large graph mining – patterns, tools and cascade analysis by christos faloutsos

Mining large graphs

Large Graph Mining - Patterns, Explanations and Cascade AnalysisChristos FaloutsosCMU

CMU SCS

Faloutsos1

Thank you!

Wei FANAlbert BIFETQiang YANGPhilip YU

KDD'13 BIGMINE(c) 2013, C. Faloutsos2

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(c) 2013, C. Faloutsos3RoadmapIntroduction MotivationWhy study (big) graphs?Part#1: Patterns in graphsPart#2: Cascade analysisConclusions[Extra: ebay fraud; tensors; spikes]

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(c) 2013, C. Faloutsos4Graphs - why should we care?

Internet Map [lumeta.com]Food Web [Martinez 91]>$10B revenue>0.5B usersKDD'13 BIGMINE

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(c) 2013, C. Faloutsos5Graphs - why should we care?web-log (blog) news propagationcomputer network security: email/IP traffic and anomaly detectionRecommendation systems....

Many-to-many db relationship -> graphKDD'13 BIGMINE

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(c) 2013, C. Faloutsos6RoadmapIntroduction MotivationPart#1: Patterns in graphsStatic graphsTime-evolving graphsWhy so many power-laws?Part#2: Cascade analysisConclusions

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KDD'13 BIGMINE(c) 2013, C. Faloutsos7Part 1:Patterns & Laws

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(c) 2013, C. Faloutsos8Laws and patternsQ1: Are real graphs random?KDD'13 BIGMINE

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(c) 2013, C. Faloutsos9Laws and patternsQ1: Are real graphs random?A1: NO!!Diameterin- and out- degree distributionsother (surprising) patternsQ2: why no good cuts?A2:

So, lets look at the dataKDD'13 BIGMINE

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(c) 2013, C. Faloutsos10Solution# S.1Power law in the degree distribution [SIGCOMM99]

log(rank)log(degree)internet domains

att.com

ibm.com

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(c) 2013, C. Faloutsos11Solution# S.1Power law in the degree distribution [SIGCOMM99]

log(rank)log(degree)

-0.82internet domains

att.com

ibm.com

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(c) 2013, C. Faloutsos12Solution# S.1Q: So what?



att.com

ibm.com

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(c) 2013, C. Faloutsos13Solution# S.1Q: So what?A1: # of two-step-away pairs:



att.com

ibm.com

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= friends of friends (F.O.F.)

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(c) 2013, C. Faloutsos14Solution# S.1Q: So what?A1: # of two-step-away pairs: O(d_max ^2) ~ 10M^2



att.com

ibm.com

KDD'13 BIGMINE~0.8PB ->a data center(!)

DCO @ CMUGaussian trap= friends of friends (F.O.F.)

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(c) 2013, C. Faloutsos15Solution# S.1Q: So what?A1: # of two-step-away pairs: O(d_max ^2) ~ 10M^2



att.com

ibm.com

KDD'13 BIGMINE~0.8PB ->a data center(!)

Such patterns ->New algorithmsGaussian trap

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(c) 2013, C. Faloutsos16Solution# S.2: Eigen Exponent EA2: power law in the eigenvalues of the adjacency matrixE = -0.48Exponent = slopeEigenvalueRank of decreasing eigenvalueMay 2001

KDD'13 BIGMINEA x = l x

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(c) 2013, C. Faloutsos17RoadmapIntroduction MotivationProblem#1: Patterns in graphsStatic graphs degree, diameter, eigen, TrianglesTime evolving graphsProblem#2: Tools

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(c) 2013, C. Faloutsos18Solution# S.3: Triangle LawsReal social networks have a lot of triangles

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(c) 2013, C. Faloutsos19Solution# S.3: Triangle LawsReal social networks have a lot of trianglesFriends of friends are friends Any patterns?2x the friends, 2x the triangles ?

