Big-O(Q) Social Network Analytics

Social Network Analytics:
Beyond the Obvious
Laks V.S. Lakshmanan
University of British Columbia
Vancouver, Canada

Acknowledgments
2
2
Suresh Venkata-
Subramanian
Utah
Francesco Bonchi
Yahoo! Research
Smriti Bhagat
Technicolor 
Facebook
Amit Goyal
Twitter
PhD (UBC)
Wei Lu
PhD Student UBC
Wei Chen
Microsoft Research
Asia

Acknowledgments
3
Cigdem Aslay
PhD Student
UPF
Sharan Vaswani
PhD Student UBC
Pei Lee
PhD Student,
UBC / LinkedIn
Keqian Li
MSc Student UBC
Glenn Bevilacqua
PhD Student UBC

Disclaimers
•No pretense of completeness.
•Personal Account – focused on problems I find
interesting.
•No “? Vs” focus.
•If you don’t hear/see your research cited, please
read on …4

Outline
•Motivation
•Event and Story Evolution Tracking
•Social Event Organization
•Influence Propagation & Viral Marketing
•Summary and Future Research
6

Online Social Networking Sites
8 Snapchat

Influence Propagation and Viral Marketing
9

Information Propagation
People are connected and perform actions
10
nice
read
indeed
!
09:3009:00
comment, link, rate, like,
retweet, post a message,
photo, or video, etc.
friends, fans,
followers, etc.

Social Influence: Real-world Story I
12
12K people, 50K links, medical records from 1971 to 2003
Obese Friend  57% increase in chances of obesity
Obese Sibling  40% increase in chances of obesity
Obese Spouse  37% increase in chances of obesity
[Christakis and Fowler New England Jl. Of Medicine 2006].

Social Influence: Real-world Story II
Key to understanding people is
understanding ties between them.
Your friend’s friends’ actions and
feelings affect your thoughts, feelings
and actions!
13
• Back pain: spread from West to East in Germany after fall of Berlin Wall
• Suicide: well known to spread throughout communities on occasion
• Sex practices: e.g., growing prevalence of oral sex among teenagers
• Politics: the denser your connections, the more intense your convictions
[Christakis and Folwer http://connectedbook.com, 2011].

Applications of Study of Information
Propagation
Viral Marketing
Social media analytics
Spread of falsehood and rumors
Interest, trust, referrals
Adoption of innovations
Human and animal epidemics
Expert finding
Behavioral targeting
Feed ranking
“Friends” recommendation
Social search
14

Event and Story Evolution Tracking
15

How do you detect and track such events?
16
[Lee et al. CIKM 2014; ICDE 2014].

Can we facilitate organization of local
events at next VLDB?
You want to plan activities/events that the
participants would enjoy with one another.
Participants have preferences for events,
however, want to be with friends. Events too
have participation constraints.
18[Li et al. KDD 2014].

19
• Influence Maximization Background
• Direct Seed Mining and Accuracy of
Diffusion Models
• Alternative Optimization Problems
• Influence vs AdoptionProfit Maximization
• Competition and Host
• Viral Marketing Meets Social Advertising
• Individual Decision Making

Vision of Viral Marketing
20
Identify influential
customers
These customers
endorse the product
among their friends
Convince them to
adopt the product –
Offer discount or free
samples

Idealized Setting
• Static social network:
• Influence diffusion process
• Seed set 𝑺: initial set of nodes selected to start the diffusion
• Node activations: Nodes are activated starting from the seed nodes, in discrete steps
and following certain stochastic diffusion models
• Influence spread 𝝈(𝑺): expected number of activated nodes when the diffusion
process starting from the seed set 𝑆 ends [Kempe et al. KDD 2003].
Diffusion Model
.1
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Independent cascade (IC) model
Linear threshold (LT) model
General threshold model
Others
Voter model
Heat diffusion model
Direct spread prediction
22

0.3
0.1
0.3
0.7
0.3
0.5
0.6
0.3
0.2
0.4
0.8
Linear threshold model
• Each edge (𝑢, 𝑣) has
weight 𝑤 𝑢, 𝑣 :
• when 𝑢, 𝑣 ∉ 𝐸, 𝑤 𝑢, 𝑣 =
0
• 𝑢 𝑤 𝑢, 𝑣 ≤ 1
• Each node 𝑣 selects a
threshold 𝜃𝑣 ∈ [0,1]
uniformly at random
• Initially some seed nodes
are activated
• At each step, node
𝑣 checks if the weighted
sum of its active neighbors
is greater than its
threshold 𝜃𝑣, if so 𝑣 is
activated
24
Inactive
Active
Not Influenced
Influenced
[Kempe et al. KDD 2003].

