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April 19, 2023 Data Mining: Concepts and Techniques 1
Data Mining: Concepts and Techniques
— Chapter 6 —Network Mining (Social Networks)
Jianlin Cheng
Department of Computer Science
University of Missouri, Columbia
©2006 Jiawei Han and Micheline Kamber. All rights reserved.
Acknowledgements: Based on the slides by Sangkyum Kim and Chen Chen
April 19, 2023 Data Mining: Concepts and Techniques 2
Network Mining
Social Network Introduction
Statistics and Probability Theory
Models of Social Network Generation
Networks in Biological System
Mining on Social Network
Summary
April 19, 2023 Data Mining: Concepts and Techniques 3
Society
Nodes: individuals
Links: social relationship (family/work/friendship/etc.)
S. Milgram (1967)
Social networks: Many individuals with diverse social interactions between them.
John Guare
Six Degrees of Separation
April 19, 2023 Data Mining: Concepts and Techniques 4
Communication networks
The Earth is developing an electronic nervous system, a network with diverse nodes and links are
-computers
-routers
-satellites
-phone lines
-TV cables
-EM waves
Communication networks: Many non-identical components with diverse connections between them.
April 19, 2023 Data Mining: Concepts and Techniques 5
Complex systemsMade of
many non-identical elements connected by diverse interactions.
NETWORK
April 19, 2023 Data Mining: Concepts and Techniques 6
“Natural” Networks and Universality
Consider many kinds of networks: social, technological, business, economic, content,…
These networks tend to share certain informal properties: large scale; continual growth distributed, democratic growth: vertices “decide” who to link
to mixture of local and long-distance connections abstract notions of distance: geographical, content, social,…
Do natural networks share more quantitative universals? What would these “universals” be? How can we make them precise and measure them? How can we explain their universality? This is the domain of social network theory Sometimes also referred to as link analysis
April 19, 2023 Data Mining: Concepts and Techniques 7
Some Interesting Quantities
Connected components: how many, and how large?
Network diameter: maximum (worst-case) or average? exclude infinite distances? (disconnected components) the small-world phenomenon
Clustering: to what extent that links tend to cluster “locally”? what is the balance between local and long-distance
connections? what roles do the two types of links play?
Degree distribution: what is the typical degree in the network? what is the overall distribution?
April 19, 2023 Data Mining: Concepts and Techniques 8
A “Canonical” Natural Network has…
Few connected components: often only 1 or a small number, indep. of network size
Small diameter: often a constant independent of network size (like 6) or perhaps growing only logarithmically with network
size or even shrink? typically exclude infinite distances
A high degree of clustering: considerably more so than for a random network in tension with small diameter
A heavy-tailed degree distribution: a small but reliable number of high-degree vertices often of power law form
April 19, 2023 Data Mining: Concepts and Techniques 9
Probabilistic Models of Networks
All of the network generation models we will study are probabilistic or statistical in nature
They can generate networks of any size They often have various parameters that can be set:
size of network generated average degree of a vertex fraction of long-distance connections
The models generate a distribution over networks Statements are always statistical in nature:
with high probability, diameter is small on average, degree distribution has heavy tail
Thus, we’re going to need some basic statistics and probability theory
April 19, 2023 Data Mining: Concepts and Techniques 10
Social Network Analysis
Social Network Introduction
Statistics and Probability Theory
Models of Social Network Generation
Networks in Biological System
Mining on Social Network
Summary
April 19, 2023 Data Mining: Concepts and Techniques 11
The Normal Distribution
The normal or Gaussian density: applies to continuous, real-valued random variables characterized by mean (average) m and standard
deviation s density at x is defined as
peaks at x = , then dies off exponentially rapidly the classic “bell-shaped curve”
exam scores, human body temperature, remarks:
can control mean and standard deviation independently can make as “broad” as we like, but always have finite
variance
April 19, 2023 Data Mining: Concepts and Techniques 12
The Normal Distribution
April 19, 2023 Data Mining: Concepts and Techniques 13
The Binomial Distribution
coin with Pr[heads] = p, flip n times probability of getting exactly k heads:
choose(n,k) pk(1-p)n-k
for large n and p fixed: approximated well by a normal with
= np, = sqrt(np(1-p)) / 0 as n grows leads to strong large deviation bounds
April 19, 2023 Data Mining: Concepts and Techniques 14
The Binomial Distribution
www.professionalgambler.com/ binomial.html
How manywins in 21 bets?
