Download Graph Mining: Introduction - Hasso-Plattner

Graph Mining: Introduction
DavideMottin,KonstantinaLazaridou
Hasso Plattner Institute
Graph Mining course Winter Semester 2016
Lecture road
CourseInformation
Introductiontographmining
Graphs:modelsandbasicconcepts
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Organization of the lecture
• LectureandslidesinEnglish
• Tuesday15.15– 16.45
• Twomandatory assignments:
• [Individual] Onepresentationofapaperofchoiceamongalistofpapersabouttopics
coveredinthelectures.Twoslots:13/12(firstpart)– 07/02(secondpart)
• [Individual]Onesmallprojectofgraphanalyticstobecompletedbeforetheendofthe
course
• Examination(inEnglish!):
• Oralexam(inthefirstthreeweeksafterthelectureperiod)
• Gradingscheme:
• 20%:Presentation
• 10%:Project
• 70%:Exam
• Lectureswillberecordedandonline(tele-task)
• Thereisnoofficialtextbookforthecourse
• Registrationisrequiredforthislecture,notifythestudienreferat and
myself:[email protected]
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About the lecturers
DavideMottin
PostdoctoralResearcher@KnowledgeDiscoveryandDataMining
PhDin2015,UniversityofTrento
ResearchInterests:GraphMining,DataMining,Graphdatabases,
Preferencemodels,Queryparadigms
KonstantinaLazaridou
PhDCandidate@InformationSystemsResearch- WebScience
MScin2015,UniversityIoannina
ResearchInterests:GraphMining,SocialNetworkAnalysis,Webdata
Mining,OpinionandSentimentAnalysis,DataStreamMining
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Course Web site
Lecturematerial(slides,papers,
books,tutorials,assignments,
…)availableonline
https://hpi.de/en/mueller/teac
hing/aktuelle-vorlesung/ws1617/graph-mining.html
§ Theslidesarealso
availableinthe
intranet!
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Objectives
§ Understanding
• Wheregraphsare,whytheyareimportant,andwhatarenewapplications
• Themainchallengesfromdataminingperspective
§ Learn
•
•
•
•
Howtoefficientlyquery,andstoreagraphusinggraphminingtechniques
Analyzenetworkstounderstandthepropertiesandthebehaviorsofindividuals
Thinkinaresearchperspective(novelty,clarity,…)
Solvepracticalproblems
§ Workonrealscaledataandexistingtools
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Prerequisites
§ Basiccomputerscienceandprogramming.
§ Data-miningknowledgeisaplusbutisnotstrictlyrequired.
§ Basicprobabilitytheoryandlinearalgebraarebeneficial,
althoughasmallrecap ofthemainconceptswillbedoneatthe
beginningoftherequiredlectures.
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Schedule (tentative)
18.10
Introduction to graph mining
25.10
Social network analysis - Diffusion
01.11
Graph Querying: exact, approximate, and reachability
08.11
Frequent subgraph mining
15.11
Graph indexing
17.11
HPI-Kolloquium – Invited speaker: prof. Danai Koutra
22.11
Node classification
29.11
Some practical graph mining framework
Project assignment
06.12
Link prediction
13.12
Student paper presentation [first part]
20.12
Christmas break
27.12
Christmas break
03.01
Non overlapping communities
10.01
Overlapping communities
17.01
Anomaly detection
24.01
Graph summarization
Report handover
31.01
Summary of algorithms for different graph models
07.02
Student paper presentation [second part]
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Course Material - 1
Thereisnoofficialbookinthecourse.However,theslidesarebasedonmaterialsfrom
thesebooks:
§
©Aggarwal,C.C.andWang,H.eds.,
2010.Managingandmininggraphdata (Vol.
40).NewYork:Springer.
§
©Chakrabarti,D.andFaloutsos,C.,2012.
Graphmining:laws,tools,andcase
studies. SynthesisLecturesonDataMiningand
KnowledgeDiscovery, 7(1),pp.1-207.
§
©Easley,D.andKleinberg,J.,2010. Networks,
crowds,andmarkets:Reasoningaboutahighly
connectedworld.CambridgeUniversityPress.