Prototypical Problem – Influence maximization
Problem
Select k individuals such that
that by activating them,
influence spread is
maximized.
Input
Output
A directed graph
representing a social
network, with influence
weights on edges
NP-hard 
#P-hard to compute exact influence

25
[Kempe et al. KDD 2003].
[Chen et al. ICDM 2010].
[Chen et al. KDD 2010].
[Chen et al. Morgan Claypool book, 2013].

Properties of 𝜎 to the Rescue!
• 𝑓: 2 𝑉 → 𝑅≥0 is monotone if 𝑓 𝑆 ≤ 𝑓 𝑇 , whenever 𝑆 ⊆ 𝑇 ⊆ 𝑉.
• It is submodular if
• 𝑓 𝑇 ∪ 𝑣 − 𝑓 𝑇 ≤ 𝑓 𝑆 ∪ 𝑣 − 𝑓 𝑆 , whenever 𝑆 ⊆ 𝑇 ⊂ 𝑉, 𝑣 ∈
𝑉 ∖ 𝑇: v’s marginal contribution (gain) diminishes as the set grows.
• The expected spread function 𝜎 is monotone and submodular for
several popular diffusion models.
• Maximization of monotone submodular function – simple Greedy
algorithm yields 1 −
1
𝑒
−approximation: repeatedly add seed with
maximum marginal gain [𝜎 𝑆 ∪ 𝑢 − 𝜎 𝑆 ] to 𝑆.
[Nemhauser et al. Mathematical Prog. 1978].
27

Influence Maximization: State of the Art
• Use Monte Carlo simulations to estimate spread and
hence marginal gain to desired levels of accuracy.
• Extremely slow.
• Significant speedup using lazy evaluation: CELF
[Leskovec et al. KDD 2007].
• Further speedup using CELF++
[Goyal et al. WWW 2010].
• Various heuristics PMIA, LDAG, IRIE [Chen at al. KDD,
ICDM 2010+], SimPath [Goyal et al. ICDM 2011].
28

Influence Maximization: State of the Art
• Scalable approximation algorithm: TIM [Tang et al. SIGMOD 2014] and its
improvement based on Martingales [ibid SIGMOD 2015].
Random RR-Set (IC model):
Sample a possible world X from G: remove every edge (u,v)
with probability 1 – puv
Pick a target node v from G uniformly at random
Form RR-set of v from the nodes that can reach v in X
TIM Algorithm:
• Estimates influence spread for the seed nodes from random
samples of RR-Sets
• #samples needed depends on desired accuracy
29
SKIM: Another elegant approach based on bottom-k hash idea.
[Cohen et al. CIKM 2014].

30
Diffusion Models
• Influence vs AdoptionProfit Maximization

31
Propagation logSocial graph
Seed set
Learn Influence
Probabilities
Efficient
Algorithm
Heuristic /
approximationDirect Mining
Direct Mining
Key idea:
• Attribute credit for observed cascades to “ancestors” of
activated node(s) in a principled way – Credit Distribution.
• CD experimentally found to be far more accurate than IC & LT on
various datasets. [Goyal et al. VLDB 2012].

32
Diffusion Models
• Influence vs Adoption
• Profit Maximization

Is IM the only worthwhile problem in
Influence Propagation
• Minimizing Budget: Given a target expected spread,
find the smallest seed set that achieves the target.
• Minimizing Propagation Time: Given a target expected
spread and a budget on #seeds, find the best seed set
under budget that achieves the target in the least
possible time.
[Goyal et al. Social Network Analysis & Mining 2012].
33

MINTSS (minimizing budget)
• Exploits monotonicity and submodularity.
• Φ is due to #P-hardness.
• Theorem: Cannot do better than this unless
34
Theorem: 𝐹𝑜𝑟 𝑎𝑛𝑦 𝜙 > 0, ∃ 𝛿 ∈ 0,1 : 𝑢𝑠𝑖𝑛𝑔
1 − 𝛿 − 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑠 𝑜𝑓 𝜎 𝑚 . , 𝑡ℎ𝑒 𝑐𝑙𝑎𝑠𝑠𝑖𝑐 𝐺𝑟𝑒𝑒𝑑𝑦
𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑠 𝑀𝐼𝑁𝑇𝑆𝑆 𝑏𝑦 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 1 + 𝜙 ⋅ 1 + ln
𝜂
𝜖
,
𝑓𝑜𝑟 𝑏𝑜𝑡ℎ 𝐼𝐶 𝑎𝑛𝑑 𝐿𝑇 𝑚𝑜𝑑𝑒𝑙𝑠.
Shortfall in target.

