A practical Time-Series Tutorial with MATLAB MATLAB 實用時間序列教程

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Tutorial|PKDD2005

ApracticalTime-SeriesTutorialwithMATLAB

MichalisVlachos

IBMT.J.WatsonResearchCenterHawthorne,NY,10532

Tutorial|Time-SerieswithMatlab

Aboutthistutorial

Thegoalofthistutorialistoshowyouthattime-seriesresearch(orresearchingeneral)canbemadefun,whenitinvolvesvisualizingideas,thatcanbeachievedwithconciseprogramming.

Matlabenablesustodothat.

WillIbeable Iamdefinately

tousethis smarterthanher,

MATLAB butIamnotatime-rightawayseriesperson,per-se.afterthe IwonderwhatIgaintutorial? fromthistutorial…

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Tutorial|Time-SerieswithMatlab

Disclaimer

IamnotaffiliatedwithMathworksinanyway

…butIdolikeusingMatlabalot–sinceitmakesmylifeeasier

Errorsandbugsaremostlikelycontainedinthistutorial.

Imightberesponsibleforsomeofthem.

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Tutorial|Time-SerieswithMatlab

Timelineoftutorial

Matlabintroduction

IwilltrytoconvinceyouthatMatlabiscool

Briefintroductiontoitsmanyfeatures

Time-serieswithMatlab

Introduction

Time-SeriesRepresentations

DistanceMeasures

LowerBounding

Clustering/Classification/Visualization

Applications

4

Tutorial|Time-SerieswithMatlab

WhatthistutorialisNOTabout

Movingaverages

OOhh...b.buuyy

Autoregressivemodels mmyybbooookkss

Forecasting/Prediction LLeett’s’snnootteessccaappeeininttoo ttoooo!!

mmaatthheemmaatticicss..LLeett’s’s

Stationarity sstticickkwwitithhrreeaaliltityy..

Seasonality

..oraboutcomplexmathematicalformulas

MichaelCrichton

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Tutorial|Time-SerieswithMatlab

PARTI:MatlabIntroduction

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Tutorial|Time-SerieswithMatlab

WhydoesanyoneneedMatlab?

Matlabenablestheefficient

ExploratoryDataAnalysis(EDA)

“Scienceprogressesthroughobservation”

--IsaacNewton

IsaacNewton

“Thegreatestvalueofapictureisthatisforcesustonoticewhatweneverexpectedtosee”

--JohnTukey

JohnTukey

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Tutorial|Time-SerieswithMatlab

Matlab

InterpretedLanguage

Easycodemaintenance(codeisverycompact)

Veryfastarray/vectormanipulation

SupportforOOP

Easyplottingandvisualization

EasyIntegrationwithotherLanguages/OS’s

InteractwithC/C++,COMObjects,DLLs

BuildinJavasupport(andcompiler)

Abilitytomakeexecutablefiles

Multi-PlatformSupport(Windows,Mac,Linux)

ExtensivenumberofToolboxes

Image,Statistics,Bioinformatics,etc

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Tutorial|Time-SerieswithMatlab

HistoryofMatlab(MATrixLABoratory)

“Themostimportantthingintheprogramminglanguageisthename.IhaverecentlyinventedaverygoodnameandnowIamlookingforasuitablelanguage”.--R.Knuth

ProgrammedbyCleveMolerasaninterfaceforEISPACK&LINPACK

CleveMoler

1957:MolergoestoCaltech.StudiesnumericalAnalysis

1961:GoestoStanford.WorkswithG.ForsytheonLaplacianeigenvalues.

1977:FirsteditionofMatlab;2000linesofFortran

–80functions(nowmorethan8000functions)

1979:MetwithJackLittleinStanford.StartedworkingonportingittoC

1984:Mathworksisfounded

Video:

/company/aboutus/founders/origins_of_matlab_wm.html

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Tutorial|Time-SerieswithMatlab

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Tutorial|Time-SerieswithMatlab

CurrentStateofMatlab/Mathworks

Matlab,Simulink,Stateflow

Matlabversion7,servicepack2

Usedinvarietyofindustries

Aerospace,defense,computers,communication,biotech

Mathworksstillisprivatelyowned

Usedin>3,500Universities,with>500,000usersworldwide

2004Revenue:300M.

