Table Of ContentSPRINGER BRIEFS IN COMPUTER SCIENCE
Berkay Aydin · Rafal A. Angryk
Spatiotemporal
Frequent Pattern
Mining from
Evolving Region
Trajectories
1 23
SpringerBriefs in Computer Science
Serieseditors
StanZdonik,BrownUniversity,Providence,RhodeIsland,USA
ShashiShekhar,UniversityofMinnesota,Minneapolis,Minnesota,USA
XindongWu,UniversityofVermont,Burlington,Vermont,USA
LakhmiC.Jain,UniversityofSouthAustralia,Adelaide,SouthAustralia,Australia
DavidPadua,UniversityofIllinoisUrbana-Champaign,Urbana,Illinois,USA
XueminShermanShen,UniversityofWaterloo,Waterloo,Ontario,Canada
BorkoFurht,FloridaAtlanticUniversity,BocaRaton,Florida,USA
V.S.Subrahmanian,UniversityofMaryland,CollegePark,Maryland,USA
MartialHebert,CarnegieMellonUniversity,Pittsburgh,Pennsylvania,USA
KatsushiIkeuchi,UniversityofTokyo,Tokyo,Japan
BrunoSiciliano,UniversitàdiNapoliFedericoII,Napoli,Italy
SushilJajodia,GeorgeMasonUniversity,Fairfax,Virginia,USA
Newton Lee, Institute for Education, Research, and Scholarships in Los Angeles,
California,USA
SpringerBriefs present concise summaries of cutting-edge research and practical
applicationsacrossawidespectrumoffields.Featuringcompactvolumesof50to
125pages,theseriescoversarangeofcontentfromprofessionaltoacademic.
Typicaltopicsmightinclude:
(cid:129) Atimelyreportofstate-of-theartanalyticaltechniques
(cid:129) A bridge between new research results, as published in journal articles, and a
contextualliteraturereview
(cid:129) Asnapshotofahotoremergingtopic
(cid:129) Anin-depthcasestudyorclinicalexample
(cid:129) A presentationofcoreconceptsthatstudentsmustunderstandinordertomake
independentcontributions
Briefs allow authors to present their ideas and readers to absorb them with
minimal time investment. Briefs will be published as part of Springer’s eBook
collection, with millions of users worldwide. In addition, Briefs will be available
forindividualprintandelectronicpurchase.Briefsarecharacterizedbyfast,global
electronic dissemination, standard publishing contracts, easy-to-use manuscript
preparation and formatting guidelines, and expedited production schedules. We
aim for publication 8−12 weeks after acceptance. Both solicited and unsolicited
manuscriptsareconsideredforpublicationinthisseries.
Moreinformationaboutthisseriesathttp://www.springer.com/series/10028
Berkay Aydin (cid:129) Rafal A. Angryk
Spatiotemporal Frequent
Pattern Mining from
Evolving Region Trajectories
123
BerkayAydin RafalA.Angryk
DepartmentofComputerScience DepartmentofComputerScience
GeorgiaStateUniversity GeorgiaStateUniversity
Atlanta,GA,USA Atlanta,GA,USA
ISSN2191-5768 ISSN2191-5776 (electronic)
SpringerBriefsinComputerScience
ISBN978-3-319-99872-5 ISBN978-3-319-99873-2 (eBook)
https://doi.org/10.1007/978-3-319-99873-2
LibraryofCongressControlNumber:2018955469
©TheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerlandAG2018
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor
theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional
claimsinpublishedmapsandinstitutionalaffiliations.
ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
To mywife, Yagmur,who relentlessly
supportsmethroughthickand thin.
Berkay Aydin
To allwonderfulwomen ofmylife:
Aleksandra,Izabela,Gabriella,Nina, and
Ella.Thankyou.
Rafal A. Angryk
Preface
Oftenmisunderstood,knowledgediscoveryisaninherentlyinterdisciplinaryfield.
Itencompassestheentireprocessofdiggingthroughthevastamountsofdatafrom
various domains, analyzing these large-scale datasets, and extracting the meaning
hidden within them. It helps us understand the underlying relationships, uncover
insightfulpatterns,andactbasedonourdiscoveries.Westronglybelievethatallthe
bigdatahype,comingtousrecentlyfromadynamicallygrowingbusinessworld,is
justthetipoftheiceberg.Beyondit,therearevastamountsoftrulyinterconnected
andincreasinglycomplexdatasets. Inthis book,we unveiljusta small, butin our
opinion very useful part of data mining—spatiotemporal frequent pattern mining
fromevolvingregiontrajectories.
Evolving region trajectory is our base data type, providing foundation for
majority of the presented works. We use this data type to represent multiple
spatial objects that continuously change their shapes and locations over time.
Such dynamically evolving spatial objects frequently occur in multiple scientific
domains,suchasheliophysics,biology,andmedicine.Inthisbookwewilldiscuss
differentrelationships between evolving regiontrajectories, methodsto assess the
significance of these relationships, and algorithms, which we developed to mine
them.
Atlanta,GA,USA BerkayAydin
July2018 RafalA.Angryk
vii
Acknowledgments
Thisbookhasbeendevelopedoutofaseriesofstudies,whichwehaveconducted
over the recent years. Many of our papers and research investigations have been
inspired or influenced by our coworkers and more distant collaborators. We are
grateful to our past and current coworkers, Piet Martens, Karthik Ganesan Pillai,
Micheal Schuh, Dustin Kempton, Juan Banda, Doug Galarus, Tim Wylie, Stuart
Jeffries,RuizheMa,SoukainaFilaliBoubrahimi,AhmetKucuk,ShahMuhammad
Hamdi, Vijay Akkineni, Sajitha Naduvil-Vadukootu,and Azim Ahmadzadeh. We
also thank our remote collaborators,specifically Jack Ireland, Kathy Reeves, Pete
Riley, Joe Gurman,Craig DeForest, Gelu Nita, AndresMunoz-Jaramillo,Alisdair
Davey,VeroniqueDelouille,andKevinReardon.