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(c) 2013, C. Faloutsos20Triangle Law: #S.3 [Tsourakakis ICDM 2008]SNReutersEpinionsX-axis: degreeY-axis: mean # trianglesn friends -> ~n1.6 triangles

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(c) 2013, C. Faloutsos21Triangle Law: Computations [Tsourakakis ICDM 2008]

But: triangles are expensive to compute(3-way join; several approx. algos) O(dmax2)Q: Can we do that quickly?A:detailsKDD'13 BIGMINE

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(c) 2013, C. Faloutsos22Triangle Law: Computations [Tsourakakis ICDM 2008]

But: triangles are expensive to compute(3-way join; several approx. algos) O(dmax2)Q: Can we do that quickly?A: Yes!#triangles = 1/6 Sum ( li3 ) (and, because of skewness (S2) , we only need the top few eigenvalues! - O(E)

detailsKDD'13 BIGMINE

A x = l x

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Triangle counting for large graphs?

Anomalous nodes in Twitter(~ 3 billion edges)[U Kang, Brendan Meeder, +, PAKDD11]23

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???

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(c) 2013, C. Faloutsos27RoadmapIntroduction MotivationPart#1: Patterns in graphsStatic graphsPower law degrees; eigenvalues; trianglesAnti-pattern: NO good cuts!Time-evolving graphs.Conclusions

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KDD'13 BIGMINE(c) 2013, C. Faloutsos28Background: Graph cut problemGiven a graph, and kBreak it into k (disjoint) communities

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Graph cut problemGiven a graph, and kBreak it into k (disjoint) communities(assume: block diagonal = cavemen graph)

k = 2

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Many algos for graph partitioningMETIS [Karypis, Kumar +]2nd eigenvector of LaplacianModularity-based [Girwan+Newman]Max flow [Flake+]KDD'13 BIGMINE(c) 2013, C. Faloutsos30

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KDD'13 BIGMINE(c) 2013, C. Faloutsos31Strange behavior of min cutsSubtle details: nextPreliminaries: min-cut plots of usual graphsNetMine: New Mining Tools for Large Graphs, by D. Chakrabarti, Y. Zhan, D. Blandford, C. Faloutsos and G. Blelloch, in the SDM 2004 Workshop on Link Analysis, Counter-terrorism and PrivacyStatistical Properties of Community Structure in Large Social and Information Networks, J. Leskovec, K. Lang, A. Dasgupta, M. Mahoney. WWW 2008.

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KDD'13 BIGMINE(c) 2013, C. Faloutsos32Min-cut plotDo min-cuts recursively.

log (# edges)log (mincut-size / #edges)

N nodesMincut size = sqrt(N)

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N nodes

New min-cut

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N nodes

New min-cut

Slope = -0.5

Bettercut

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KDD'13 BIGMINE(c) 2013, C. Faloutsos35Min-cut plot


Slope = -1/dFor a d-dimensional grid, the slope is -1/d


For a random graph(and clique), the slope is 0

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KDD'13 BIGMINE(c) 2013, C. Faloutsos36ExperimentsDatasets:Google Web Graph: 916,428 nodes and 5,105,039 edgesLucent Router Graph: Undirected graph of network routers from www.isi.edu/scan/mercator/maps.html; 112,969 nodes and 181,639 edgesUser Website Clickstream Graph: 222,704 nodes and 952,580 edgesNetMine: New Mining Tools for Large Graphs, by D. Chakrabarti, Y. Zhan, D. Blandford, C. Faloutsos and G. Blelloch, in the SDM 2004 Workshop on Link Analysis, Counter-terrorism and Privacy

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KDD'13 BIGMINE(c) 2013, C. Faloutsos37Min-cut plotWhat does it look like for a real-world graph?


?

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KDD'13 BIGMINE(c) 2013, C. Faloutsos38ExperimentsUsed the METIS algorithm [Karypis, Kumar, 1995]

log (# edges)log (mincut-size / #edges) Google Web graph Values along the y-axis are averaged lip for large # edges Slope of -0.4, corresponds to a 2.5-dimensional grid!

Slope~ -0.4


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KDD'13 BIGMINE(c) 2013, C. Faloutsos39ExperimentsUsed the METIS algorithm [Karypis, Kumar, 1995]

log (# edges)log (mincut-size / #edges) Google Web graph Values along the y-axis are averaged lip for large # edges Slope of -0.4, corresponds to a 2.5-dimensional grid!

