MATLAB高斯混合数据的生成

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, '
');
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
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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
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0.730358994297656	1.98972700194211	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
-2.13339943346212	6.46315559386203	3
-3.02101000134472	6.28320929687944	3
-5.25130856752767	5.12603408807742	3
-5.59803186523091	3.26150858527381	3
-5.69301728266434	2.11993425665485	3
-5.58200771470702	0.879147529661482	3
-5.75547440020193	2.38389935224039	3
-6.38355622563180	4.48307844365673	3
-4.71212878642699	3.75762092589917	3
-4.14495549006060	2.18789588281711	3
-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
-3.95410257082111	3.92228119811007	3
-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
-4.93485685527032	2.79678180870763	3
-3.48504201208711	6.26622339218588	3
-4.54778116908779	4.53678733910660	3
-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
-1.66410091182604	-6.54273715357697	4
-4.64450490872372	-4.03634872386426	4
-6.06611766638436	-3.75980150984485	4
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-4.18487396930512	-4.03317654889994	4
-4.94396440446167	-3.99816469680926	4
-5.90500974456669	-0.658597778449720	4
-4.80674949908200	-2.12197424958233	4
-6.53625885527321	-4.96538843253712	4
-6.67118214488468	-3.85329368548873	4
-5.08548875004801	-3.02479056014923	4
-4.94199867939672	-5.97539351893420	4
-6.16431877278395	-2.08464799600191	4
-3.54905294343501	-4.64416276395015	4
-4.34651923612607	-4.60275778691262	4
-4.40655863311961	-3.89710437970330	4
-4.83813790882019	-3.50063589897614	4
-5.47137155975461	-0.633027093974476	4
-2.45351326558628	-6.64985635880677	4
-5.19013185289929	-2.14267250944901	4
-6.48490166569892	-3.23069729729028	4
-4.97850262601172	-3.56174043414819	4
-5.52493818792063	-3.11696548001527	4
-2.65756545002045	-3.77786643835108	4
-6.86367695213169	-2.14826102222898	4
-4.20123561303810	-2.65343044360313	4
-4.54764420476797	-3.07361975587910	4
-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, '
');
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
1.99411324341624	-0.0965621653282794	-0.204162416163832	1
0.612290358680033	0.164542950693545	0.121884852921529	1
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0.925030468575763	-0.910070871855287	-1.65902513235640	1
-1.50298384459762	1.03159565518800	1.31384919551221	1
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0.689413026615452	4.74387814905321	1.24695271109973	2
4.54086597015512	2.55613015933163	1.39896264244928	2
1.69690723483602	4.46825622520101	1.47510918748751	2
5.55238975032377	-0.295635003555867	1.82089013916159	2
3.62626258261583	1.30566471288204	-0.133898012480930	2
3.73735026690620	3.26583235654822	3.70607753584556	2
2.16345737090853	2.76313852722265	3.70449327772986	2
3.66795486609899	2.75982149307769	0.953949844125312	2
3.34992926613246	2.80886852240528	2.94729101721180	2
2.80042557814606	3.39384245921333	4.12217252869437	2
3.10489926411870	3.95786809475060	1.29603218400640	2
0.0469984056864776	4.46843416465705	3.53712151726741	2
2.47585448507785	3.08706469590746	2.92082143150995	2
1.68083372956454	3.59697916051383	0.985854370865028	2
3.42914884555317	2.33181599368835	0.634141522744353	2
1.86386784349807	4.33465483002277	2.44553950185964	2
1.23584151178778	4.75064663837965	1.29295114341203	2
2.92206222231454	3.34382592996769	0.960717672132152	2
4.33424030463856	1.89265524114487	1.22129258331317	2
0.681039763013596	3.79968449293932	0.385670737536172	2
3.40749585853358	3.88607766490946	2.46385697332908	2
4.27014672014641	2.91273702579306	2.05521378456440	2
2.97723849649204	2.38340459726243	0.447356760347354	2
0.524044407934072	3.34771412925916	1.41646566990192	2
2.83733404725494	2.69651695523908	1.03406301520104	2
2.51175607927568	3.85640741108295	2.46578392847227	2
0.439496748973050	3.63796684378395	2.81960085715231	2
3.02916636555290	3.65846733347827	1.77894885249181	2
2.90058863403041	2.29274769872908	1.32609145625505	2
2.95807930336693	3.08693005408050	0.752822925845977	2