2004Employees:1,000

Pricing:

~2000$(Commercialuse),

~100$(StudentEdition)

Moneyisbetterthanpoverty,ifonlyforfinancialreasons.–WoodyAllen 11

Tutorial|Time-SerieswithMatlab

WhoneedsMatlab?

R&Dcompaniesforeasyapplicationdeployment

Professors

Labassignments

Matlaballowsfocusonalgorithmsnotonlanguagefeatures

Students

Batchprocessingoffiles

Nomoreincomprehensibleperlcode!

Greatenvironmentfortestingideas

Quickcodingofideas,thenportingtoC/Javaetc

Easyvisualization

It’scheap!(forstudentsatleast…)

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Tutorial|Time-SerieswithMatlab

StartingupMatlab

PersonallyI'malwaysreadytolearn,althoughIdonotalwayslikebeingtaught.

SirWinstonChurchill

Dos/Unixlikedirectorynavigation

Commandslike:

cd

pwd

mkdir

Fornavigationitiseasiertojustcopy/pastethepathfromexplorerE.g.:

cd‘c:\documents\’

MatlabEnvironment

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Tutorial|Time-SerieswithMatlab

Workspace:

LoadedVariables/Types/Size

CommandWindow:

typecommands

loadscripts

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Tutorial|Time-SerieswithMatlab

MatlabEnvironment

CommandWindow:

typecommands

loadscripts

Workspace:

LoadedVariables/Types/Size

Helpcontainsacomprehensiveintroductiontoallfunctions

15

-type

-load

Tutorial|Time-SerieswithMatlab

MatlabEnvironment

CommandWindow:

commandsscripts

Workspace:

LoadedVariables/Types/Size

Excellentdemosandtutorialofthevariousfeaturesandtoolboxes

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Tutorial|Time-SerieswithMatlab

StartingwithMatlab

Everythingisarrays

Manipulationofarraysisfasterthanregularmanipulationwithfor-loops

a=[1234567910]%defineanarray

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Tutorial|Time-SerieswithMatlab

Populatingarrays

Plotsinusoidfunction

a=[0:0.3:2*pi]%generatevaluesfrom0to2pi(withstepof0.3)

b=cos(a)%accesscosatpositionscontainedinarray[a]

plot(a,b)%plota(x-axis)againstb(y-axis)

Related:

linspace(-100,100,15);%generate15valuesbetween-100and100

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Tutorial|Time-SerieswithMatlab

ArrayAccess

Accessarrayelements

>>a(1) >>a(1:3)

ans= ans=

0 0.3000 0.6000

0

Setarrayelements

>>a(1)=100 >>a(1:3)=[100100100]

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Tutorial|Time-SerieswithMatlab

2DArrays

Canaccesswholecolumnsorrows

–Let’sdefinea2Darray

>>a=[123;456] >>a(1,:) Row-wiseaccess

a=

ans=

1 2 3

4 5 6 1 2 3

>>a(2,2) >>a(:,1) Column-wiseaccess

ans= ans=

5 1

4

Agoodlistenerisnotonlypopulareverywhere,butafterawhilehegetstoknowsomething.–WilsonMizner20

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Tutorial|Time-SerieswithMatlab

Column-wisecomputation

Forarraysgreaterthan1D,allcomputationshappencolumn-by-column

>>a=[123;321] >>max(a)

a=

ans=

1 2 3

3 2 1 3 2 3

>>mean(a) >>sort(a)

ans= ans=

2.0000 2.0000 2.0000 1 2 1

3 2 3

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>>a=[123];

>>b=[456];

>>c=[ab]

Rownexttorow

>>a=[1;2];

c=

1

2

3

4

5

6

>>a=[123];

>>a=[1;2];

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>>b=[3;4];

>>c=[a;b]c=

1

2

3

4

3

6

2

5

1

4

>>b=[456];