WewouldliketothanktheNationalScienceFoundation(NSF),NationalAero-
nauticsandSpaceAdministration(NASA),andGeorgiaStateUniversity(GSU)for
generouslysupportingour research. The research presentedin this bookhas been
supportedin parts by fundingfrom the Division of AdvancedCyberinfrastructure
withintheDirectorateforComputerandInformationScienceandEngineering,the
Division of Astronomical Sciences within the Directorate for Mathematical and
PhysicalSciences,andtheDivisionofAtmosphericandGeospaceScienceswithin
theDirectorateforGeosciences,underNSFawards#1443061and#1812964.Itwas
also supported in parts by funding from NASA through awards #NNX09AB03G,
#NNX11AM13A,and#NNX15AF39G.WehavealsobenefitedfromGeorgiaState
University’sSecondCenturyInitiativeandNextGenerationprograms.
Any opinions expressed herein are those of the authors and do not necessarily
representtheviewsoftheNationalScienceFoundation(NSF),NationalAeronautics
andSpaceAdministration(NASA),orGeorgiaStateUniversity(GSU).
ix
Contents
1 AGentleIntroductiontoSpatiotemporalDataMining ................. 1
1.1 TypesofSpatiotemporalKnowledge................................... 2
1.2 MotivationandChallenges ............................................. 3
1.2.1 SolarPhysics.................................................... 4
1.2.2 BiomedicalSciences............................................ 5
1.2.3 Epidemiology................................................... 6
1.3 Challenges............................................................... 7
2 ModelingSpatiotemporalTrajectories.................................... 9
2.1 BasicSpatiotemporalDataTypes...................................... 9
2.2 MovingObjects ......................................................... 10
2.3 EvolvingRegionTrajectories........................................... 11
2.3.1 ModelingSpatiotemporalEventInstancesandExamples.... 13
3 ModelingSpatiotemporalRelationshipsAmongTrajectories.......... 17
3.1 GenericSpatialandTemporalRelationships .......................... 17
3.1.1 TemporalRelationships ........................................ 18
3.1.2 SpatialRelationships ........................................... 19
3.1.3 SpatialCo-locations ............................................ 21
3.2 SpatiotemporalRelationships .......................................... 22
3.2.1 SpatiotemporalCo-occurrence................................. 23
3.2.2 SpatiotemporalSequences...................................... 25
4 SignificanceMeasurementsforSpatiotemporalCo-occurrences....... 29
4.1 TheFamilyofJaccardMeasures....................................... 31
4.1.1 J Measure....................................................... 32
+
4.1.2 J Measure...................................................... 32
∗
4.1.3 J Measure ...................................................... 36
4.1.4 AlgorithmsforCalculatingJaccard-DerivedMeasures....... 40
4.2 OverlapMeasures....................................................... 45
4.2.1 KeyPropertiesofOverlapMeasures........................... 45
4.2.2 OMINandOMAXCalculationAlgorithms................... 47
xi
xii Contents
4.3 CosineMeasure......................................................... 49
4.3.1 KeyPropertiesofCosineMeasure............................. 50
4.3.2 AlgorithmforCalculatingCosineMeasure ................... 51
4.4 Summary ................................................................ 51
5 SpatiotemporalCo-occurrencePattern(STCOP)Mining .............. 55
5.1 PreliminariesofSTCOPMining....................................... 56
5.2 SignificanceandPrevalenceMeasurements........................... 57
5.3 STCOPMiningfromEvolvingRegionTrajectories .................. 58
5.4 EfficientSpatiotemporalJoinsforSTCOPMining.................... 62
5.4.1 Grid-MappedIntervalTrees(GITs)............................ 62
5.4.2 ChebyshevPolynomialIndexing............................... 65
5.5 Summary ................................................................ 68
6 SpatiotemporalEventSequence(STES)Mining......................... 71
6.1 ModelingSpatiotemporalEventSequences ........................... 73
6.1.1 HeadandTailWindowofanInstance......................... 74
6.1.2 GeneratingHeadandTailWindows ........................... 74
6.1.3 StrategiesforHeadandTailWindowGeneration............. 76
6.2 SpatiotemporalFollowRelationshipandMeasuringthe
Significance ............................................................. 79
6.2.1 SignificanceofInstanceSequences............................ 80
6.2.2 PrevalenceoftheEventSequences ............................ 82
6.3 Apriori-BasedAlgorithmsforMiningSpatiotemporalEvent
Sequences ............................................................... 83
6.3.1 Initialization..................................................... 83
6.3.2 SequenceConnectAlgorithm................................... 83
6.3.3 AvoidingSpatiotemporalJoins................................. 85
6.4 APatternGrowth-BasedApproachforMiningSpatiotemporal
EventSequences ........................................................ 87
6.4.1 EventSequencesandGraphRepresentation .................. 88
6.4.2 EsGrowthAlgorithm ........................................... 91
6.5 MiningtheMostPrevalentSpatiotemporalEventSequences:
Top-(R%,K)Approach................................................. 93
6.6 Summary ................................................................ 95
References......................................................................... 97
Index............................................................................... 105
