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Graph Mining and Social Network

AnalysisData Mining and Text Mining (UIC 583 @ Politecnico di Milano)

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Daniele Loiacono

q Jiawei Han and Micheline Kamber, "DataMining: Concepts and Techniques", TheMorgan Kaufmann Series in DataManagement Systems (Second Edition)

" Chapter 9

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Graph Mining

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q Graphs are becoming increasingly important to model manyphenomena in a large class of domains (e.g., bioinformatics,computer vision, social analysis)

q To deal with these needs, many data mining approacheshave been extended also to graphs and trees

q Major approaches" Mining frequent subgraphs" Indexing" Similarity search" Classification" Clustering

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q Given a labeled graph data setD = {G1,G2,,Gn}

q We define as theq A subgraph in D is a subgraph with a support

greater than

q How to find frequent subgraph?" Apriori-based approach" Pattern-growth approach

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Daniele Loiacono

q Apply a level-wise iterative algorithm1. Choose two subgraphs in S two similar subgraphs in a subgraph3. If the new subgraph is add to S4. Restart from 2. until all similar subgraphs have been

considered. Otherwise restart from 1. and move to k+1.

q What is subgraph size?" Number of vertex" Number of edges" Number of edge-disjoint paths

q Two subgraphs of size-k are similar if they have the samesize-(k-1) subgraph

q AprioriGraph has a big computational cost (due to themerging step)

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q Closed subgraphs" G is iff there is no proper supergraph G with thesame support of G" Reduce the growth of subgraphs discovered" Is a more compact representation of knowledge

q Unlabeled (or partially labeled) graphs" Introduce a special label " can match any label or only itself

q Constrained subgraphs" Containment constraint (edges, vertex, subgraphs)" Geometric constraint" Value constraint

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q Indexing is basilar for effective search and query processingq How to index graphs?q approach takes the as indexing unit

" All the path up to maxLlength are indexed" Does not scale very well

q approach takes and as indexing unit" A subgraph is frequent if it has a support greater than a

threshold

" A subgraph is discriminative if its support cannot be wellapproximated by the intersection of the graph sets thatcontain one of its subgraphs

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q Mining of frequent subgraphs can be effectively used forclassification and clustering purposes

q Classification" and subgraphs are used as toperform the classification task" A subgraph is discriminative if it is frequent only in one class ofgraphs and infrequent in the others

" The threshold on frequency and discriminativeness should betuned to obtain the desired classification results

q Clustering" The mined frequent subgraphs are used to define between graphs

" Two graphs that should beconsidered and grouped in the same cluster

" The threshold on frequency can be tuned to find the desirednumber of clusters

q As the mining step affects heavily the final outcome, this is anintertwined process rather tan a two-steps process

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Social Network Analysis

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q Are social networks random graphs?q

NO!

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Daniele Loiacono

Peter

Jane

SarahRalph

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q Definitions" Nodes is the number of incident edges" Network is the max distance within 90% of

the network

q Properties"

""

n: number of nodes

e: number of eges1

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q Several tasks can be identified in the analysis ofsocial networks

q Link based object classification" Classification of objects on the basis of its attributes, its

links and attributes of objects linked to it

" E.g., predict topic of a paper on the basis of Keywords occurrence

q Link type prediction" Prediction of link type on the basis of objects attributes" E.g., predict if a link between two Web pages is an

advertising link or not

q Predicting link existence" Predict the presence of a link between two objects

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q Link cardinality estimation" Prediction of the number of links to an object" Prediction of the number of objects reachable from a

specific object

q Object reconciliation" Discover if two objects are the same on the basis of their

attributes and links" E.g., predict if two websites are mirrors of each otherq Group detection

" Clustering of objects on the basis both of their attributesand their links

q Subgraph detection" Discover characteristic subgraphs within network

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q Feature construction"Not only the objects attributes need to be considered butalso attributes of" and techniques must beapplied to reduce the size of search space

q Collective classification and consolidation" Unlabeled data cannot be classified independently" New objects can be and need to be consideredto consolidate the current model

q Link prediction" The prior probability of link between two objects may bevery low

q Community mining from multirelational networks" Many approaches assume an

while social networks usually representand

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q Link Predictionq Viral Marketing

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q What edges will be added to the network?q

Given a snapshot of a network at time t, aimsto predict the edges that will be added before a given futuretime t

q Link prediction is generally solved assigning to each pair ofnodes a weight

q The higher the scorethe more likely that link will be added inthe near future

q The score(X,Y)can be computed in several way" : the shortest he path between X and Y thehighest is their score" : the greater the number of neighborsX and Y have in common, the highest is their score

" : weighted sum of paths thatconnects X and Y (shorter paths have usually largerweights)

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q Several marketing approaches" Mass marketing is targeted on specific segment ofcustomers" Direct marketing is target on specific customers solely on

the basis of their characteristics

" tries to exploit the tomaximize the output of marketing actions

q Each customer has a specific based on" The number of connections" Its role in the network (e.g., opinion leader, listener)" Role of its connections

q Viral marketing aims to exploit the network value ofcustomers to predict their influence and to maximize theoutcome of marketing actions

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q 500 randomly chosen customers are given a product (from 5000).

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q The 500 most connected consumers are given a product.