>>c=[a;b]

c=

Columnbelowcolumn

Rowbelowtorow

3

4

1

2

>>b=[3;4];

>>c=[ab]c=

Columnnexttocolumn

Concatenatingarrays

Column-wiseorrow-wise

Tutorial|Time-SerieswithMatlab

Tutorial|Time-SerieswithMatlab

Initializingarrays

Createarrayofones[ones]

>>a=ones(1,3)a=

1 1 1

>>a=ones(1,3)*infa=

InfInfInf

>>a=ones(2,2)*5;a=

5 5

5 5

Createarrayofzeroes[zeros]

–Goodforinitializingarrays

>>a=zeros(1,4)a=

0 0 0 0

>>a=zeros(3,1)+[123]’

a=

1

2

3

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Tutorial|Time-SerieswithMatlab

ReshapingandReplicatingArrays

Changingthearrayshape[reshape]

–(eg,foreasiercolumn-wisecomputation)

>>a=[123456]’;%makeitintoacolumn reshape(X,[M,N]):

>>reshape(a,2,3) [M,N]matrixof

columnwiseversion

ans= ofX

1 3 5

2 4 6

Replicatinganarray[repmat]

>>a=[123]; repmat(X,[M,N]):

>>repmat(a,1,2) make[M,N]tilesofX

ans= 1 2 3 1 2 3

>>repmat(a,2,1)ans=

1 2 3

1 2 3

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UsefulArrayfunctions

Lastelementofarray[end]

Lengthofarray[length]

Length=4

a= 1 3 2 5

Dimensionsofarray[size]

columns=4

1 2 3 5

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Tutorial|Time-SerieswithMatlab

>>[rows,columns]=size(a)rows=1

columns=4

>>length(a)ans=

4

>>a=[1325];

>>a(end-1)ans=

2

>>a=[1325];

>>a(end)ans=

5

rows=1

Tutorial|Time-SerieswithMatlab

UsefulArrayfunctions

Findaspecificelement[find]**

>>a=[132510523];

>>b=find(a==2)b=

3 7

Sorting[sort]***

>>a=[1325];

>>[s,i]=sort(a) a= 1 3 2 5

s=

1 2 3 5

s= 1 2 3 5

i=

1324 i=1324Indicatestheindexwheretheelementcamefrom

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Tutorial|Time-SerieswithMatlab

VisualizingDataandExportingFigures

UseFisher’sIrisdataset

>>loadfisheriris

4dimensions,3species

Petallength&width,sepallength&width

Iris:

virginica/versicolor/setosa

meas(150x4array):

Holds4Dmeasurements

...

'versicolor''versicolor''versicolor''versicolor'

'versicolor'species(150x1cellarray):

'virginica'Holdsnameofspeciesfor'virginica'thespecificmeasurement'virginica'

'virginica‘

...

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VisualizingData(2D)

idx_setosa

...1

1

1

0

0

0

...

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Theworldisgovernedmorebyappearancesratherthanrealities…--DanielWebster

Anarrayofzerosandonesindicatingthepositionswherethekeyword‘setosa’wasfound

strcmp,scatter,holdon

Tutorial|Time-SerieswithMatlab

>>idx_setosa=strcmp(species,‘setosa’);%rowsofsetosadata

>>idx_virginica=strcmp(species,‘virginica’);%rowsofvirginica

>>

>>setosa=meas(idx_setosa,[1:2]);

>>virgin=meas(idx_virginica,[1:2]);

>>scatter(setosa(:,1),setosa(:,2));%plotinbluecirclesbydefault

>>holdon;

>>scatter(virgin(:,1),virgin(:,2),‘rs’);%red[r]squares[s]forthese

Tutorial|Time-SerieswithMatlab

scatter3

VisualizingData(3D)

>>idx_setosa=strcmp(species,‘setosa’);%rowsofsetosadata

>>idx_virginica=strcmp(species,‘virginica’);%rowsofvirginica

>>idx_versicolor=strcmp(species,‘versicolor’);%rowsofversicolor

>>setosa=meas(idx_setosa,[1:3]);