April 19, 2023 Data Mining: Concepts and Techniques 15
The Poisson Distribution
like binomial, applies to variables taken on integer values > 0
often used to model counts of events number of phone calls placed in a given time period number of times a neuron fires in a given time period
single free parameter probability of exactly x events:
mean and variance are both binomial distribution with n large, p = /n ( fixed)
converges to Poisson with mean
April 19, 2023 Data Mining: Concepts and Techniques 16
The Poisson Distribution
single photoelectron distribution
April 19, 2023 Data Mining: Concepts and Techniques 17
Heavy-tailed Distributions
April 19, 2023 Data Mining: Concepts and Techniques 18
Heavy-Tailed Distributions
April 19, 2023 Data Mining: Concepts and Techniques 19
Distributions vs. Data
All these distributions are idealized models In practice, we do not see distributions, but data Thus, there will be some largest value we observe Also, can be difficult to “eyeball” data and choose model So how do we distinguish between Poisson, power law, etc? Typical procedure:
might restrict our attention to a range of values of interest accumulate counts of observed data into equal-sized bins look at counts on a log-log plot note that
power law: log(Pr[X = x]) = log(1/x) = - log(x) linear, slope –
Normal: log(Pr[X = x]) = log(a exp(-x/b)) = log(a) – x/b non-linear, concave near mean
Poisson: log(Pr[X = x]) = log(exp(-) x/x!) also non-linear
April 19, 2023 Data Mining: Concepts and Techniques 20
Zipf’s Law Look at the frequency of English words:
“the” is the most common, followed by “of”, “to”, etc.
claim: frequency of the n-th most common ~ 1/n (power law, α = 1)
General theme: rank events by their frequency of occurrence resulting distribution often is a power law!
Other examples: North America city sizes personal income file sizes
April 19, 2023 Data Mining: Concepts and Techniques 21
Linear scales on both axes
Logarithmic scales on both axes
The same data plotted on linear and logarithmic scales. Both plots show a Zipf distribution with 300 datapoints
Zipf’s Law
April 19, 2023 Data Mining: Concepts and Techniques 22
Social Network Analysis
Social Network Introduction
Statistics and Probability Theory
Models of Social Network Generation
Networks in Biological System
Mining on Social Network
Summary
April 19, 2023 Data Mining: Concepts and Techniques 23
Some Models of Network Generation
Random graphs (Erdös-Rényi models): gives few components and small diameter does not give high clustering and heavy-tailed degree
distributions is the mathematically most well-studied and understood model
Watts-Strogatz models: give few components, small diameter and high clustering does not give heavy-tailed degree distributions
Scale-free Networks: gives few components, small diameter and heavy-tailed
distribution does not give high clustering
Hierarchical networks: few components, small diameter, high clustering, heavy-tailed
Affiliation networks: models group-actor formation
April 19, 2023 Data Mining: Concepts and Techniques 24
Models of Social Network Generation
Random Graphs (Erdös-Rényi models)
Watts-Strogatz models
Scale-free Networks
April 19, 2023 Data Mining: Concepts and Techniques 25
The Erdös-Rényi (ER) Model(Random Graphs)
All edges are equally probable and appear independently NW size N > 1 and probability p: distribution G(N,p)
each edge (u,v) chosen to appear with probability p N(N-1)/2 trials of a biased coin flip
The usual regime of interest is when p ~ 1/N, N is large e.g. p = 1/2N, p = 1/N, p = 2/N, p=10/N, p = log(N)/N, etc. in expectation, each vertex will have a “small” number of
neighbors will then examine what happens when N infinity can thus study properties of large networks with bounded
degree Degree distribution of a typical G drawn from G(N,p):