MINTIME (minimizing propagation time)
Problem: Achieve a spread of η with budget k, in
minimum possible propagation time.
• Theorem: tri-criteria approximation is possible!
35
))/ln(1()1(budget   k
 spread
OPT n timepropagatiovoila!

MINTIME
• Theorem: No polynomial time tricriteria
approximation algorithm exists that can do with
smaller budget (k) overrun or with less
underachievement of the target (𝜂).
36

37
Diffusion Models

Influence vs. Adoption
•Influenced  Adopt?
•Classical models:
•Assume influenced  adopt.
•Profit captured by proxy: expected spread!
•Need models and algorithms for VM taking these
distinctions into account.
38
[Bhagat et al. WSDM 2012]

Influence ⇏ Adoption
• Observation: Only a subset of influenced users
actually adopt the marketed product
Influenced Adopt
 Awareness/information spreads in an epidemic-like
manner while adoption depends on factors such as
product quality and price
39

LT-C – LT Model with Colors
• Model Parameters
• A is the set of active friends
• fv(A) is the activation function
• ru,i is the (predicted) rating for product i given by user u
• αv is the probability of user v adopting the product
• βv is the probability of user v promoting the product
Inactive
Tattle
Adopt
Active
Inhibit
Promote
f v (A)
1 − f v (A)
αv
1− αv
1− βv
βv
User vActive Friends
41

Maximizing Product Adoption
• Problem: Given a social network and product ratings,
find k users such that by targeting them the expected
spread (expected number of adopters) under the LT-C
model is maximized
• Problem is NP-hard
• The spread function is monotone and submodular
yielding a 1 −
1
𝑒
− 𝜖 −approximation to the optimal
using a greedy approach
• Better prediction of actual spread on real datasets than
previous (“color-blind”) models.
42

44
Diffusion Models

Customer Valuations
• Users may have their own valuation for the marketed
product.
• Adopt only if 𝒗𝒂𝒍𝒖𝒂𝒕𝒊𝒐𝒏 ≥ 𝒐𝒇𝒇𝒆𝒓 − 𝒑𝒓𝒊𝒄𝒆.
• Even a seed may reject an offer!
• Seeding costs the marketer!
• Traditional 𝜎(𝑆) as #activated nodes no longer works!
[Lu and L. ICDM 2012].
45

Customer Valuations
• Only adopting nodes propagate info., but extensions possible.
Inactive Influenced Adopt
influence < threshold valuation < price
influence ≥ threshold v𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛 ≥ price
46

Profit Maximization
Input
Output
A directed graph
representing a social
network, with influence
weights on edges
Problem
Find seeds S and offer prices
𝑝: 𝜋(𝑆, 𝑝) is maximized under
the LT-V model.
Contrast with classic Influence Maximization!
47

A Special Case
• Valuations degenerate to a single point 𝑝 ∈ (0,1] for every user.
• Seeds get a free sample.
• Offer item at price 𝑝 for everyone else.
• Restricted ProMax: find seeds 𝑆: 𝜋 𝑆 ≔ (𝜎𝐿 𝑆 − |𝑆|) ∗ 𝑝 − 𝑐 ∗ |𝑆|
is maximized.
Expected spread
under LT-V model.
Seeding cost.
Submodular but not monotone.
48

Profit Maximization Algorithm
• PAGE (Price Aware GrEedy):
0 1
offer-price
valuation
Optimal myopic price: pi
m
= arg max
p∈[0,1]
𝑝(1 − 𝐹𝑖(𝑝))
Grow seed set along with offer price: Given current seed set S (along w/
decided offer prices), what is the next best (seed candidate, offer price)
combo. that brings the max. marginal gain? 49