>>virgin=meas(idx_virginica,[1:3]);

>>versi=meas(idx_versicolor,[1:3]);

>>scatter3(setosa(:,1),setosa(:,2),setosa(:,3));%plotinbluecirclesbydefault

>>holdon;

>>scatter3(virgin(:,1),virgin(:,2),virgin(:,3),‘rs’);%red[r]squares[s]forthese

>>scatter3(versi(:,1),virgin(:,2),versi(:,3),‘gx’);%greenx’s

7

6

5

>>gridon;%showgridonaxis

4

>>rotate3Don;%rotatewithmouse

3

2

1

4.5

4 8

3.5 77.5

3 66.5

2.5 55.5

4.5

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ChangingPlotsVisually

Zoomout

Zoomin

Createline

CreateArrow

SelectObject Addtext

Computersareuseless.Theycanonlygiveyouanswers.–PabloPicasso 30

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Tutorial|Time-SerieswithMatlab

ChangingPlotsVisually

Addtitles

Addlabelsonaxis

Changeticklabels

Addgridstoaxis

Changecolorofline

Changethickness/Linestyle

etc

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Tutorial|Time-SerieswithMatlab

ChangingPlotsVisually(Example)

Changecolorandwidthofaline

A

Rightclick

C

B

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Tutorial|Time-SerieswithMatlab

ChangingPlotsVisually(Example)

Theresult…

OtherStyles:

3

2

1

0

-1

-2

-3

0

10

20

30

40

50

60

70

80

90 100

3

2

1

0

-1

-2

-3

0

33

10

20

30

40

50

60

70

80

90 100

Tutorial|Time-SerieswithMatlab

ChangingFigurePropertieswithCode

GUI’sareeasy,butsoonerorlaterwerealizethatcodingisfaster

>>a=cumsum(randn(365,1));%randomwalkof365values

Ifthisrepresentsayear’sworthofmeasurementsofanimaginaryquantity,wewillchange:

x-axisannotationtomonths

Axislabels

Puttitleinthefigure

Includesomegreeklettersinthetitlejustforfun

Realmendoitcommand-line…--Anonymous 34

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Tutorial|Time-SerieswithMatlab

ChangingFigurePropertieswithCode

Axisannotationtomonths

>>axistight;%irrelevantbutuseful...

>>xx=[15:30:365];

>>set(gca,‘xtick’,xx) Theresult…

Realmendoitcommand-line…--Anonymous 35

Tutorial|Time-SerieswithMatlab

ChangingFigurePropertieswithCode

Axisannotationtomonths

>>set(gca,’xticklabel’,[‘Jan’;...

‘Feb’;‘Mar’])

Theresult…

Realmendoitcommand-line…--Anonymous 36

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Realmendoitcommand-line…--Anonymous

>>xlabel(‘Monthof2005’)

>>ylabel(‘ImaginaryQuantity’)

Tutorial|Time-SerieswithMatlab

>>title(‘Mymeasurements(\epsilon/\pi)’)

ChangingFigurePropertieswithCode

Axislabelsandtitle

Otherlatexexamples:

\alpha,\beta,e^{-\alpha}etc

Tutorial|Time-SerieswithMatlab

SavingFigures

Matlaballowstosavethefigures(.fig)forlaterprocessing

.figcanbelateropenedthroughMatlab

Youcanalwaysput-offfortomorrow,whatyoucandotoday.-Anonymous 38

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Tutorial|Time-SerieswithMatlab

ExportingFigures

Exportto:emf,eps,jpg,etc

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Tutorial|Time-SerieswithMatlab

Exportingfigures(code)

YoucanalsoachievethesameresultwithMatlabcode

Matlabcode:

%extracttocoloreps

print-depscmyImage.eps;%fromcommand-line

print(gcf,’-depsc’,’myImage’)%usingvariableasname

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Tutorial|Time-SerieswithMatlab

VisualizingData-2DBars

colormap

bars

time=[1001208070];%ourdata

h=bar(time);%gethandle

cmap=[100;010;001;.501];%colors

colormap(cmap);%createcolormap

cdata=[1234];%assigncolors

set(h,'CDataMapping','direct','CData',cdata);

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1

2

3

4

Tutorial|Time-SerieswithMatlab

VisualizingData-3DBars

data colormap

10

108 7 0 0 0

8 9 6 5 0.01980.01240.0079

6 8 6 4 0.03970.02480.0158

4 6 5 4 0.05950.03720.0237

2 6 3 2 0.07940.04960.0316

3 2 1 64 0.09920.06200.0395

0

...