draw G according to G(N,p); look at a random vertex u in G what is Pr[deg(u) = k] for any fixed k? Poisson distribution with mean degree: λ = p(N-1) ~ pN Sharply concentrated; not heavy-tailed
Especially easy to generate NWs from G(N,p)
April 19, 2023 Data Mining: Concepts and Techniques 26
Erdös-Rényi Model (1960)
- Democratic
- Random
Pál ErdösPál Erdös (1913-1996)
Connect with
probability pp=1/6 N=10
k~1.5 Poisson distribution
April 19, 2023 Data Mining: Concepts and Techniques 27
A Closely Related Model
For any fixed m <= N(N-1)/2, define distribution G(N,m): choose uniformly at random from all
graphs with exactly m edges G(N,m) is “like” G(N,p) with p = m/(N(N-
1)/2) ~ 2m/N2
this intuition can be made precise, and is correct
if m = cN then p = 2c/(N-1) ~ 2c/N mathematically trickier than G(N,p)
April 19, 2023 Data Mining: Concepts and Techniques 28
Another Closely Related Model
Graph process model: start with N vertices and no edges at each time step, add a new edge choose new edge randomly from among all
missing edges Allows study of the evolution or emergence of
properties: as the number of edges m grows in relation to N equivalently, as p is increased
April 19, 2023 Data Mining: Concepts and Techniques 29
Evolution of a Random Network
We 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?
have a “large” clique?
How gradually or suddenly do these properties
appear?
April 19, 2023 Data Mining: Concepts and Techniques 30
Combining and Formalizing Familiar Ideas
Explaining universal behavior through statistical models our models will always generate many networks almost all of them will share certain properties (universals)
Explaining tipping through incremental growth we gradually add edges, or gradually increase edge probability p many properties will emerge very suddenly during this process
size of police force
crim
e r
ate
number of edges
pro
b. N
W c
onnect
ed
April 19, 2023 Data Mining: Concepts and Techniques 31
So Which Properties Tip?
Just about all of them! The following properties all have threshold
functions: having a “giant component” being connected having a perfect matching (N even) having “small” diameter
With remarkable consistency (N = 50): giant component (~ 40 edges), connected (~
100 edges), small diameter (~ 180 edges)
April 19, 2023 Data Mining: Concepts and Techniques 32
Ever More Precise…
April 19, 2023 Data Mining: Concepts and Techniques 33
Erdos-Renyi Summary
A model in which all connections are equally likely each of the N(N-1)/2 edges chosen randomly &
independently As we add edges, a precise sequence of events
unfolds: graph acquires a giant component graph becomes connected graph acquires small diameter
Many properties appear very suddenly (tipping, thresholds)
All statements are mathematically precise But is this how natural networks form? If not, which aspects are unrealistic?
may all edges are not equally likely!
April 19, 2023 Data Mining: Concepts and Techniques 34
The Clustering Coefficient of a Network
Let nbr(u) denote the set of neighbors of u in a graph all vertices v such that the edge (u,v) is in the graph
The clustering coefficient of u: let k = |nbr(u)| (i.e., number of neighbors of u) choose(k,2) = k*(k-1) / 2: max possible # of edges between vertices
in nbr(u) c(u) = (actual # of edges between vertices in nbr(u))/choose(k,2) 0 <= c(u) <= 1; measure of cliquishness of u’s neighborhood
Clustering coefficient of a graph: average of c(u) over all vertices u
k = 4choose(k,2) = 6c(u) = 4/6 = 0.666…
u
April 19, 2023 Data Mining: Concepts and Techniques 35
Clustering: My friends will likely know each other!
Probability to be connected C » p
C =# of links between 1,2,…n neighbors
n(n-1)/2
Networks are clustered [large C(p)]
but have a small characteristic path length
[small L(p)].
