Social Network Analysis

Social Network AnalysisBYHani Maher Ahmad What is Social NetworkSocial Network is heterogynous and multirelational data set represented by graphSocial networks need not to be social in contextExamples : Electrical power gridsThe webCoauthorshipWhy do we study Social Network Small world effect & universal behavior 100th Monkey effect & tipping behaviorIt is a complex Dynamical System More information in Data Mining Links information and structure of data are involved in the mining processMore realistic applicationsNew types of patterns (e.g. link prediction)

What do you thinkSmall world ExperimentPeople in city X are asked to direct message to stranger in city YBy forwarding it to friend they think he know the strangerWhat is the number of intermediate peoples links until message is received? Small WorldIt is a graph have high degree of local clustering Six degree of separation

E.g. Science CoauthorshipGraphSmall World

What Do you think100th monkey effect

What do you thinkWhy there are a sudden events in our life?

How dose on product or movie or idea spread at once ?

Why do the most smart students became smart suddenly ?

Why dose we change our mind suddenly?Evolution of a Random NetworkWe have a large number n of verticesWe start randomly adding edges one at a timeAt what time t will the network:have at least one large connected component?have a single connected component?have small diameter?9SHOW EVOLUTION EXAMPLE HERE?Formalizing Familiar IdeasExplaining universal behavior through statistical modelsour models will always generate many networksalmost all of them will share certain properties (universals)Explaining tipping through incremental growthwe gradually add edgesmany properties will emerge very suddenly during this process

size of police forcecrime ratenumber of edgesprob. NW connected10How to study SNRandom graph generation models

E.g. Forest Fire model1. chooses an ambassador node w.2. selects x links incident to w randomly . Let w1;w2; ;wx denote the nodes at the other end of the selected edges.3. Our new node, v, forms out-links to w1;w2; ;wx and then applies step 2 recursivelyto w1;w2;;wx. The process continues until it dies outHow to study SNThe models are realistic and tell how the reality will be It is seen that rich become richer But it is blind and cant tell how things happen exactly

Very hard to predict exactly since most of the problems are NP-hardDynamical SystemIt is a state and a rule changing that state E.g. pupation number is a state and logistic growth is a rule

Dynamical Systems Dynamical Systems has important property of attractors (points of stability )

Dynamical SystemsBut some times a chaotic behavior or divergence occur like when traffic network become stuckWe study social network to control its stability and prevent chaos

Social Network Characteristics Densification power Law Number of edges grows exponentially with number of nodsShrinking diameterThe effective diameter of network shrink with network growth Heavy-tailed out degree and in degree The number of out and in degree follow the heavy tail distributionWhat do you thinkWhat are things can be mined from social network?What is the difference and similarity of data and network mining ?Dose the graph need to be labeled or not ?Dose the graph need to be directed or not ?Can we mine the graph for all and exact patterns?Link Mining tasksLink based object classificationCategory is classified based on links and attributes (generalize data classification)Object type predictionLink type predictionPredicting link existenceLink cardinality estimation

Link mining tasksObject reconciliationTo detect if two objects are the same E.g. if two desires are the same or two paper sites are the sameGroup detectionSub graph detection

What is the difference between 7 and 8 ?Are you looking for herWho is the most perfect woman ?

In other word how can we find the most valuable object in the network and how can we find the rank of an object ?

How can we find her prestige .Representing Network in suitable way for computationWe can represent the graph with matrices Adjacency matrix the rows and columns represent nodes with entries equal 1 if there is an edge and 0 else Incidence matrix the rows and columns represent nodes and edges with entries equal 1 if the edge is incident to node and 0 else

Adjacency matrix of a network

Three algorithms Prestige algorithmPage rankHITS authority and hubs

Note :the first two compute the prestige vectored of the network representing the prestige of each nodethe third algorithm compute the hub score vector and authority score vectorPrestige algorithmThe prestige of a node depend on the prestige of nodes pointing to it.That is for node i : P[i] = AT[i].P sum of nodes pointing to it * there prestigeFor all nodes P = AT.PStarting from all prestige in the beginning = 1Apply the multiplication until converge i.e. Pt+1 = AT.PtPage Rank AlgorithmFor node prestige dose not depend only on the prestige of nodes pointing to it but also on a randomly chosen nodesRandom surfing model: At any page, With prob. , randomly jumping to a pageWith prob. (1 ), randomly picking a link to followPage rank = prestige + random walkPage Rank Algorithm

Note that the adjacency matrix is normalizedThis is the main algorithm behind googleHITS AlgorithmThis algorithm give two ranks to the node .As authority if it has been pointed to by many good hubs and hub if it point to many good authorities.

HITS

Application : Viral Marketing The marketing has many models Direct marketing : based on customer attributes classification problemMassive marketing : based on the population segment the person belong to clustering problem have advantage that it capture indirect costumers Viral marketing : massive marketing + optimize word of mouth effectApplication : Viral Marketing E.g. a person how buy a car motivate his friends to buy a car

Aim is to find Network value of person

If the person is a good hub it is potential customer that can maximize the network profit so spend more money in marketing product to him

If the person have negative effect dont market to him Application : Viral Marketing Viral Marketing can be used in non marketing tasksE.g.Fighting teenage smoking Stopping virus spreadSpread an ideamarketing for a Political men e.g. election So What do you thinkShe has the best authority score all hubs are pointing to her.Is it a good idea to marry her ??Yes or NOWhat do you thinkShe can have best authority because of Rich become richer Some tipping phenomena She is modda She have more hubsBecause of butterfly effect and divergenceShe can appear due to marketing effort

She also can be good authority So What do you thinkGoogle use the page rank and HITS do you think that the result are perfect or just popularDose that make sense when working with real people in the real world

So for me it is Big NOSocial Networks out of controlIf the social network is not controlled Rich will become richer and all the capital will accumulate with him

Most people like the wrong things due to joy of adrenaline and self prodding

Many stuck in the relation ships will occur as bas ideas , drugs , bad practices spreading

Many silly persons will appear as authority due to there strange or bad ideasSocial Networks out of controlThe number of links will become Extremely large making life harder and noisy and much loose in time

The diameter will shrink making the spy and crimes easy

Some tipping events will destroy the society

More effort will be on marketing instead of industry

The civilization will stop and we only will focus on communication

Social Networks out of controlHidden persons can control the network and affection others by making adjusting links and spreading ideas program the SN to there benefits

It is not proved but I guess a sudden death of the network will occur . we are running into Chaos What is the solution ??

References The text bookThe another slidesDr Mohammed Zaki lectures one of the leading data mining researcherhttp://www.cs.rpi.edu/~zaki/www-new/pmwiki.php/Dmcourse/MainSATNAM ALAG : Collective Intelligence in ActionWikipedia : small worlds , social networks articlesKathleen T. Alligood : CHAOS An Introduction to Dynamical Systems

Thank youQuestions ???