1 1.00000.74400.4738

2

3 1.00000.75640.4817

5 1.00000.76880.4896

6 3

7 2 1.00000.78120.4975

1

3

data=[1087;965;864;654;632;321];

bar3([123567],data);

c=colormap(gray);%getcolorsofcolormapc=c(20:55,:);%getsomecolorscolormap(c);%newcolormap

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Tutorial|Time-SerieswithMatlab

VisualizingData-Surfaces

data

10

9 123… 10

8

1

7

6

5 910

4 1 10

3

2

1

10 Thevalueatposition

8 10 x-yofthearray

6 8

4 6 indicatestheheightof

4

2 2 thesurface

00

data=[1:10];

data=repmat(data,10,1);%createdata

surface(data,'FaceColor',[111],'Edgecolor',[001]);%plotdata

view(3);gridon;%changeviewpointandputaxislines

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Tutorial|Time-SerieswithMatlab

Creating.mfiles

Standardtextfiles

Script:AseriesofMatlabcommands(noinput/outputarguments)

Functions:Programsthatacceptinputandreturnoutput

Rightclick

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Tutorial|Time-SerieswithMatlab

Creating.mfiles

Meditor

Doubleclick

45

Creating.mfiles

Thefollowingscriptwillcreate:

Anarraywith10randomwalkvectors

Willsavethemundertextfiles:1.dat,…,10.dat

myScript.m SampleScript

Acumsum(A)

1 1

2 3

3 6

4 10

Writethisinthe 5

Arandomwalktime-series Meditor…

10

5

0 …andexecutebytypingthe

nameontheMatlab

-5 commandline

0 10 20 30 40 50 60 70 80 90100

cumsum,num2str,save

Tutorial|Time-SerieswithMatlab

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a=cumsum(randn(100,10));%10randomwalkdataoflength100

fori=1:size(a,2), %numberofcolumns

data=a(:,i);

fname=[num2str(i)‘.dat’];%astringisavectorofcharacters!

save(fname,’data’,’-ASCII’);%saveeachcolumninatextfile

end

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Tutorial|Time-SerieswithMatlab

Functionsin.mscripts

Whenweneedto:

Organizeourcode

Frequentlychangeparametersinourscripts

keywordoutputargumentfunctionname

inputargument

functiondataN=zNorm(data)

%ZNORMzNormalizationofvector HelpText

%subtractmeananddividebystd (helpfunction_name)

if(nargin<1),%checkparameters

error(‘Notenougharguments’);

end

data=data–mean(data);%subtractmean FunctionBody

data=data/std(data);%dividebystd

dataN=data;

function[a,b]=myFunc(data,x,y)%pass&returnmorearguments

Seealso:varargin,varargout

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Tutorial|Time-SerieswithMatlab

CellArrays

CellsthatholdotherMatlabarrays

–Let’sreadthefilesofadirectory

>>f=dir(‘*.dat’)%readfilecontents

f=

15x1structarraywithfields:name

date StructArray

bytes name

isdir 1 date

fori=1:length(f), bytes

isdir

a{i}=load(f(i).name); 2

N=length(a{i});

plot3([1:N],a{i}(:,1),a{i}(:,2),... 3

‘r-’,‘Linewidth’,1.5);

gridon; 4

pause; 600 5

cla; 500

end 400

300

200

100

0

1000

1500

500 1000 48

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Tutorial|Time-SerieswithMatlab