Network C Crand L N
WWW 0.1078 0.00023 3.1 153127
Internet 0.18-0.3 0.001 3.7-3.763015-6209
Actor 0.79 0.00027 3.65 225226
Coauthorship 0.43 0.00018 5.9 52909
Metabolic 0.32 0.026 2.9 282
Foodweb 0.22 0.06 2.43 134
C. elegance 0.28 0.05 2.65 282
The Clustering Coefficient of a Network
L: diameter?
April 19, 2023 Data Mining: Concepts and Techniques 36
Erdos-Renyi: Clustering Coefficient
Generate a network G according to G(N,p) Examine a “typical” vertex u in G
choose u at random among all vertices in G what do we expect c(u) to be?
Answer: exactly p. In G(N,m), expect c(u) to be 2m/N(N-1) Both cases: c(u) entirely determined by overall
density Baseline for comparison with “more clustered”
models Erdos-Renyi has no bias towards clustered or
local edges
April 19, 2023 Data Mining: Concepts and Techniques 37
Models of Social Network Generation
Random Graphs (Erdös-Rényi models)
Watts-Strogatz models
Scale-free Networks
April 19, 2023 Data Mining: Concepts and Techniques 38
Caveman and Solaria Erdos-Renyi:
sharing a common neighbor makes two vertices no more likely to be directly connected than two very “distant” vertices
every edge appears entirely independently of existing structure
But in many settings, the opposite is true: you tend to meet new friends through your old friends two web pages pointing to a third might share a topic two companies selling goods to a third are in related
industries Watts’ Caveman world:
overall density of edges is low but two vertices with a common neighbor are likely connected
April 19, 2023 Data Mining: Concepts and Techniques 39
Making it (Somewhat) Precise: the -model
The -model has the following parameters or “knobs”: N: size of the network to be generated k: the average degree of a vertex in the network to be generated p: the default probability two vertices are connected : adjustable parameter dictating bias towards local connections
For any vertices u and v: define m(u,v) to be the number of common neighbors (so far)
Key quantity: the propensity R(u,v) of u to connect to v if m(u,v) >= k, R(u,v) = 0 (share too many friends not to connect) if m(u,v) = 0, R(u,v) = p (no mutual friends no bias to connect) else, R(u,v) = p + (m(u,v)/k) (1-p)
Generate NW incrementally using R(u,v) as the edge probability; details omitted
Note: = infinity is “like” Erdos-Renyi (but not exactly)
April 19, 2023 Data Mining: Concepts and Techniques 40
Small Worlds and Occam’s Razor
For small , should generate large clustering coefficients we “programmed” the model to do so Watts claims that proving precise statements is hard…
But we do not want a new model for every little property Erdos-Renyi small diameter -model high clustering coefficient
In the interests of Occam’s Razor, we would like to find a single, simple model of network generation… … that simultaneously captures many properties
Watt’s small world: small diameter and high clustering
April 19, 2023 Data Mining: Concepts and Techniques 41
Meanwhile, Back in the Real World…
Watts examines three real networks as case studies: the Kevin Bacon graph the Western states power grid the C. elegans nervous system
For each of these networks, he: computes its size, diameter, and clustering coefficient compares diameter and clustering to best Erdos-
Renyi approx. shows that the best -model approximation is better important to be “fair” to each model by finding best
fit Overall moral:
if we care only about diameter and clustering, is better than p
April 19, 2023 Data Mining: Concepts and Techniques 42
Case 1: Kevin Bacon Graph
Vertices: actors and actresses Edge between u and v if they appeared in a film together
Is Kevin Bacon the most
connected actor?
NO!