Slope~ -0.4


Bettercut

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KDD'13 BIGMINE(c) 2013, C. Faloutsos40ExperimentsSame results for other graphs too

log (# edges)log (# edges)log (mincut-size / #edges)log (mincut-size / #edges)Lucent Router graphClickstream graph

Slope~ -0.57

Slope~ -0.45

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Why no good cuts?Answer: self-similarity (few foils later)KDD'13 BIGMINE(c) 2013, C. Faloutsos41

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(c) 2013, C. Faloutsos42RoadmapIntroduction MotivationPart#1: Patterns in graphsStatic graphsTime-evolving graphsWhy so many power-laws?Part#2: Cascade analysisConclusions

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(c) 2013, C. Faloutsos43Problem: Time evolutionwith Jure Leskovec (CMU -> Stanford)

and Jon Kleinberg (Cornell sabb. @ CMU)

KDD'13 BIGMINEJure Leskovec, Jon Kleinberg and Christos Faloutsos: Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations, KDD 2005

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(c) 2013, C. Faloutsos44T.1 Evolution of the DiameterPrior work on Power Law graphs hints at slowly growing diameter:[diameter ~ O( N1/3)]diameter ~ O(log N)diameter ~ O(log log N)What is happening in real data?KDD'13 BIGMINE

diameter

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Faloutsos44Diameter first, DPL secondCheck diameter formulasAs the network grows the distances between nodes slowly grow

(c) 2013, C. Faloutsos45T.1 Evolution of the DiameterPrior work on Power Law graphs hints at slowly growing diameter:[diameter ~ O( N1/3)]diameter ~ O(log N)diameter ~ O(log log N)What is happening in real data?Diameter shrinks over time

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T.1 Diameter PatentsPatent citation network25 years of [email protected] M nodes16.5 M edges

time [years]diameterKDD'13 BIGMINE

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(c) 2013, C. Faloutsos47T.2 Temporal Evolution of the GraphsN(t) nodes at time tE(t) edges at time tSuppose thatN(t+1) = 2 * N(t)Q: what is your guess for E(t+1) =? 2 * E(t)KDD'13 BIGMINESay, k friends on average

k

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(c) 2013, C. Faloutsos48T.2 Temporal Evolution of the GraphsN(t) nodes at time tE(t) edges at time tSuppose thatN(t+1) = 2 * N(t)Q: what is your guess for E(t+1) =? 2 * E(t)A: over-doubled! ~ 3xBut obeying the ``Densification Power Law

KDD'13 BIGMINESay, k friends on average

Gaussian trap

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(c) 2013, C. Faloutsos49T.2 Temporal Evolution of the GraphsN(t) nodes at time tE(t) edges at time tSuppose thatN(t+1) = 2 * N(t)Q: what is your guess for E(t+1) =? 2 * E(t)A: over-doubled! ~ 3xBut obeying the ``Densification Power Law

KDD'13 BIGMINESay, k friends on average

Gaussian trap

logloglinlin

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(c) 2013, C. Faloutsos50T.2 Densification Patent CitationsCitations among patents [email protected] M nodes16.5 M edgesEach year is a datapoint

N(t)E(t)

1.66KDD'13 BIGMINE

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MORE Graph PatternsKDD'13 BIGMINE(c) 2013, C. Faloutsos51

RTG: A Recursive Realistic Graph Generator using Random Typing Leman Akoglu and Christos Faloutsos. PKDD09.

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RTG: A Recursive Realistic Graph Generator using Random Typing Leman Akoglu and Christos Faloutsos. PKDD09.

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Mary McGlohon, Leman Akoglu, Christos Faloutsos. Statistical Properties of Social Networks. in "Social Network Data Analytics (Ed.: Charu Aggarwal)

Deepayan Chakrabarti and Christos Faloutsos, Graph Mining: Laws, Tools, and Case Studies Oct. 2012, Morgan Claypool.

