exploratory data analysis - grape.ics.uci.edu · Stats 170A: Project in Data Science Data...

Stats170A:ProjectinDataScience

DataVisualizationandExploratoryDataAnalysis

Padhraic SmythDepartmentofComputerScienceBrenSchoolofInformationandComputerSciencesUniversityofCalifornia,Irvine

PadhraicSmyth,UCIrvine:Stats170AB,Winter 2018: 2

Overview

• Lectures/Homeworks uptothispoint– Datamanagement(relationalDBs,query languages,PostgreSQL)– Datamanipulation inPython (Pandas)– Dataformats(JSON,XML)– PracticalexperiencewithTwitterdata,IMDBdata

• Next2weeks– Reviewofdatavisualizationandexploration– Basicprinciplesofmachinelearning (andsomestatistics)– Machinelearningwithtextdata


HowthisCoursewillwork

• Q1:Weeks1to6:LecturesandAssignments– Reviewgeneralprinciplesofdatascience– Weeks1to3:databases,dataextraction,datacleaning– Weeks4to6:textanalysis,dataexploration,machinelearning– Combination oflectures,assignments,andbackground reading

• Q1:Weeks7to10:ProjectProposals– Projectproposals fromstudent teams– Feedbackfrom instructors, refineproposal, oralpresentationatendofquarter

• Q2:WorkonProjects– Buildanduseaprototype system/pipeline – Develop ideas,implement algorithms,makeuseoflibrariesandpackages– Conductexperimentswithrealdatasets– Testandevaluateyoursysteminasystematicmanner– Communicateyour results(presentations andreports)


Assignment5

RefertotheWikipage

DuenoononMondayFebruary12th toEEEdropbox

Notechange:duebeforeclass(by2pm)


TypesofData


TypesofDataforaSingleVariable

• Real-valued,continuous– e.g.,aperson’sweightorincome– valuesmaybediscretrized andbounded, butwewillthinkofasontherealline

• Integer– e.g.Yearofbirth,numberofyearsincollege– Couldabeareal-valuedvariablethatisquantized (ageinyears)

• Ordinal– e.g.,education level={kindergarten, highschool, college,gradschool,…}

• Categorical– e.g.,{red,blue,yellow}or{CA,MA,NY,AZ,….}ortextstrings

(Notethatmanyvisualizationandmachinelearningtechniquesimplicitlyassumereal-valueddata,andotherdatatypesareconvertedtorealsorrep)


MultipleVariables

• Morethan1variable,oftenreferredtoasmultivariateormultidimensional

• Ofteninterestedinrelationshipsbetweenvariablesandgeometricstructureofthedata(forreal-valueddata),e.g.,isitclustered?

• Smallnumbersofvariablescanplotthedataandlookatrelationships

• Forlargenumbersweuseexploratorytechniques– E.g.,clusteringanddimension reduction

• Notethatmanyvisualizationandmachinelearningtechniques implicitlyassumereal-valueddata….categoricaldatatypesareoftenconvertedtoreals(e.g.,binary)orrepresented viagrouping, colors,oricons


DatawithContext

• Time-seriesdata– Avariablewhosevaluesareindexedbytime– Wecanalsohavemultidimensional time-series

• Sequencedata– Avariableindexedbyposition– E.g.,words(categorical)intext,orDNAsequences

• Spatialdata– Datawhosevaluesareindexedspatially,e.g.,bylat/lon orbycity– Canalsohavemultidimensional time-series

• Spatio-temporal– Indexedbybothspaceandtime,e.g.,stormtracks,vehicletrajectories, etc


StockMarketIndiceslastweek


NightLightsfromNorthandSouthKorea

Fromhttps://www.vox.com


WherePeopleRun

From:https://flowingdata.com/2014/02/05/where-people-run/#jp-carousel-33695


RelationalData

• Nentities,i =1,….N• NxNrelations:

– canberepresentedasanarrayy(i,j)=1ifi isconnectedtoj,0otherwise– Example:asocialnetwork

• Cancombinewithotherdata,e.g.,– Eachrelationcouldhavemetadata,e.g.,text– Eachrelationcouldbetime-dependent, y(i,j,t)isatimeseriesovertimet


Visualizationofanemailnetworkusing2-dimensionalgraphdrawingor“embedding”

Datafrom500researchersatHewlett-Packardoverapproximately1year.

Variousstructuralelementsofthenetworkareapparent


PhilosophybehindthisClass

• Provideanexperienceofhowdatascienceworksinthereal-world– Defining aproblem– Identifying, understanding, exploring relevantdata– Extracting,cleaning,managementofdata– Explorationandanalysisofdata– Buildingmodels fromdata(e.g.,viamachinelearning)– Evaluatingmodels:howwelldotheypredict– Communicating yourresultstoothers

• Tietogetherideasfromdifferentcoursesyouhavetakenandgiveyouexperienceinapplyingtheseideastoreal-worlddata– Databases,software,algorithms,machinelearning, statistics


DataScience:fromDatatoActions

DataManagement

RawData

PredictiveModeling

ExploratoryDataAnalysis

Consumers

ExternalBusinessCustomers

InternalBusinessCustomers

Scientists

Government

DataWrangling

Databases,Algorithms,SoftwareEngineering

MachineLearning,Statistics

DomainknowledgeBusinessknowledge


WhyVisualizationandExploration?