Rank NameAveragedistance
# ofmovies
# oflinks
1 Rod Steiger 2.537527 112 25622 Donald Pleasence 2.542376 180 28743 Martin Sheen 2.551210 136 35014 Christopher Lee 2.552497 201 29935 Robert Mitchum 2.557181 136 29056 Charlton Heston 2.566284 104 25527 Eddie Albert 2.567036 112 33338 Robert Vaughn 2.570193 126 27619 Donald Sutherland 2.577880 107 2865
10 John Gielgud 2.578980 122 294211 Anthony Quinn 2.579750 146 297812 James Earl Jones 2.584440 112 3787…
876 Kevin Bacon 2.786981 46 1811…
876 Kevin Bacon 2.786981 46 1811
Kevin Bacon
No. of movies : 46 No. of actors : 1811 Average separation: 2.79
April 19, 2023 Data Mining: Concepts and Techniques 43
Rod Steiger
Martin Sheen
Donald Pleasence
#1
#2
#3
#876Kevin Bacon
April 19, 2023 Data Mining: Concepts and Techniques 44
Case 2: New York State Power Grid
Vertices: generators and substations Edges: high-voltage power transmission lines and transformers Line thickness and color indicate the voltage level
Red 765 kV, 500 kV; brown 345 kV; green 230 kV; grey 138 kV
April 19, 2023 Data Mining: Concepts and Techniques 45
Case 3: C. Elegans Nervous System
Vertices: neurons in the C. elegans worm Edges: axons/synapses between neurons
April 19, 2023 Data Mining: Concepts and Techniques 46
Two More Examples
M. Newman on scientific collaboration networks coauthorship networks in several distinct
communities differences in degrees (papers per author) empirical verification of
giant components small diameter (mean distance) high clustering coefficient
Alberich et al. on the Marvel Universe purely fictional social network two characters linked if they appeared together in an
issue “empirical” verification of
heavy-tailed distribution of degrees (issues and characters) giant component rather small clustering coefficient
April 19, 2023 Data Mining: Concepts and Techniques 47
One More (Structural) Property… A properly tuned -model can simultaneously explain
small diameter high clustering coefficient
But what about heavy-tailed degree distributions? -model and simple variants will not explain this intuitively, no “bias” towards large degree all vertices are created equal
As always, we want a “natural” model
April 19, 2023 Data Mining: Concepts and Techniques 48
Models of Social Network Generation
Random Graphs (Erdös-Rényi models)
Watts-Strogatz models
Scale-free Networks
April 19, 2023 Data Mining: Concepts and Techniques 49
World Wide Web
800 million documents (S. Lawrence, 1999)
ROBOT: collects all URL’s found in a document and follows them recursively
Nodes: WWW documents Links: URL links
R. Albert, H. Jeong, A-L Barabasi, Nature, 401 130 (1999)
April 19, 2023 Data Mining: Concepts and Techniques 50
k ~ 6
P(k=500) ~ 10-99
NWWW ~ 109
N(k=500)~10-90
Expected Result Real Result
Pout(k) ~ k-out
P(k=500) ~ 10-6
out= 2.45 in = 2.1
Pin(k) ~ k- in
NWWW ~ 109 N(k=500) ~ 103
J. Kleinberg, et. al, Proceedings of the ICCC (1999)
World Wide Web
April 19, 2023 Data Mining: Concepts and Techniques 51
< l
>
Finite size scaling: create a network with N nodes with Pin(k) and Pout(k)
< l > = 0.35 + 2.06 log(N)
l15=2 [125]
l17=4 [1346 7]
… < l > = ??
