BYHani 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 webCoauthorship

Why 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 process

More 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 Coauthorship

Graph

Small 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 vertices

We start randomly adding edges one at a

time

At what time t will the network:have at least one “large” connected component?

have a single connected component?

have “small” diameter?

Formalizing Familiar IdeasExplaining universal behavior through statistical models

our 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 force

crim

e ra

te

number of edges

prob

. NW

con

nect

ed

How 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 out

How 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-hard

Dynamical 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 stuck

We study social network to control its stability and prevent chaos

Social Network Characteristics Densification power Law

Number of edges grows exponentially with number of nods

Shrinking 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 distribution

What 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 tasks1. Link based object classification

Category is classified based on links and attributes (generalize data classification)

2. Object type prediction3. Link type prediction4. Predicting link existence5. Link cardinality estimation

Link mining tasks6. Object reconciliation

• To detect if two objects are the same • E.g. if two desires are the same or two paper

sites are the same

7. Group detection8. Sub 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 node

the third algorithm compute the hub score vector and authority score vector

Prestige 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.Pt

Page Rank AlgorithmFor node prestige dose not depend only on

the prestige of nodes pointing to it but also on a randomly chosen nodes

Random surfing model: At any page, With prob. , randomly jumping to a page With prob. (1 – ), randomly picking a

link to followPage rank = prestige + random walk

Page Rank Algorithm

• Note that the adjacency matrix is normalized

• This is the main algorithm behind google

HITS 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 problem

Massive 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 effect

Application : 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 don’t market to him

Application : Viral Marketing

Viral Marketing can be used in non marketing tasks

E.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 NO

What 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 think

Google use the page rank and HITS do you think that the result are perfect or just popular

Dose that make sense when working with real people in the real world

So for me it is

Big NO

Social 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 ideas

Social 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 researcher”http://www.cs.rpi.edu/~zaki/www-new/pmwiki.php/

Dmcourse/Main

SATNAM ALAG : Collective Intelligence in Action

Wikipedia : small worlds , social networks articles

Kathleen T. Alligood : CHAOS An Introduction to Dynamical Systems

Thank you

Questions ???