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2.40706405937875	1.51966708315590	1.16733326999331	2
5.27976775583405	2.86568767230792	1.51629429757050	2
0.819505859681578	3.67526851879069	1.67070013463305	2
0.248876280042175	5.00707421658782	4.18523616304716	2
1.41951079147412	3.84593900162790	2.38723714551302	2
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1.60475249163368	4.40476024265404	2.07056306224623	2
4.77176905876137	2.58796643331653	3.23080180166649	2
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1.91574150233070	2.82139467093036	2.79833162843550	2
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2.25229309431098	4.47048252156054	2.52917803278316	2
2.42817876409434	3.89826379622712	1.89148821213051	2
4.35256215050249	4.68795729113736	1.83000399979505	2
3.86508035164427	3.10284399721756	2.91003235721308	2
1.33880835606307	4.46475122224117	1.71249996579546	2
2.62630515719235	3.52174113124233	2.60106484284540	2
2.41743571368160	3.54684195854090	1.08247360198120	2
5.17571247612839	2.28100186183683	2.11140418355563	2
5.04102282380700	3.37729812739364	0.961767638237232	2
2.54568168952880	3.98990734828420	0.603584159177279	2
4.77263468615723	2.55806365037606	2.58149505930596	2
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3.55509753930443	2.72631775475948	2.43532671450374	2
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1.33331636051282	-1.65467576516620	3.45622366175556	4
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0.428093789093011	-1.96334763094052	3.02833109758407	4
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0.0116823082654330	-3.50710801593278	0.104134944048182	4
1.02453030520208	-2.58544171242681	2.80564732820050	4
0.414250131046115	-3.15690929041373	4.51059850461767	4
1.19386114434319	-3.30638711175454	4.58555961651307	4
0.780005261335646	-2.91165958951020	3.16598377247417	4
1.87150094001271	-2.01978903736524	2.54464144391102	4
-0.439561754856433	-2.21594471986265	3.18600135326228	4
-0.913714341038988	-2.21528156955696	3.68970810993789	4
-0.249824032848876	-2.51430111341078	1.65317401912326	4
0.103777442256180	-2.73753272708219	4.15180338769778	4
1.19324005147759	-2.81002870519776	4.99519867822902	4
-0.917643550254731	-3.25997120404773	2.82213086959837	4
-0.663075301616082	-3.66982459556690	1.40901989936731	4
-2.87851810686916	-4.48182492708991	4.02680127369587	4
-2.12890511402542	-4.50873649593186	2.69794203316502	4
2.22813281755404	-2.38430973514096	3.34993158970401	4
-1.74788390396755	-4.21686713211102	0.644742012856163	4
0.174794977143914	-3.07432186306627	2.91644953420847	4
1.32298056369243	-2.35285215869710	2.57437538044201	4
0.990118643852932	-2.53782769779243	2.81064635018736	4
0.600124191071625	-1.85101033139258	4.05416330122172	4
-0.0967760196414198	-4.21226230416848	2.24114814716840	4
-0.396976481943450	-3.46366659326573	2.99650528372319	4
-0.485960802144072	-2.72985363739582	2.30866094147011	4
-2.01465084778777	-4.14087185077986	2.23256810348066	4
-2.17865514264397	-4.44680003551516	2.10118582466872	4
0.963926321018170	-3.45751277549925	1.75129564916121	4
-0.557996526520347	-3.23381260813215	2.95049391817198	4
-1.23659835212312	-3.37639190992010	1.47977331160717	4
-0.582856668791474	-3.66914965806761	1.87372822344828	4
1.00675649164874	-2.22584775126702	3.02391043995622	4
2.21609797517856	-2.30528160857168	4.56187102866309	4
-2.20134054722955	-4.04963095153435	3.67050791360018	4
-1.29664452484300	-4.29471862586000	1.98178782575738	4
2.32277202602564	-2.06887315464342	4.64131666740505	4
-0.298931764282035	-3.62972358552214	2.55689372378307	4
1.64816183264570	-1.43841392213983	1.73130158006818	4
-0.367112948627741	-3.99177416806065	0.0670818408840961	4
0.707997752729741	-3.06472202223881	1.47060866018998	4
0.402205572099213	-2.95876779195876	0.365276172356610	4
0.412636525528479	-2.35469826701889	3.06147294454164	4
0.0325337036934696	-2.93295394305355	0.927232248680667	4
-1.25502992814249	-4.13029902475207	3.76331494205327	4
1.00453032860667	-2.53333531105143	1.63173646457279	4
-1.42844136055175	-2.84596770235026	2.73704022851764	4

同时数据已存入当前目录的文件“gauss_data.txt”中。