• Peoplearegoodatpatternrecognition– Atspottingclusters,trends,outliers, structure…thatcomputersmanymiss

• Usuallytwotypesofusers1. Thedatascientistwhowantstoexplore/analyze/understand

- Forthedatascientist,visualizationandexplorationarepartofaniterativeprocess

2. Thepersonwhoneedsaquicksummary tomakeadecision- Fortheconsumerwewanttocommunicateinformationquicklyandclearly- e.g.,foramedicaldoctor,forapolicy-maker,foraconsumer

- Fordatascientists…itsalwaysagoodideatolookatyourdata- Helpstounderstandwherethesemanticsofthedata…whatthemeasurements

actuallymean


WhatisExploratoryDataAnalysis?

• Broaderthanjustvisualization

• EDA={visualization,clustering,dimensionreduction,….}

• Forsmallnumbersofvariables,EDA=visualization

• Forlargenumbersofvariables,weneedtobecleverer– Clustering,dimension reduction, embedding algorithms– Thesearetechniques thatessentiallyreducehigh-dimensional datato

something wecanlookat

• PioneeredbyJohnTukey (statisticianatBellLabs,Princeton)inthe1960’s– “letthedataspeak”


ExploratoryDataAnalysis:SingleVariables


SummaryStatistics

Mean:“centerofdata”Mode:locationofhighestdatadensityVariance:“spreadofdata”Skew:indicationofnon-symmetry

Range:max- minMedian:50%ofvaluesbelow,50%aboveQuantiles:e.g.,valuessuchthat25%,50%,75%aresmaller

NotethatsomeofthesestatisticscanbemisleadingE.g.,meanfordatawith2clustersmaybeinaregionwithzerodata


HistogramofUnimodal Data

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1000datapoints simulatedfromaNormaldistribution, mean10,variance1,30bins


Histograms:Unimodal Data

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HistogramofMultimodalData

15000datapoints simulatedfromamixtureof3Normaldistributions, 300bins

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HistogramofMultimodalData

15000datapoints simulatedfromamixtureof3Normaldistributions, 300bins

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SkewedData

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5000datapoints simulatedfromanexponentialdistribution, 100bins


AnotherSkewedDataSet

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10000datapoints simulatedfromamixtureof2exponentials, 100bins


SameSkewedDataaftertakingLogs(base10)

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10000datapoints simulatedfromamixtureof2exponentials, 100bins


Whatwillthemeanormediantellusaboutthisdata?

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HistogramwithOutliers

Xvalues

Numberof

Individuals

PimaIndiansDiabetesData,FromUCIrvineMachineLearningRepository


HistogramwithOutliers

bloodpressure=0?

DiastolicBloodPressure

Numberof

Individuals

PimaIndiansDiabetesData,FromUCIrvineMachineLearningRepository


BoxPlots:DiabetesData

BodyMassIndex

HealthyIndividuals

DiabeticIndividuals

Twoside-by-sidebox-plotsofindividualsfromthePimaIndiansDiabetesDataSet

Note:significantoverplotting herethatcouldeasilybemissed


BoxPlots:DiabetesData

BodyMassIndex

HealthyIndividuals

DiabeticIndividuals

Box = middle 50% of data

Plotsalldatapoints outside“whiskers”

1.5xQ3-Q1

Q2(median)

Q3

Q1

UpperWhisker

LowerWhisker

Twoside-by-sidebox-plotsofindividualsfromtheDiabetesDataSet


MultipleBoxPlots:DiabetesData

healthy diabetic healthy diabetic

DiastolicBloodPressure

24-hourSerumInsulin

PlasmaGlucose

Concentration

BodyMassIndex


HorizontalBoxPlot forPlanetData

From:https://seaborn.pydata.org/examples/horizontal_boxplot.html


ExploringPairsofVariables


RelationshipsbetweenPairsofVariables

• SaywehaveavariableYwewanttopredictandmanyvariablesXthatwecouldusetopredictY

• InexploratorydataanalysiswemaybeinterestedinquicklyfindingoutifaparticularXvariableispotentiallyusefulatpredictingY

• Options?– Linearcorrelation

– Scatterplot:plotYvaluesversusXvalues


LinearDependencebetweenPairsofVariables

• Covarianceandcorrelationmeasurelineardependence

• AssumewehavetwovariablesorattributesXandYandnobjectstaking valuesx(1),…,x(n)andy(1),…,y(n).ThesamplecovarianceofXandYis:

• ThecovarianceisameasureofhowXandYvarytogether.– largeandpositive iflargevaluesofXareassociatedwith largevaluesofY

andsmallX⇒ smallY

• (PearsonLinear)Correlation=scaledcovariance,variesbetween-1and1

∑=

−−=n

iyiyxix

nYXCov

1

))()()((1),(

21

1

2

1

2

1

))(())((

))()()((),(

⎟⎠

⎞⎜⎝

⎛−−

−−=

∑ ∑

∑

= =

=

n

i

n

i

n

i

yiyxix

yiyxixYXρ


DataSetonHousingPricesinBoston

1 CRIM percapitacrimeratebytown

2 ZN proportionofresidentiallandzonedforlotsover25,000ft2

3 INDUS proportionofnon-retailbusiness acrespertown

4 NOX Nitrogen oxide concentration(partsper10million)

5 RM averagenumberofroomsperdwelling

6 AGE proportionofowner-occupiedunitsbuiltpriorto1940

7 DIS weighteddistancestofiveBostonemploymentcentres

8 RAD indexofaccessibilitytoradialhighways

9 TAX full-valueproperty-taxrateper$10,000

10 PTRATIO pupil-teacherratiobytown

11 MEDV Medianvalueofowner-occupiedhomesin$1000's

(widely useddatasetinresearchinregression(prediction) research)


MatrixofPairwiseLinearCorrelations

Industry

Nitrousoxide

Percentageoflargeresidentiallots

CrimeRate

-1 0 +1

DataoncharacteristicsofBostonhousing

Average#rooms

Medianhousevalue

Proportionofoldhouses

Distancetoemployment

centers

Highwayaccessibility

Propertytaxrate

Student-teacherratio


ExamplesofX-Yplotsandlinearcorrelationvalues


LinearDependence

Non-LinearDependence

Lackoflinearcorrelationdoesnotimply lackofdependence


SummaryStatisticsforAnscombe’s 4DataSets

SummaryStatisticsofDataSet1N =11MeanofX =9.0MeanofY =7.5




Anscombe,Francis(1973),GraphsinStatisticalAnalysis,TheAmericanStatistician,pp.195-199.

4datasets,eachwith2variablesXandY,withthesamesummarystatistics(imagine thatPython reports thesesummariesandwehavenotyetlookedatthedata)


Anscombe’s 4DataSets


GuesstheLinearCorrelationValuesforeachDataSet


SummaryStatisticsforeachDataSet

SummaryStatisticsofDataSet1N =11MeanofX =9.0MeanofY =7.5Intercept=3Slope=0.5Correlation=0.82





Lesson:summarystatisticscanbemisleading


Dangersofsearchingforcorrelationsinhigh-dimensionaldata

Simulated 50randomGaussian/normaldatavectors,eachwith100variablesResultsina50x100datamatrix

Belowisahistogramof the100choose2pairsofcorrelationcoefficients

Evenifdataareentirelyrandom(nodependence) thereisaveryhighprobabilitysomevariableswillappeardependent justbychance.


CorrelationsinaLargeRandomDataSet

From:https://seaborn.pydata.org/examples/many_pairwise_correlations.html


Conclusionssofar?

• Summarystatisticsareuseful…..uptoapoint

• Linearcorrelationmeasurescanbemisleading

• Therereallyisnosubstituteforplotting/visualizingthedata


ScatterPlots

• Plotthevalueofonevariableagainsttheother

• Simple…butcanbeveryinformative,canrevealmorethansummarystatistics

• Forexample,wecan…– Seeifvariablesaredependentoneachother (beyond lineardependence)– Detectifoutliersarepresent– Cancolor-codetooverlaygroup information (e.g.,colorpointsbyclasslabelfor

classificationproblems)


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MEDIAN PERCAPITA INCOME

MEDIANHOUSEHOLD INCOME

(from US Zip code data: each point = 1 Zip code)

units = dollars


ConstantVarianceversusChangingVariance

variationinYdoesnotdependonX variationinY changeswiththevalueofXe.g.,Y=annualtaxpaid,X=income


Scatter-PlotMatrices:ExampleforDiabetesData


UsingColortoShowGroupInformationinScatterPlots

Figurefromwww.originlab.com

Irisclassificationdataset,3classes


AnotherExamplewithGroupingbyColor

Figurefromhci.stanford.edu


OutlierDetection

• Definitionofanoutlier?– Noprecisedefinition– Generally….”Adatapoint thatissignificantlydifferent totherestofthedata”– Buthowdowedefine“significantlydifferent”? (manyanswerstothis…..)– Typicallyassumedtomeanthatthepointwasmeasuredinerror,orisnotatrue

measurement insomesense

Outliersin1dimension Outlierin2dimensions

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X VALUES

Y VA

LUES


Assignment5

RefertotheWikipage

DuenoononMondayFebruary12th toEEEdropbox

Notechange:duebeforeclass(by2pm)

exploratory data analysis - grape.ics.uci.edu · Stats 170A: Project in Data Science Data...

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