Reading/WritingFiles

Load/SavearefasterthanCstyleI/Ooperations

–Butfscanf,fprintfcanbeusefulforfileformattingorreadingnon-Matlabfiles

fid=fopen('fischer.txt','wt');fori=1:length(species),

fprintf(fid,'%6.4f%6.4f%6.4f%6.4f%s\n',meas(i,:),species{i});

endfclose(fid);

Outputfile: ■Elementsareaccessedcolumn-wise(again…)

x=0:.1:1;y=[x;exp(x)];

fid=fopen('exp.txt','w');fprintf(fid,'%6.2f%12.8f\n',y);fclose(fid);

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

11.10521.22141.34991.49181.64871.8221 2.0138

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Tutorial|Time-SerieswithMatlab

FlowControl/Loops

if(else/elseif),switch

Checklogicalconditions

while

Executestatementsinfinitenumberoftimes

for

Executestatementsafixednumberoftimes

break,continue

return

Returnexecutiontotheinvokingfunction

Lifeispleasant.Deathispeaceful.It’sthetransitionthat’stroublesome.–IsaacAsimov 50

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Tutorial|Time-SerieswithMatlab

tic,toc,clearall

For-Looporvectorization?

clearall; elapsed_time=

tic;

fori=1:50000 5.0070

a(i)=sin(i);

endtoc

clearall; elapsed_time=

a=zeros(1,50000);

tic; 0.1400

fori=1:50000

a(i)=sin(i);

endtoc

clearall;

tic; elapsed_time=

i=[1:50000];

a=sin(i); 0.0200

toc;

Pre-allocatearraysthat

storeoutputresults

–NoneedforMatlabto

resizeeverytime

Functionsarefasterthan

scripts

–Compiledintopseudo-

code

Load/Savefasterthan

MatlabI/Ofunctions

Afterv.6.5ofMatlabthere

isfor-loopvectorization

(interpreter)

Vectorizationshelp,but

notsoobvioushowto

achievemanytimes

Timenotimportant…onlylifeimportant.–TheFifthElement

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Tutorial|Time-SerieswithMatlab

MatlabProfiler

Findwhichportionsofcodetakeupmostoftheexecutiontime

Identifybottlenecks

Vectorizeoffendingcode

Timenotimportant…onlylifeimportant.–TheFifthElement 52

Tutorial|Time-SerieswithMatlab

Hints&Tips

Thereisalwaysaneasier(andfaster)way

Typicallythereisaspecializedfunctionforwhatyouwanttoachieve

Learnvectorizationtechniques,by‘peaking’attheactualMatlabfiles:

edit[fname],eg

editmean

editprincomp

MatlabHelpcontainsmanyvectorizationexamples

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Tutorial|Time-SerieswithMatlab

Debugging Bewareofbugsintheabovecode;Ihaveonlyproveditcorrect,nottriedit

--R.Knuth

NotasfrequentlyrequiredasinC/C++

–Setbreakpoints,step,stepin,checkvariablesvalues

Setbreakpoints

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Tutorial|Time-SerieswithMatlab

Debugging

Fullcontrolovervariablesandexecutionpath

–F10:step,F11:stepin(visitfunctions,aswell)

A

B

F10

C

Eitherthismanisdeadormywatchhasstopped.–GrouchoMarx 55

Tutorial|Time-SerieswithMatlab

AdvancedFeatures–3Dmodeling/VolumeRendering

Veryeasyvolumemanipulationandrendering

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Tutorial|Time-SerieswithMatlab

AdvancedFeatures–MakingAnimations(Example)

Createanimationbychangingthecameraviewpoint

3 3

2 2

1 1

3 0 0

2 -1

-1

1 -2

-2

0 -3

0 -3

0

-1 0

-2 50 3

50 50 2

-3 1

-1 0 1 2 100 0

3 4 100 1 2 3 4 100-1

-1 0

azimuth=[50:10099:-1:50];%azimuthrangeofvalues

fork=1:length(azimuth),

plot3(1:length(a),a(:,1),a(:,2),'r','Linewidth',2);gridon;

view(azimuth(k),30);%changenew

M(k)=getframe;%savetheframe

end

movie(M,20);%playmovie20times

4

Seealso:movie2avi

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Tutorial|Time-SerieswithMatlab