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(c) 2013, C. Faloutsos54RoadmapIntroduction MotivationPart#1: Patterns in graphsWhy so many power-laws?Why no good cuts?Part#2: Cascade analysisConclusions

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2 Questions, one answerQ1: why so many power lawsQ2: why no good cuts?KDD'13 BIGMINE(c) 2013, C. Faloutsos55

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2 Questions, one answerQ1: why so many power lawsQ2: why no good cuts?A: Self-similarity = fractals = RMAT ~ Kronecker graphs

KDD'13 BIGMINE(c) 2013, C. Faloutsos56possible

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20 intro to fractalsRemove the middle triangle; repeat-> Sierpinski triangle(Bonus question - dimensionality?>1 (inf. perimeter (4/3) ) no char. scale-> power laws, eg:2x the radius, 3x the #neighbors nn(r) nn(r) = C r log3/log2

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20 intro to fractals

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59Self-similarity -> no char. scale-> power laws, eg:2x the radius, 3x the #neighbors nn(r) nn(r) = C r log3/log2

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KDD'13 BIGMINE(c) 2013, C. Faloutsos60Self-similarity -> no char. scale-> power laws, eg:2x the radius, 3x the #neighbors nn = C r log3/log2

N(t)E(t)

1.66Reminder:Densification P.L.(2x nodes, ~3x edges)

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2x the radius,4x neighborsnn = C r log4/log2 = C r 2

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2x the radius,4x neighborsnn = C r log4/log2 = C r 2 Fractal dim.

=1.58

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2x the radius,4x neighborsnn = C r log4/log2 = C r 2

Fractal dim.

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How does self-similarity help in graphs?A: RMAT/Kronecker generatorsWith self-similarity, we get all power-laws, automatically,And small/shrinking diameterAnd `no good cuts

KDD'13 BIGMINE(c) 2013, C. Faloutsos64R-MAT: A Recursive Model for Graph Mining, by D. Chakrabarti, Y. Zhan and C. Faloutsos, SDM 2004, Orlando, Florida, USARealistic, Mathematically Tractable Graph Generation and Evolution, Using Kronecker Multiplication,by J. Leskovec, D. Chakrabarti, J. Kleinberg, and C. Faloutsos, in PKDD 2005, Porto, Portugal

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KDD'13 BIGMINE(c) 2013, C. Faloutsos65Graph gen.: Problem dfnGiven a growing graph with count of nodes N1, N2, Generate a realistic sequence of graphs that will obey all the patterns Static PatternsS1 Power Law Degree DistributionS2 Power Law eigenvalue and eigenvector distribution Small DiameterDynamic PatternsT2 Growth Power Law (2x nodes; 3x edges)T1 Shrinking/Stabilizing Diameters

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Adjacency matrixKronecker Graphs

Intermediate stage

Adjacency matrix

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Intermediate stage

Adjacency matrix

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Intermediate stageAdjacency matrix

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KDD'13 BIGMINE(c) 2013, C. Faloutsos69Kronecker GraphsContinuing multiplying with G1 we obtain G4 and so on

G4 adjacency matrix

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G4 adjacency matrix

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G4 adjacency matrix

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G4 adjacency matrix

Holes within holes;Communities within communities

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KDD'13 BIGMINE(c) 2013, C. Faloutsos73Properties:We can PROVE thatDegree distribution is multinomial ~ power lawDiameter: constantEigenvalue distribution: multinomialFirst eigenvector: multinomialnewSelf-similarity -> power laws

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KDD'13 BIGMINE(c) 2013, C. Faloutsos74Problem DefinitionGiven a growing graph with nodes N1, N2, Generate a realistic sequence of graphs that will obey all the patterns Static PatternsPower Law Degree DistributionPower Law eigenvalue and eigenvector distributionSmall DiameterDynamic PatternsGrowth Power LawShrinking/Stabilizing DiametersFirst generator for which we can prove all these properties