50
Diffusion Models

Previous work in Competitive VM
•Mainly follower’s perspective: given state
(say of seed selection) of previous
companies (agents/players):
• what’s the best strategy for the “follower” to
maximize its spread in the face of the competition?
• What’s the best strategy for the follower to
maximize its blocked influence against opponent?
•Most competitive VM algorithms not
scalable or assume unfettered access to the
n/w for all players.
51

But …
Campaign runners don’t necessarily have unfettered access to the network!
There is an owner of the network.
Campaigns need owner’s permission.
May need to pay the owner. 52

A New Business Model – Introducing
…
Network owner
Provides VM service.
How should the host select/allocate seeds?
I need 100 seeds
I need 250 seeds
Competition starts after host
selects/allocates seeds.
53
[Lu et al. KDD 2013].

Business Model (contd.)
•
54

Why is fairness important?
Imaginary scenario:
SONY NEX-VG30H
50 seeds
Spread 1000
JVC HD Everio GZ-VX815
30 seeds
Spread 240
For comparable products, if the b4b is substantially different,
dissatisfied company(ies) may take their VM business elsewhere!
55

Propagation Model
inactive influenced active
Should I buy a
camcorder?
Which CC should
I buy?
I’ve chosen my color!
Seeds influence out-neighbors (followers).
Active nodes influence followers.
Once influenced, relative weights of different (campaign) influences induce a
random decision making trial.
56

Propagation Model
• Two phases.
Nodes activated at time t.
• Phase 1: decision to adopt a product – joint influence.
• Phase 2: choice of product – campaigns compete.
57

What should we optimize?
• Obvious candidate: 𝜎 𝑎𝑙𝑙 𝑺 ≔ 𝑖 𝜎 𝑖 𝑺 , where 𝑺 = 𝑆1, … , 𝑆 𝐾 .
• Easy proposition: 𝜎 𝑎𝑙𝑙 𝑺 = 𝜎𝐿𝑇( 𝑖 𝑆𝑖).
Allocations differ only in the extent of fairness.
• Different measures of fairness based on bang for the buck:
𝜎 𝑖 𝑺
𝑏 𝑖
.
• Min-max: minimize the maximum amplification factor (b4b).
• Theorem: Fair seed allocation is NP-hard for 𝐾 ≥ 3.
58

Fair Seed Allocation
• Needy Greedy Algorithm:
• Find the “best” set of seeds 𝑆: 𝑆 = 𝑖 𝑏𝑖 using state of the art
algorithm for single product campaign: e.g., TIM!
• Allocate those selected seeds to advertisers so as to maximize
fairness:
• Arrange seeds in non-increasing order of “adjusted” marginal gain:
• 𝐴𝑀𝐺 𝑢 𝑆 ≔ 𝜎 𝑉−𝑆+𝑢 ( 𝑢 ).
• Allocate the next best seed to the advertiser whose current B4B is the
worst.
• NG beats various natural baselines on all datasets tested.
59

60
Diffusion Models

Viral Marketing Meets Social Advertising
Sponsored ads (aka promoted posts) served along with social feeds
on several social networking platforms. 61

Social Ads ∧ Viral Marketing
• I may not click on just any ad (aka promoted post): topic matters for
click through probability.
• By clicking on an ad, I provide endorsement or social proof to my
friends.
• Promoted posts propagate virally just like normal posts.
• They can show up on your feeds disguised as a normal post, i.e., they
don’t count against FB/LI’s promoted post budget for you!
62

• My followers may/may not take my endorsement seriously: topic
matters again!
• Host offers social advertising service and collects a fixed price per
click – cost per engagement.
• Limit on how many promoted posts/user can be shown at a time.
• Advertisers have budgets. 𝜎 𝑖
• Host’s regret: 𝜎 𝑖
• I wish I’d maxed out the advertiser’s budget.
• I wish I hadn’t given away so much!
63[Aslay et al. VLDB 2015].
𝑏𝑖

• How can the host allocate ads to users so as to minimize the regret?
• Come to Cigdem Aslay’s talk, Research Session 19, Queens 4 on
Wednesday, 3:30—5:00 pm, and Poster Session 2, Kohala Ballroom,
on Thursday 5:15—7:00 pm.
64

65
Diffusion Models

Complexity of the Marketplace
• Competition is real and capturing it is good.
• But complementation (value-added service) is just as common.
66