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Course Material - 2
Somematerialisinspired,importedandmodifiedfromseveral
existingcourses.
§ GraphMiningandExplorationatScale(prof.Danai Koutra)
• http://web.eecs.umich.edu/~dkoutra/courses/F15_598/
§ SocialandInformationNetworkAnalysis(prof.JureLeskovec)
• http://web.stanford.edu/class/cs224w/
§ OnlineSocialNetworksandMedia(prof.Evaggelia Pitoura,prof.
Panayotis Tsaparas)
• http://www.cs.uoi.gr/~tsap/teaching/cs-l14/
§ DataMiningmeetsGraphMining(prof.LemanAkoglu)
• http://www3.cs.stonybrook.edu/~leman/courses/14CSE590/index.htm
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How to send emails
To:[email protected]
Subject:Problem– Help
Text:
DearDr.DavideMottin,
✗
I’mastudentatthethirdyear,attendingthecourse,
numberofshoes,quantityoffoodeatenyesterday
To:[email protected]
Subject:[GraphMining]Subgraphisomorphism
Theslidesarenotclear.Idon’tunderstandthethings
theres.
Text:
Yoursincerely,
HiDavide,
BigBug92
thesubgraphisomorphismconceptisnotentirelyclear
tome.Whyisthefunctionbijective?
✔
Thanks,
[FirstName-LastName]
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Some rule of thumbs
§ I’mavailableforanykindofconcern
§ Usethemailinglist:https://lists.hpi.unipotsdam.de/listinfo/graphmining-ws1617
§ Seldomsendemailtomedirectly,unlessitisaveryimportant
concern
§ Bequickandpreciseintheemails
§ Askmequestionsinthecourse,orrightafter/beforethelecture.If
thequestionrequiresmoretimeaskforameetingwithme:
• BetterifyouclusterandcomeingroupinsteadofalonesoIcananswertomany
questionsatthesametime
§ Ifyouthinkthecourseload/organizationisunfairpleaseletmeknow
beforetheendofthesemester.AfterthattherewillbeNOpossibility
fordiscussion.
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Feedback
§ Thecourseistaughtforthefirsttime:
•
•
•
•
Anyfeedbackisappreciated
Anycommentsonslidesandclarityaswell
Theremightbesomemistakehereandthere(butwewilldoourbest)
Askquestionsifyoudon’tunderstandsomething.Betteraquestioninclassthana
doubtduringtheexam!
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(There's) no such thing as a stupid question
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Content of the course
Backgroundconcepts:probabilitytheory/statistics,basiclinearalgebra,basicgraph
concepts(morphisms,degrees,matrixrepresentation,...)
Socialnetworkanalysis:
§
Firstpart
§
• Diffusion
• Powerlaws
• Influencepropagation
§
Secondpart
•
•
•
•
Graphqueryingandindexing:
Exactandapproximatequeries
Reachabilityqueries
Frequentsubgraphmining
Graphindexing
§
Nodeclassificationandnodesimilarity
§
§
Linkprediction
Communitiesandanomalies
• Overlapping/Nonoverlappingcommunities
• Anomalydetection
§
§
§
Graphsummarization
Summaryofalgorithmsfordifferentmodels(graphstreams,evolvinggraphs,probabilistic
graphs,coloredgraphs)
Graphminingframeworks
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About the presentations
§ Thepresentationwillbe15minsintotal
• 10minutespresentation
• 5minutesquestions
§ Thegroupwillbedividedintotwohalves:
• OnehalfwillpresentonDecember13papersregardingthefirstpartofthecourse
• TheotherhalfwillpresentonFebruary7 regardingthesecondpartofthecourse
§ Everypersonpresentsonepaper
§ Firstcomefirstserved
• iftwopeopleasktopresentthesamepaper,thesecondhastochangethechoice
Paperlistforthefirstpartofthecourse:https://goo.gl/YMR0wD
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Questions?
