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 -1.72933045779437 -1.54142367954478 1 -0.598896004160902 -0.105925554825273 1 -1.31011037743746 -1.58021974549522 1 2.36570028887232 -1.09880959658705 1 -1.26743690700607 0.0837653841878213 1 1.23414029010661 1.30262183813727 1 1.10550496182430 -1.15415172874195 1 1.67104117072622 0.135275892935019 1 1.70798624510336 0.882302210646749 1 0.563155580569765 1.81376295782830 1 -0.251182581897459 1.33566417915374 1 -1.88295982534046 0.575127428345159 1 0.169665209677480 0.874143372144739 1 1.66500477262456 -0.177812863248393 1 -1.52518812841798 -0.664826413112643 1 -0.310696321302611 -0.883332521493689 1 0.400332024230491 0.530777065822867 1 0.230678403945063 0.426444757506126 1 -1.49437426451061 -2.42389297892765 1 -0.359152477917947 0.151728546222352 1 -2.00864455513353 2.32358798338343 1 -0.979477048746326 1.38118885402575 1 1.54448192457976 0.151875567931926 1 -0.293612697408936 -0.436934755150954 1 1.35489766124073 2.34256831156063 1 0.597498265543298 0.121733895853054 1 0.581096571550465 1.17453838970134 1 -0.561552403053525 -0.771004698512474 1 0.917751266060919 -0.657506326182589 1 -0.641924288663851 -0.479375568051963 1 -0.363404932649308 0.676855927372856 1 -1.11415448619610 0.235979896507873 1 0.986335597529911 -0.655301174154837 1 -0.251493520240138 1.09713018877592 1 1.24781504258504 -1.42003482739768 1 -0.699650589017584 1.26589092346096 1 1.26999492311366 0.810680984781717 1 -0.429850276664512 -0.198687954797670 1 -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 -2.06965874587350 0.110515274540505 1 -0.204421480496499 -0.769171619841190 1 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 -4.91302254323549 -3.37229009600523 4 -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, '\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 1.99411324341624 -0.0965621653282794 -0.204162416163832 1 0.612290358680033 0.164542950693545 0.121884852921529 1 0.291149162823226 -0.955916506466084 -1.73459429211643 1 -0.647215619249269 -0.655955642766331 1.20508858042327 1 0.495121953506736 0.881847619515268 -0.279462203814666 1 1.36893754821876 0.0580880581352123 -0.998666427666221 1 -2.00542485916349 -1.25539294619184 0.0369730707026779 1 0.293348876186443 -0.589359819346870 -0.358772856873272 1 -0.818658558703714 2.06751728279068 1.09599054124806 1 -0.293309049600295 -0.0634639175716548 0.967794251039837 1 0.925030468575763 -0.910070871855287 -1.65902513235640 1 -1.50298384459762 1.03159565518800 1.31384919551221 1 -1.82830676992021 0.708726157033793 -1.23244228382176 1 4.05647056505806 3.15779278067951 1.33554596356026 2 2.80821058515555 3.81742131283227 2.15083179871381 2 0.689413026615452 4.74387814905321 1.24695271109973 2 4.54086597015512 2.55613015933163 1.39896264244928 2 1.69690723483602 4.46825622520101 1.47510918748751 2 5.55238975032377 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4.87751358021832 4 -2.38693051290703 -3.98270070767969 2.00999885540562 4 -1.43182162708173 -4.28375083055211 2.90176624249130 4 -0.124389742785265 -2.05240365803053 2.95928334739365 4 0.946793618432931 -2.08015638120217 1.37590463910991 4 -1.85801457845449 -4.14880160699021 3.93819062450857 4 -0.229903497356306 -2.34391707293308 4.08775618836319 4 -0.814298261208425 -2.27198760934433 3.68117956957402 4 -0.683736687178923 -4.96446986083207 2.34882682377545 4 2.63689862291621 -0.216030357755463 2.03177864141412 4 -0.324148754902210 -3.71497221225087 1.16135570068792 4 0.973437538238595 -2.87963739856514 1.97581684514724 4 -0.820470694934185 -2.61830712387681 1.93964175764496 4 -0.380558983783297 -2.50057231453796 2.74731798184348 4 1.23586727718266 -0.866653428369626 2.24702855223593 4 1.11360441968992 -3.35936278709867 3.09898443428252 4 1.13063156152804 -1.88951921088285 5.66320937891763 4 -1.12497988463671 -3.80568086048409 1.84163066787352 4 0.757409709699232 -2.18278194909850 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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。
若已知数据与标签后，对其进行作图：
clear
clc
data=dlmread('gauss_data.txt');
data1=data(data(:, end)==1, 1:end-1);
data2=data(data(:, end)==2, 1:end-1);
data3=data(data(:, end)==3, 1:end-1);
data4=data(data(:, end)==4, 1:end-1);
%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');
与上面的三维图出来的效果一样。