1
2
3
4
5
6
7
nd.edu
19 degrees of separation R. Albert et al Nature (99)
based on 800 million webpages [S. Lawrence et al Nature (99)]
A. Broder et al WWW9 (00)IBM
World Wide Web
L is the length of shortest paths
April 19, 2023 Data Mining: Concepts and Techniques 52
What does that mean?Poisson distribution
Exponential Network
Power-law distribution
Scale-free Network
April 19, 2023 Data Mining: Concepts and Techniques 53
Scale-free Networks
The number of nodes (N) is not fixed Networks continuously expand by additional new
nodes WWW: addition of new nodes Citation: publication of new papers
The attachment is not uniform A node is linked with higher probability to a node
that already has a large number of links WWW: new documents link to well known sites
(CNN, Yahoo, Google) Citation: Well cited papers are more likely to be
cited again
April 19, 2023 Data Mining: Concepts and Techniques 54
Scale-Free Networks Start with (say) two vertices connected by an edge For i = 3 to N:
for each 1 <= j < i, d(j) = degree of vertex j so far let Z = S d(j) (sum of all degrees so far) add new vertex i with k edges back to {1, …, i-1}:
i is connected back to j with probability d(j)/Z Vertices j with high degree are likely to get more links! “Rich get richer” Natural model for many processes:
hyperlinks on the web new business and social contacts transportation networks
Generates a power law distribution of degrees exponent depends on value of k
April 19, 2023 Data Mining: Concepts and Techniques 55
Preferential attachment explains heavy-tailed degree distributions small diameter (~log(N), via “hubs”)
Will not generate high clustering coefficient no bias towards local connectivity, but towards
hubs
Scale-Free Networks
April 19, 2023 Data Mining: Concepts and Techniques 56
Case1: Internet Backbone
(Faloutsos, Faloutsos and Faloutsos, 1999)
Nodes: computers, routers Links: physical lines
April 19, 2023 Data Mining: Concepts and Techniques 57
April 19, 2023 Data Mining: Concepts and Techniques 58
Case2: Actor Connectivity
Nodes: actors Links: cast jointly
N = 212,250 actors k = 28.78
P(k) ~k-
Days of Thunder (1990) Far and Away
(1992) Eyes Wide Shut (1999)
=2.3
April 19, 2023 Data Mining: Concepts and Techniques 59
Case 3: Science Citation Index
( = 3)
Nodes: papers Links: citations
(S. Redner, 1998)
P(k) ~k-
2212
25
1736 PRL papers (1988)
Witten-SanderPRL 1981
April 19, 2023 Data Mining: Concepts and Techniques 60
Nodes: scientist (authors) Links: write paper together
(Newman, 2000, H. Jeong et al 2001)
Case 4: Science Coauthorship
April 19, 2023 Data Mining: Concepts and Techniques 61
Case 5: Food Web
Nodes: trophic species Links: trophic interactions
R.J. Williams, N.D. Martinez Nature (2000)R. Sole (cond-mat/0011195)
April 19, 2023 Data Mining: Concepts and Techniques 62
Case 6: Sex-Web
Nodes: people (Females; Males)Links: sexual relationships
Liljeros et al. Nature 2001
4781 Swedes; 18-74; 59% response rate.
April 19, 2023 Data Mining: Concepts and Techniques 63
Robustness of Random vs. Scale-Free Networks
The accidental failure of a number of nodes in a random network can fracture the system into non-communicating islands.
Scale-free networks are more robust in the face of such failures.
Scale-free networks are highly vulnerable to a coordinated attack against their hubs.
April 19, 2023 Data Mining: Concepts and Techniques 64
Social Network Analysis
Social Network Introduction
Statistics and Probability Theory
Models of Social Network Generation
Networks in Biological System
Mining on Social Network
Summary
April 19, 2023 Data Mining: Concepts and Techniques 65
protein-gene interactions
protein-protein interactions
PROTEOME
GENOME
Citrate Cycle
METABOLISM
Bio-chemical reactions
Bio-Map
April 19, 2023 Data Mining: Concepts and Techniques 66
Citrate Cycle METABOLISM Bio-chemical reactions
Metabolic Network
April 19, 2023 Data Mining: Concepts and Techniques 67
April 19, 2023 Data Mining: Concepts and Techniques 68
Nodes: chemicals (substrates)
Links: bio-chemical reactions
Metabolic Network
April 19, 2023 Data Mining: Concepts and Techniques 69
Organisms from all three domains of life are scale-free networks!