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Lecture road
CourseInformation
Introductiontographmining
Graphs:modelsandbasicconcepts
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The web
August2016
>=50billionsofpages
Atleast4.73billionpagesindexedbysearchengines
Source:http://www.worldwidewebsize.com/
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Social graphs
facebook
1.5Bln users
450Bln Relationships
600Mln groups
10.5USDperuser
Twitter
313Mln users
500Mln Tweets/day
Avg 208followers/user
Theyarecomplex:Groups,links,preferences,attributes
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Knowledge graphs
20Mlnentities
100Mlnrelationships
2500typesof
relationships
Otherknowledgegraphs:
• YAGO
• DBPedia
• DBLP
• Pubmed
• Linkmdb
• …
Connectentitiessuchaspersons,organizations,countries,
objectsthroughsemanticrelationships(e.g.ownsacompany)
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Biological networks
Protein-proteininteractionnetworks
Nodes:Proteins
Edges:Physicalinteractions
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Metabolicnetworks
Nodes:Metabolitesandenzymes
Edges:Chemicalreactions
22
What else?
Source:http://screenrant.com/game-thrones-protagonist-tyrion-math/
Source: http://phys.org/news/2016-02-math-reveals-unseen-worlds-star.html
Anythingthatinvolvesrelationships(implicitorexplicit)
canbemodeledasagraph!
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Graphs are everywhere
SocialNetworks
RecommendationGraphs
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Complex
Ubiquituous
Large RoadNetworks
Valuable
KnowledgeGraphs
24
Why Graphs? Why now?
§ Describecomplexdatawithasimplestructure
• Nature,social,concepts,roads,circuits…
§ Samerepresentationformanydisciplines
• Computerscience,biology,physics,economics,...
§ Availabilityof(BIG)data
• Largenetworksarenowavailableandrequirecomplexalgorithms
• Networksareevolvingovertime(e.g.,newusers/friendsinFacebook)
§ Usefulness
• Analysiswilldiscovernontrivialpatterns,andallowsimplesmoothexplorations
• Theyrevealuserbehaviors
• Theyarevaluable(Facebook,Twitter,Amazon...Allofthembasedongraphs!!!)
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”Graph mining is the process of discovering,
retrieving and analyzing non trivial patterns
in graph shaped data”
Graph
mining
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What can we do with graph mining?
§ Compressinggraphswithoutlosinginformation
§ Findingcomplexstructuresfast
§ Recognizingcommunitiesandsocialpatterns
§ Studythepropagationofviruses
§ Predictingiftwopeoplewillbecomefriends
§ Understandingwhataretheimportantnodes
§ Showinghowthenetworkwillevolve
§ Helpingthevisualizationofcomplexstructures
§ Findingroles,positiveandnegativeinfluenceprediction
§ …
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What is involved in graph mining?
§ Basicgraphalgorithms(shortestpaths,BFS,DFS,isomorphisms,
traversals,randomwalks…)
§ Storageandindexing
§ Smartrepresentationsforcompactness
§ Modelingofproblemsasgraphs
§ Distancemetricsandsimilaritymeasures
§ Exact,Approximate,andheuristicalgorithms
§ Evolvingstructures
§ Interactivityandonlineupdates
§ Complexity(mostoftheproblemsarenotpolynomially
solvable)
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Practical applications of graph mining
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Finding substructures
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Community detection
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Influence propagation
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Link prediction
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Graph evolution
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Detecting frauds
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Visualization
Severalvisualizationtools:
• General:Gephi,GraphViz,…
• Biological:Cytoscape,Network
Workbench
• Social:EgoNet,NodeXL,...
• Relational:Tulip
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Lost in the graph?
Hopefullynotafterthiscourse;)
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Current: Query languages
SELECT ?name ?email
WHERE
{
?person a foaf:Person .
?person foaf:name ?name .
?person foaf:mbox ?email .
}
QuerylanguagesARE:
• Expressive
• Powerful
• Scalable
• Compact
SPARQL
g.V().hasLabel('movie').as('a','b').
where(inE('rated').count().is(gt(10))).
select('a','b').
by('name').
by(inE('rated').values('stars').mean()).
order().
by(select('b'),decr). limit(10
GREMLIN
but
Not userfriendly
Not interactive
MATCH (node1:Label1)-->(node2:Label2)
WHERE node1.propertyA ={value}
RETURN node2.propertyA, node2.propertyB
CYPHER
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Lecture road
CourseInformation
Introductiontographmining
Graphs:modelsandbasicconcepts
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Network or graphs?