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Impact: Graph500Based on RMAT (= 2x2 Kronecker)Standard for graph benchmarkshttp://www.graph500.org/Competitions 2x year, with all major entities: LLNL, Argonne, ITC-U. Tokyo, Riken, ORNL, Sandia, PSC, KDD'13 BIGMINE(c) 2013, C. Faloutsos75R-MAT: A Recursive Model for Graph Mining, by D. Chakrabarti, Y. Zhan and C. Faloutsos, SDM 2004, Orlando, Florida, USATo iterate is human, to recurse is devine

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(c) 2013, C. Faloutsos76RoadmapIntroduction MotivationPart#1: Patterns in graphsQ1: Why so many power-laws?Q2: Why no good cuts?Part#2: Cascade analysisConclusions

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A: real graphs -> self similar -> power laws

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Q2: Why no good cuts?A: self-similarityCommunities within communities within communities KDD'13 BIGMINE(c) 2013, C. Faloutsos77

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KDD'13 BIGMINE(c) 2013, C. Faloutsos78Kronecker Product a GraphContinuing multiplying with G1 we obtain G4 and so on

G4 adjacency matrix

REMINDER

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G4 adjacency matrix

REMINDERCommunities within communities within communities

Linux usersMac userswin users

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G4 adjacency matrix


How many Communities?3?9?27?

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KDD'13 BIGMINE(c) 2013, C. Faloutsos81Kronecker Product a GraphContinuing multiplying with G1 we obtain G4 and so on G4 adjacency matrix


How many Communities?3?9?27?A: one butnot a typical, block-likecommunity

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Communities?(Gaussian)Clusters?Piece-wise flat parts?

age# songs

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Wrong questions to ask!age# songs

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Summary of Part#1*many* patterns in real graphsSmall & shrinking diametersPower-laws everywhereGaussian trapno good cutsSelf-similarity (RMAT/Kronecker): good model


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KDD'13 BIGMINE(c) 2013, C. Faloutsos85Part 2:Cascades & Immunization

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Why do we care?Information DiffusionViral MarketingEpidemiology and Public HealthCyber SecurityHuman mobility Games and Virtual Worlds Ecology........

(c) 2013, C. Faloutsos86

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(c) 2013, C. Faloutsos87RoadmapIntroduction MotivationPart#1: Patterns in graphsPart#2: Cascade analysis(Fractional) ImmunizationEpidemic thresholdsConclusions

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Fractional Immunization of NetworksB. Aditya Prakash, Lada Adamic, Theodore Iwashyna (M.D.), Hanghang Tong, Christos Faloutsos

SDM 2013, Austin, TX

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Whom to immunize?Dynamical Processes over networks

Each circle is a hospital ~3,000 hospitals More than 30,000 patients transferred [US-MEDICARE NETWORK 2005]Problem: Given k units of disinfectant, whom to immunize?(c) 2013, C. Faloutsos89KDD'13 BIGMINE

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Whom to immunize?

CURRENT PRACTICEOUR METHOD[US-MEDICARE NETWORK 2005]

~6x fewer!(c) 2013, C. Faloutsos90KDD'13 BIGMINEHospital-acquired inf. : 99K+ lives, $5B+ per year

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Fractional Asymmetric Immunization

HospitalAnother Hospital

Drug-resistant Bacteria (like XDR-TB) (c) 2013, C. Faloutsos91KDD'13 BIGMINE

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Problem: Given k units of disinfectant, distribute them to maximize hospitals saved


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Problem: Given k units of disinfectant, distribute them to maximize hospitals saved @ 365 days


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Straightforward solution:Simulation:Distribute resourcesinfect a few nodesSimulate evolution of spreading (10x, take avg)Tweak, and repeat step 1KDD'13 BIGMINE(c) 2013, C. Faloutsos96

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Running TimeSimulationsSMART-ALLOC> 1 weekWall-Clock Time

14 secs> 30,000x speed-up!better(c) 2013, C. Faloutsos100KDD'13 BIGMINE

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Experiments

K = 120better(c) 2013, C. Faloutsos101KDD'13 BIGMINE# epochs# infecteduniformSMART-ALLOC

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What is the silver bullet?A: Try to decrease connectivity of graph

Q: how to measure connectivity?Avg degree? Max degree?Std degree / avg degree ?Diameter?Modularity?Conductance (~min cut size)?Some combination of above?KDD'13 BIGMINE(c) 2013, C. Faloutsos102

14 secs> 30,000x speed-up!