AdvancedFeatures–GUI’s

Built-inDevelopmentEnvironment

–Buttons,figures,Menus,sliders,etc

SeveralExamplesinHelp

Directorylisting

Addressbookreader

GUIwithmultipleaxis

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Tutorial|Time-SerieswithMatlab

AdvancedFeatures–UsingJava

MatlabisshippedwithJavaVirtualMachine(JVM)

AccessJavaAPI(egI/Oornetworking)

ImportJavaclassesandconstructobjects

PassdatabetweenJavaobjectsandMatlabvariables

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Tutorial|Time-SerieswithMatlab

AdvancedFeatures–UsingJava(Example)

StockQuoteQuery

ConnecttoYahooserver

/matlabcentral/fileexchange/loadFile.do?

objectId=4069&objectType=file

disp('ContactingYAHOOserverusing...');disp(['url=.URL('urlString')']);

end;

url=.URL(urlString);

try

stream=openStream(url);

ireader=java.io.InputStreamReader(stream);breader=java.io.BufferedReader(ireader);connect_query_data=1;%connectmade;

catch

connect_query_data=-1;%couldnotconnectcase;

disp(['URL:'urlString]);

error(['Couldnotconnecttoserver.Itmaybeunavailable.Tryagainlater.']);

stockdata={};return;

end

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MatlabToolboxes

YoucanbuymanyspecializedtoolboxesfromMathworks

ImageProcessing,Statistics,Bio-Informatics,etc

Therearemanyequivalentfreetoolboxestoo:

SVMtoolbox

http://theoval.sys.uea.ac.uk/~gcc/svm/toolbox/

Wavelets

/~ojanen/wavekit/

SpeechProcessing

http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html

BayesianNetworks

http://www.cs.ubc.ca/~murphyk/Software/BNT/bnt.html

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IncaseIgetstuck…

help[command](onthecommandline)eg.helpfft

Menu:help->matlabhelp

Excellentintroductiononvarioustopics

Matlabwebinars

II’v’veehhaaddaawwoonnddeerrffuulleevveenniningg..BBuutttthhisiswwaassnn’t’titit……

/company/events/archived_webinars.html?fp

Googlegroups

comp.soft-sys.matlab

Youcanfind*anything*here

Someoneelsehadthesameproblembeforeyou!

Tutorial|Time-SerieswithMatlab

PARTII:TimeSeriesAnalysis

EEigighhttppeerrcceennttooffssuucccceessssisissshhoowwiningguupp..

63

Definition:Asequenceofmeasurementsovertime

Tutorial|Time-SerieswithMatlab

Whatisatime-series

Definition:Asequenceofmeasurementsovertime

ECG

Medicine 64.0

StockMarket 62.8

62.0

Meteorology 66.0

Geology 62.0

32.0

Astronomy 86.4 Sunspot

...

Chemistry 21.6

Biometrics 45.2

43.2

Robotics 53.0

43.2 Earthquake

42.8

43.2

36.4

16.9

10.0

…

time

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Tutorial|Time-SerieswithMatlab

Applications(ImageMatching)

Cluster1

Manytypesofdatacanbeconvertedtotime-series

Image

ColorHistogram

600

400 Cluster2

200

0

50100150200250

400

200

0

50100150200250

800

600

400

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0

50100150200250

Time-Series

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Tutorial|Time-SerieswithMatlab

Applications(Shapes)

Recognizetypeofleafbasedonitsshape

Ulmuscarpinifolia Acerplatanoides Salixfragilis Tilia Quercusrobur

Convertperimeterintoasequenceofvalues

SpecialthankstoA.Ratanamahatana&

E.Keoghfortheleafvideo.

