -3.89428860055849 4
3.17302980178845 -5.39031953879009 5
4.45960273242076 -2.36846155877649 5
5.24099720742394 -5.69962995830296 5
3.56899925360007 -6.28570690919855 5
4.20159066008819 -1.58986296682819 5
6.13798449363983 -2.02253957739510 5
5.06700175465161 -3.80479250240493 5
2.86247020041003 -6.02094889758587 5
3.77035825050206 -2.32677099886967 5
4.99518069973419 -5.16267665183900 5
2.10263236352861 -8.34806464740769 5
4.12985525865002 -5.77249471085627 5
5.22783306815519 -2.71136270887530 5
1.80804441328560 -4.95427032123393 5
1.81079007671092 -4.43865538009938 5
5.05426328485665 -3.21994804948600 5
4.39956086448591 -1.27681521098911 5
-0.0791554892517015 -8.31170377350323 5
2.82799553567766 -4.03949663519130 5
3.20361435469073 -4.89917919754429 5
2.97719190341939 -5.35014527781680 5
7.48957765290125 -1.70834454697736 5
3.94557969039702 -3.39325860845618 5
3.66144920989468 -4.21774086304387 5
5.12352713663710 -2.89875162602726 5
3.97463780486113 -2.55353097282383 5
1.95572161389881 -6.79713136111470 5
4.15455541179760 -3.08278711709991 5
3.89909907570780 -2.58134994204057 5
7.02778219584157 -3.39646965696710 5
3.47794604458990 -5.91509213081594 5
5.19288006346659 -4.67919733613364 5
4.89042010198797 -3.46282598001945 5
4.04483939390608 -3.58599481578122 5
5.03792687927419 -4.66925536085279 5
5.21171110193382 -4.86589708577224 5
4.06913858477176 -3.12572398674435 5
4.46932412600276 -5.19551962881950 5
3.52508022350430 -4.19734682862160 5
5.45374435410425 -3.54101673467541 5
3.53811357548697 -5.22688932165462 5
4.47819796042730 -4.44919901840050 5
2.75688743817806 -5.60458322936945 5
2.50534610439532 -5.35941563176474 5
2.08963538325247 -6.14523524386922 5

同时数据已存入当前目录的文件“gauss_data.txt”中。

2. 三维数据生成

2.1. 程序

function data=generate_GMM()
%前两列是数据,最后一列是类标签
%数据规模
N=300;
%数据维度
dim=3;
%%
%混合比例
para_pi=[0.1 0.2 0.3 0.4];
%第一类数据
mul=[0 0 0]; % 均值
S1=[1 0 0;0 1 0;0 0 1]; % 协方差
data1=mvnrnd(mul, S1, para_pi(1)*N); % 产生高斯分布数据
%第二类数据
mu2=[3 3 2];
S2=[2 -1 0;-1 1 0;0 0 1];
data2=mvnrnd(mu2,S2,para_pi(2)*N);
%第三类数据
mu3=[-3 3 1];
S3=[2 1 0;1 2 0;0 0 1];
data3=mvnrnd(mu3,S3,para_pi(3)*N);
%第四类数据
mu4=[0 -3 3];
S4=[2 1 0;1 1 0;0 0 2];
data4=mvnrnd(mu4,S4,para_pi(4)*N);
%显示数据
plot3(data1(:,1),data1(:, 2),data1(:,3),'bo');
hold on;
grid on
xlabel('x');
ylabel('y');
zlabel('z');
plot3(data2(:,1),data2(:,2),data2(:,3),'ro');
plot3(data3(:,1),data3(:,2),data3(:,3),'go');
plot3(data4(:,1),data4(:,2),data4(:,3),'ko');
data = [data1, ones(para_pi(1)*N,1); data2, 2*ones(para_pi(2)*N,1); data3, 3*ones(para_pi(3)*N,1); data4, 4*ones(para_pi(4)*N,1)];
%%
%将数据集存入文件
fid1=fopen('gauss_data.txt','w');
for i=1:N
for d=1:dim+1
fprintf(fid1, '%.4f ', data(i, d));
end
fprintf(fid1, '\n');
end
fclose(fid1);

2.2. 图像

2.3. 数据

2.49843747778172	-0.460263982717900	0.926213263510532	1
0.344363940565677 0.183803197329987 -0.592596618971808 1
1.51495409493848 -1.00077063634156 1.42720702412040 1
-2.22985506128415 0.443834535891559 2.27820838669181 1
-0.720939190484627 1.18580789933626 -1.62476852958396 1
-0.308579945523786 -1.35024988178629 -2.44577799952649 1
-0.321837686711218 -0.482587253319734 0.0125282318746073 1
-1.13246932505719 -0.0324602353944920 0.705875854273454 1
-1.17979116037789 0.0170636084606657 0.0121834842846798 1
-1.59495940633115 -0.0960891860381253 -1.23860565163178 1
-0.238072926666054 -0.293133285171206 3.13633987972424 1
-0.900087525142363 -1.03924742019756 1.38542294580792 1
-1.28191166393303 0.605731890499142 1.04241118916645 1
-1.82870431878706 1.50570356578587 -2.19237656562187 1
0.475589087694975 0.410717730270373 1.20028305951021 1
0.150260875174452 0.916252656197516 -0.747712381188694 1
-1.60246504874026 -0.405372454001307 1.26780393762904 1
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同时数据已存入当前目录的文件“gauss_data.txt”中。

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