H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature, 407 651 (2000)
Archaea Bacteria Eukaryotes
Metabolic Network
April 19, 2023 Data Mining: Concepts and Techniques 70
protein-gene interactions
protein-protein interactions
PROTEOME
GENOME
Citrate Cycle
METABOLISM
Bio-chemical reactions
Bio-Map
April 19, 2023 Data Mining: Concepts and Techniques 71
protein-protein interactions
PROTEOME
Protein Network
April 19, 2023 Data Mining: Concepts and Techniques 72
Nodes: proteins
Links: physical interactions (binding)
P. Uetz, et al. Nature 403, 623-7 (2000).
Yeast Protein Network
April 19, 2023 Data Mining: Concepts and Techniques 73
)exp()(~)( 00
k
kkkkkP
H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001)
Topology of the Protein Network
April 19, 2023 Data Mining: Concepts and Techniques 74
Nature 408 307 (2000)
…
“One way to understand the p53 network is to compare it to the Internet. The cell, like the Internet, appears to be a ‘scale-free network’.”
p53 Network
April 19, 2023 Data Mining: Concepts and Techniques 75
p53 Network (mammals)
April 19, 2023 Data Mining: Concepts and Techniques 76
Social Network Analysis
Social Network Introduction
Statistics and Probability Theory
Models of Social Network Generation
Networks in Biological System
Mining on Social Network
Summary
April 19, 2023 Data Mining: Concepts and Techniques 77
Information on the Social Network
Heterogeneous, multi-relational data represented as a graph or network Nodes are objects
May have different kinds of objects Objects have attributes Objects may have labels or classes
Edges are links May have different kinds of links Links may have attributes Links may be directed, are not required to be
binary Links represent relationships and interactions
between objects - rich content for mining
April 19, 2023 Data Mining: Concepts and Techniques 78
What is New for Link Mining Here
Traditional machine learning and data mining approaches assume: A random sample of homogeneous objects from
single relation Real world data sets:
Multi-relational, heterogeneous and semi-structured
Link Mining Newly emerging research area at the intersection
of research in social network and link analysis, hypertext and web mining, graph mining, relational learning and inductive logic programming
April 19, 2023 Data Mining: Concepts and Techniques 79
A Taxonomy of Common Link Mining Tasks
Object-Related Tasks Link-based object ranking Link-based object classification Object clustering (group detection) Object identification (entity resolution)
Link-Related Tasks Link prediction
April 19, 2023 Data Mining: Concepts and Techniques 80
What Is a Link in Link Mining?
Link: relationship among data Two kinds of linked networks
homogeneous vs. heterogeneous Homogeneous networks
Single object type and single link type Single model social networks (e.g., friends) WWW: a collection of linked Web pages
Heterogeneous networks Multiple object and link types Medical network: patients, doctors, disease,
contacts, treatments Bibliographic network: publications, authors, venues
April 19, 2023 Data Mining: Concepts and Techniques 81
Link-Based Object Ranking (LBR)
LBR: Exploit the link structure of a graph to order or prioritize the set of objects within the graph Focused on graphs with single object type and single
link type This is a primary focus of link analysis community Web information analysis
PageRank and Hits are typical LBR approaches In social network analysis (SNA), LBR is a core analysis
task Objective: rank individuals in terms of “centrality” Degree centrality vs. eigen vector/power centrality Rank objects relative to one or more relevant objects in
the graph vs. ranks object over time in dynamic graphs
April 19, 2023 Data Mining: Concepts and Techniques 82
PageRank: Capturing Page Popularity (Brin & Page’98)
Intuitions Links are like citations in literature A page that is cited often can be expected to be
more useful in general PageRank is essentially “citation counting”, but
improves over simple counting Consider “indirect citations” (being cited by a
highly cited paper counts a lot…) Smoothing of citations (every page is assumed
to have a non-zero citation count) PageRank can also be interpreted as random
surfing (thus capturing popularity)
April 19, 2023 Data Mining: Concepts and Techniques 83
The PageRank Algorithm (Brin & Page’98)
1( )
0 0 1/ 2 1/ 2
1 0 0 0
0 1 0 0
1/ 2 1/ 2 0 0
1( ) (1 ) ( ) ( )
1( ) [ (1 ) ] ( )
( (1 ) )
j i
t i ji t j t kd IN d k
i ki kk
T
M
p d m p d p dN
p d m p dN
p I M p
d1
d2
d4
“Transition matrix”
d3
Iterate until converge
Same as/N (why?)