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Tutorial|Time-SerieswithMatlab

Applications(MotionCapture)

Motion-Capture(MOCAP)Data(Movies,Games)

Trackpositionofseveraljointsovertime

3*17joints=51parametersperframe

MMOOCCAAPPddaattaa……

……mmyypprreeccioiouuss……

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Tutorial|Time-SerieswithMatlab

Applications(Video)

Video-tracking/Surveillance

Visualtrackingofbodyfeatures(2Dtime-series)

SignLanguagerecognition(3Dtime-series)

VideoTrackingofbodyfeatureovertime(Athens1,Athens2)

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Tutorial|Time-SerieswithMatlab

Time-SeriesandMatlab

Time-seriescanberepresentedasvectorsorarrays

Fastvectormanipulation

Mostlinearoperations(egeuclideandistance,correlation)canbetriviallyvectorized

Easyvisualization

Manybuilt-infunctions

SpecializedToolboxes

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Tutorial|Time-SerieswithMatlab

BBeeccoommiinnggssuuffffiicciieennttllyyffaammiilliiaarrwwiitthhssoommeetthhiinnggiissaassuubbssttiittuutteeffoorruunnddeerrssttaannddiinnggiitt..

PARTII:TimeSeriesMatchingIntroduction

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Tutorial|Time-SerieswithMatlab

BasicData-Miningproblem

Today’sdatabasesarebecomingtoolarge.Searchisdifficult.

Howcanweovercomethisobstacle?

Basicstructureofdata-miningsolution:

Representdatainanewformat

Searchfewdatainthenewrepresentation

Examineevenfeweroriginaldata

Provideguaranteesaboutthesearchresults

Providesometypeofdata/resultvisualization

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Databasewithtime-series:

– Medicalsequences

– Images,etc

SequenceLength:100-1000ptsDBSize:1TByte

Tutorial|Time-SerieswithMatlab

BasicTime-SeriesMatchingProblem

Distance

query

D=7.3

LinearScan: D=10.2

Objective:ComparethequerywithallsequencesinDBandreturn

thekmostsimilarsequencesto D=11.8

thequery.

Databasewithtime-series: D=17

Medicalsequences

Images,etc D=22

SequenceLength:100-1000ptsDBSize:1TByte

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Tutorial|Time-SerieswithMatlab

Whatotherproblemscanwesolve?

Clustering:“Placetime-seriesinto‘similar’groups”

Classification:“Towhichgroupisatime-seriesmost‘similar’to?”

query

? ?

?

73

HierarchicalClustering

Verygeneric&powerfultool

Providesvisualdatagrouping

Pairwisedistances

74

Mergeobjectswithsmallestdistance

Reevaluatedistances

Repeatprocess

Tutorial|Time-SerieswithMatlab

Z=linkage(D);

H=dendrogram(Z);

D1,1

D2,1

DM,N

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1.4

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00.10.20.30.40.50.60.70.8 0.9

75

See:kmeans

K-MeansAlgorithm:

Initializekclusters(kspecifiedbyuser)randomly.

Repeatuntilconvergence

Assigneachobjecttothenearestclustercenter.

Re-estimateclustercenters.

PartitionalClustering

Fasterthanhierarchicalclustering

Typicallyprovidessuboptimalsolutions(localminima)

Notgoodperformanceforhighdimensions

Tutorial|Time-SerieswithMatlab

K-MeansDemo

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Tutorial|Time-SerieswithMatlab

K-MeansClusteringforTime-Series

SohowiskMeansappliedforTime-Seriesthatarehigh-dimensional?

PerformkMeansonacompresseddimensionality

Original Compressed Clustering

sequences sequences space

0.4

0.2

0

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-0.4

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Tutorial|Time-SerieswithMatlab

Classification

TypicallyclassificationcanbemadeeasierifwehaveclusteredtheobjectsClassA

0.4

Q 0.2

0

-0.2

Projectqueryinthe -0.4 So,queryQismore

newspaceandfind -0.6 similartoclassB

itsclosestcluster -0.6-0.4-0.200.20.40.6 0.8

ClassB

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NearestNeighborClassification

Weneednotperformclusteringbeforeclassification.Wecanclassifyanobjectbasedontheclassmajorityofitsnearestneighbors/matches.

Elfs

Hobbits 10

9