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What is the silver bullet?A: Try to decrease connectivity of graph

Q: how to measure connectivity?A: first eigenvalue of adjacency matrix

Q1: why??(Q2: dfn & intuition of eigenvalue ? )KDD'13 BIGMINE(c) 2013, C. Faloutsos103Avg degreeMax degreeDiameterModularityConductance

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Why eigenvalue?A1: G2 theorem and eigen-drop:

For (almost) any type of virusFor any network-> no epidemic, if small-enough first eigenvalue (1 ) of adjacency matrix

Heuristic: for immunization, try to min 1The smaller 1, the closer to extinction.KDD'13 BIGMINE(c) 2013, C. Faloutsos104Threshold Conditions for Arbitrary Cascade Models on Arbitrary Networks, B. Aditya Prakash, Deepayan Chakrabarti, Michalis Faloutsos, Nicholas Valler, Christos Faloutsos, ICDM 2011, Vancouver, Canada

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Why eigenvalue?A1: G2 theorem and eigen-drop:

For (almost) any type of virusFor any network-> no epidemic, if small-enough first eigenvalue (1 ) of adjacency matrix

Heuristic: for immunization, try to min 1The smaller 1, the closer to extinction.KDD'13 BIGMINE(c) 2013, C. Faloutsos105

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Threshold Conditions for Arbitrary Cascade Models on Arbitrary Networks B. Aditya Prakash, Deepayan Chakrabarti, Michalis Faloutsos, Nicholas Valler, Christos FaloutsosIEEE ICDM 2011, Vancouver

extended version, in arxivhttp://arxiv.org/abs/1004.0060

G2 theorem~10 pages proof

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Our thresholds for some modelss = effective strengths < 1 : below threshold

(c) 2013, C. Faloutsos107KDD'13 BIGMINEModelsEffective Strength (s)Threshold (tipping point)SIS, SIR, SIRS, SEIRs = .

s = 1 SIV, SEIVs = . (H.I.V.)s = .

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Our thresholds for some modelss = effective strengths < 1 : below threshold

(c) 2013, C. Faloutsos108KDD'13 BIGMINEModelsEffective Strength (s)Threshold (tipping point)SIS, SIR, SIRS, SEIRs = .

s = 1 SIV, SEIVs = . (H.I.V.)s = .

No immunityTemp.immunityw/ incubation

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(c) 2013, C. Faloutsos109RoadmapIntroduction MotivationPart#1: Patterns in graphsPart#2: Cascade analysis(Fractional) Immunizationintuition behind 1Conclusions

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Intuition for Official definitions:Let A be the adjacency matrix. Then is the root with the largest magnitude of the characteristic polynomial of A [det(A xI)].Also: A x = l x

Neither gives much intuition!

Un-official Intuition For homogeneous graphs, == degree

~ avg degreedone right, for skewed degree distributions(c) 2013, C. Faloutsos110KDD'13 BIGMINE

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Largest Eigenvalue ()

2 = N = N-1

N = 1000 nodes 2= 31.67= 999better connectivity higher (c) 2013, C. Faloutsos111KDD'13 BIGMINE

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Largest Eigenvalue ()

2 = N = N-1

N = 1000 nodes 2= 31.67= 999better connectivity higher (c) 2013, C. Faloutsos112KDD'13 BIGMINE

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Examples: Simulations SIR (mumps)

Fraction of InfectionsFootprintEffective StrengthTime ticks(c) 2013, C. Faloutsos113KDD'13 BIGMINE

(a) Infection profile (b) Take-off plotPORTLAND graph: synthetic population, 31 million links, 6 million nodes

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Examples: Simulations SIRS (pertusis)

Fraction of InfectionsFootprintEffective StrengthTime ticks(c) 2013, C. Faloutsos114KDD'13 BIGMINE

(a) Infection profile (b) Take-off plotPORTLAND graph: synthetic population, 31 million links, 6 million nodes