Stationary (“stable”) distribution, so we
ignore time
Random surfing model: At any page,
With prob. , randomly jumping to a pageWith prob. (1 – ), randomly picking a link to follow
Iij = 1/N
Initial value p(d)=1/N
April 19, 2023 Data Mining: Concepts and Techniques 84
Link-Based Object Classification (LBC)
Predicting the category of an object based on its attributes, its links and the attributes of linked objects
Web: Predict the category of a web page, based on words that occur on the page, links between pages, anchor text, html tags, etc.
Citation: Predict the topic of a paper, based on word occurrence, citations, co-citations
Epidemics: Predict disease type based on characteristics of the patients infected by the disease
Communication: Predict whether a communication contact is by email, phone call or mail
April 19, 2023 Data Mining: Concepts and Techniques 85
Group Detection
Cluster the nodes in the graph into groups that share common characteristics Web: identifying communities Citation: identifying research
communities
April 19, 2023 Data Mining: Concepts and Techniques 86
Entity Resolution
Predicting when two objects are the same, based on their attributes and their links
Also known as: deduplication, reference reconciliation, co-reference resolution, object consolidation
Applications Web: predict when two sites are mirrors of each
other Citation: predicting when two citations are
referring to the same paper Epidemics: predicting when two disease strains
are the same Biology: learning when two names refer to the
same protein
April 19, 2023 Data Mining: Concepts and Techniques 87
Entity Resolution Methods
Earlier viewed as pair-wise resolution problem: resolved based on the similarity of their attributes
Importance at considering links Coauthor links in bib data, hierarchical links
between spatial references, co-occurrence links between name references in documents
Use of links in resolution Collective entity resolution: one resolution
decision affects another if they are linked Propagating evidence over links in a depen.
graph Probabilistic models interact with different
entity recognition decisions
April 19, 2023 Data Mining: Concepts and Techniques 88
Link Prediction
Predict whether a link exists between two entities, based on attributes and other observed links
Applications Web: predict if there will be a link between two
pages Citation: predicting if a paper will cite another
paper Epidemics: predicting who a patient’s contacts are
Methods Often viewed as a binary classification problem Local conditional probability model, based on
structural and attribute features Difficulty: sparseness of existing links Collective prediction, e.g., Markov random field
model
April 19, 2023 Data Mining: Concepts and Techniques 89
Link Cardinality Estimation
Predicting the number of links to an object Web: predict the authority of a page based on the
number of in-links; identifying hubs based on the number of out-links
Citation: predicting the impact of a paper based on the number of citations
Epidemics: predicting the number of people that will be infected based on the infectiousness of a disease
Predicting the number of objects reached along a path from an object Web: predicting number of pages retrieved by
crawling a site Citation: predicting the number of citations of a
particular author in a specific journal
April 19, 2023 Data Mining: Concepts and Techniques 90
Social Network Analysis
Social Network Introduction
Statistics and Probability Theory
Models of Social Network Generation
Networks in Biological System
Mining on Social Network
Summary
April 19, 2023 Data Mining: Concepts and Techniques 91
Ref: Mining on Social Networks
D. Liben-Nowell and J. Kleinberg. The Link Prediction Problem for Social Networks. CIKM’03
P. Domingos and M. Richardson, Mining the Network Value of Customers. KDD’01
M. Richardson and P. Domingos, Mining Knowledge-Sharing Sites for Viral Marketing. KDD’02
D. Kempe, J. Kleinberg, and E. Tardos, Maximizing the Spread of Influence through a Social Network. KDD’03.
P. Domingos, Mining Social Networks for Viral Marketing. IEEE Intelligent Systems, 20(1), 80-82, 2005.
S. Brin and L. Page, The anatomy of a large scale hypertextual Web search engine. WWW7.
S. Chakrabarti, B. Dom, D. Gibson, J. Kleinberg, S.R. Kumar, P. Raghavan, S. Rajagopalan, and A. Tomkins, Mining the link structure of the World Wide Web. IEEE Computer’99
D. Cai, X. He, J. Wen, and W. Ma, Block-level Link Analysis. SIGIR'2004.
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