§ Network referstorealsystems
• Web,Social,Biological,…
• Terminology:Network,node,link/relationship
§ Graph isanabstractmathematicalmodelofanetwork
• Webgraph,Socialgraph
• Terminology:Graph,vertex/node,edge
BUT
weoftenusebothwithoutdistinction
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Graphs
G=(V,E)
G=(V,E,p)
G=(V,E,l)
0.1
a
0.9
a 0.2b
0.2
c
Verteces Edges
Labeling
Probability
function
𝑙: 𝑉 ∪ 𝐸 → Σ
0.5
a
𝐸 ⊆ 𝑉×𝑉
0.3
b
0.6
c
• UndirectedGraphs
•
Co-authorship,Roads,Biological
• Directedgraphs
0.8
b
•
Follows,…
• Labeled(orcolored)Graphs
•
Knowledgegraphs,…
• Probabilisticgraphs
•
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Causalgraphs
41
Graph databases (set of graphs)
a
a
c
a
b
a
d
c
a
b
a
c
b
G1
a
b
…
b
G2
G3
𝐷 = 𝐺- , 𝐺/ , … , 𝐺1 , 𝐺2 = 𝑉2 , 𝐸2 , 𝑙2 , 𝑙2 : 𝐸2 ∪ 𝑉2 → Σ
Setofsmalllabeledgraphs
Chemicalcompounds,Businessmodels,3Dobjects
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An example?
Givemeanexampleofnetworkyouknow.
Whatarethenodes?
Whataretheedges?
Whatshape?
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Important Terminology
§ Degreeofanode:
• Numberof”neighbors”ofanode
• Indirectedgraphs
⁃ In-degree:numberofinboundlinks
⁃ Out-degree:numberofoutgoinglinks
Degreeofv:3
In-degree:1
Out-degree:2
a
v
a
§ Adjacentnode:
• Anodeuisadjacenttoanodevifthereisanedgebetweenuandv,i.e. 𝑢, 𝑣 ∈ 𝐸
§ Path:
• Sequenceofadjacent,non-repeatingnodesinagraph
• Lengthofapath=numberofedges
§ Diameterofagraph:
• Sizeofthelongestshortestpath
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Graph representation
1
2
3
4
A =
5
6
1=>{2}
2=>{4}
3=>{1,2,4,6}
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
Adjacency
matrix
𝑎27 = 8
1 𝑖, 𝑗 ∈ 𝐸
0𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Adjacencylist
Whataretheadvantages/disadvantagesofoneoranother
representation?
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Static vs Evolving graph
tn
A1
A1
…
A1
A1
A1
t1
Staticgraph
Dynamic,temporal
graph
Adjacency
matrixA
3DMatrix
(tensor)
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Graph Isomorphism
G2
G1
f
Giventwographs,𝐺- : 𝑉- , 𝐸- , 𝑙- , 𝐺/ : 〈𝑉/ , 𝐸/ , 𝑙/ 〉𝐺- isisomorphic
𝐺/ iff existsabijective function𝑓: 𝑉- → 𝑉/ s.t.:
1. Foreach𝑣- ∈ 𝑉- , 𝑙 𝑣- = 𝑙(𝑓 𝑣- )
2. 𝑣- , 𝑢- ∈ 𝐸- iff 𝑓 𝑣- , 𝑓 𝑢- ∈ 𝐸/
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Subgraph Isomorphism
Q
G’
G
Agraph,𝑄: 𝑉M , 𝐸M , 𝑙M issubgraphisomorphictoagraph
𝐺: 〈𝑉, 𝐸, 𝑙〉 ifexistsasubgraph𝐺 N ⊑ 𝐺,isomorphictoQ
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Frequent Subgraph Mining
a
a
c
c
a
b
c
b
Problem
FindallsubgraphsofGthatappearatleast
𝜎 times
Suppose𝜎 = 2,thefrequentsubgraphsare
(onlyedgelabels)
• a,b,c
• a-a,a-c,b-c,c-c
• a-c-a…
Exponentialnumberofpatterns!!!
G
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Questions?
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