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Immunization - conclusionIn (almost any) immunization setting,Allocate resources, such that toMinimize 1(regardless of virus specifics)

Conversely, in a market penetration settingAllocate resources toMaximize 1KDD'13 BIGMINE(c) 2013, C. Faloutsos115

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(c) 2013, C. Faloutsos116RoadmapIntroduction MotivationPart#1: Patterns in graphsPart#2: Cascade analysis(Fractional) ImmunizationEpidemic thresholdsWhat next?Acks & Conclusions[Tools: ebay fraud; tensors; spikes]

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Challenge #1: Connectome brain wiringKDD'13 BIGMINE(c) 2013, C. Faloutsos117Which neurons get activated by beeHow wiring evolvesModeling epilepsy

N. SidiropoulosGeorge KarypisV. PapalexakisTom Mitchell

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Challenge#2: Time evolving networks / tensorsPeriodicities? Burstiness?What is typical behavior of a node, over timeHeterogeneous graphs (= nodes w/ attributes)KDD'13 BIGMINE(c) 2013, C. Faloutsos118

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(c) 2013, C. Faloutsos119RoadmapIntroduction MotivationPart#1: Patterns in graphsPart#2: Cascade analysis(Fractional) ImmunizationEpidemic thresholdsAcks & Conclusions[Tools: ebay fraud; tensors; spikes]

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Off line

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(c) 2013, C. Faloutsos120ThanksKDD'13 BIGMINEThanks to: NSF IIS-0705359, IIS-0534205, CTA-INARC; Yahoo (M45), LLNL, IBM, SPRINT, Google, INTEL, HP, iLab

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Faloutsos et al8/10/13120

(c) 2013, C. Faloutsos121ThanksKDD'13 BIGMINEThanks to: NSF IIS-0705359, IIS-0534205, CTA-INARC; Yahoo (M45), LLNL, IBM, SPRINT, Google, INTEL, HP, iLabDisclaimer: All opinions are mine; not necessarily reflecting the opinions of the funding agencies

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(c) 2013, C. Faloutsos122Project info: PEGASUS

KDD'13 BIGMINEwww.cs.cmu.edu/~pegasusResults on large graphs: with Pegasus + hadoop + M45Apache licenseCode, papers, manual, videoProf. U Kang

Prof. Polo Chau

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(c) 2013, C. Faloutsos123Cast

Akoglu, LemanChau, PoloKang, UMcGlohon, Mary

Tong, Hanghang

Prakash,AdityaKDD'13 BIGMINE

Koutra,Danai

Beutel,AlexPapalexakis,Vagelis

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(c) 2013, C. Faloutsos124CONCLUSION#1 Big dataLarge datasets reveal patterns/outliers that are invisible otherwiseKDD'13 BIGMINE

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(c) 2013, C. Faloutsos125CONCLUSION#2 self-similaritypowerful tool / viewpointPower laws; shrinking diametersGaussian trap (eg., F.O.F.)no good cutsRMAT graph500 generatorKDD'13 BIGMINE

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(c) 2013, C. Faloutsos126CONCLUSION#3 eigen-dropCascades & immunization: G2 theorem & eigenvalueKDD'13 BIGMINE

CURRENT PRACTICEOUR METHOD[US-MEDICARE NETWORK 2005]

~6x fewer!

14 secs> 30,000x speed-up!

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(c) 2013, C. Faloutsos127ReferencesD. Chakrabarti, C. Faloutsos: Graph Mining Laws, Tools and Case Studies, Morgan Claypool 2012http://www.morganclaypool.com/doi/abs/10.2200/S00449ED1V01Y201209DMK006

KDD'13 BIGMINE

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TAKE HOME MESSAGE:Cross-disciplinarityKDD'13 BIGMINE(c) 2013, C. Faloutsos128

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TAKE HOME MESSAGE:Cross-disciplinarityKDD'13 BIGMINE(c) 2013, C. Faloutsos129

QUESTIONS?

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0.005

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0.025

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0.035

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large graph mining – patterns, tools and cascade analysis by christos faloutsos

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