Node Decision Making for Two Products
A-suspended
A-adopted
A-rejected
A-idle &
B-idle / B-
suspended
A-idle &
B-adopted
𝑞 𝐴|∅
1 − 𝑞 𝐴|∅
𝑞 𝐴|𝐵
1 − 𝑞 𝐴|𝐵
𝜌 𝐴
1 − 𝜌 𝐴
(informed of A) (informed of A)
(adopted B)
67

Seed Selection with
Complementation/Competition
• Monotonicity and submodularity do not hold in general.
• Different choices of optimization objectives.
• Node automaton – rich and expressive framework for capturing
individual decision making which meshes nicely with network
propagation.
• Complexity issues and optimization algorithms, including an extension
to TIM for any monotone & submodular model & a novel “sandwich”
optimization strategy for non-submodular models 
[Lu et al. VLDB 2016; http://arxiv.org/abs/1507.00317].
68

Summary & Future Work
• Story and Event Evolution Tracking.
• Social Event Organization.
• Influence Propagation and Viral Marketing.
70

• Several questions studied but not discussed:
• Learning influence probabilities from action cascades.
[Goyal et al. WSDM 2010].
• Learning influence probabilities when no cascades exist.
[Vaswani & L. 2015].
• Adaptive influence maximization. [Vaswani & L. 2015].
• Explanations for seed selection. [Bevilacqua & L. 2015].
• Running a viral campaign over a recommender system.
[Goyal & L. KDD 2012].
71

• Significant advances in IM & VM, but there is miles to go to “take it out of
the lab”.
• Evolving data: social network, actions.
• Adaptive is closer to reality but is fraught with difficulties: e.g.,
submodularity quickly breaks down.
• Active learning is the way to go for learning parameters while running
campaigns: pure exploration? min. regret?
• Real marketplace is far more complex than studied models: competition,
host, privacy issues, economic considerations, budgets, bids, complex
decision models of users, …
• Tractable but expressive framework capturing these and designing scalable
algorithms – a tremendous challenge.
72

73
Shameless Ad for two other talks by my students at this VLDB which have nothing to
do with this talk:
Wei Lu et al. Show Me the Money: Dynamic Recommendations for Revenue
Maximization, Research Session 8; Tuesday, 3:30—5:00 pm. Queens5.
Min Xie et al. Generating Top-k Packages via Preference Elicitation. Research
Session 20; Wednesday 3:30—5:00 pm. Queens5.

References
• N.A. Christakis and J.H. Fowler. The Spread of Obesity in a Large Social Network over 32 Years. New
England Journal of Medicine. 2006.
• N.A. Christakis and J.H. Fowler. Connected: The Surprising Power of our Social Networks and How They
Shape our Lives. http://connectedbook.com, 2011.
• Pei Lee, L., and Evangelos E. Milios: CAST: A Context-Aware Story-Teller for Streaming Social
Content. CIKM 2014: 789-798.
• ibid. Incremental cluster evolution tracking from highly dynamic network data. ICDE 2014: 3-14.
• Keqian Li, Wei Lu, Smriti Bhagat, L., and Cong Yu: On social event organization. KDD 2014: 1206-1215.
• D. Kempe, J. Kleinberg, and E Tardos. Maximizing the spread of influence through a social network. KDD
2003.
• Wei Chen, Yifei Yuan, and Li Zhang: Scalable Influence Maximization in Social Networks under the Linear
Threshold Model. ICDM 2010: 88-97
• Wei Chen, Chi Wang, and Yajun Wang: Scalable influence maximization for prevalent viral marketing in
large-scale social networks. KDD 2010: 1029-1038.
• George L. Nemhauser, Laurence A. Wolsey, and Marshall L. Fisher:
An analysis of approximations for maximizing submodular set functions - I. Math. Program. 14(1): 265-
294 (1978). 74

References
• J. Leskovec, Andreas Krause, and C. Guestrin. Cost-effective outbreak detection in networks. KDD 2007.
• Amit Goyal, Wei Lu, and L. CELF++: optimizing the greedy algorithm for influence maximization in social
networks. WWW 2011. ACM, New York, NY, USA, 47-48.
• Amit Goyal, Wei Lu, and L. SimPath: An efficient algorithm for influence maximization under the linear
threshold model. ICDM'11, Vancouver, B.C., December 2011.
• Wei Chen, Chi Wang, and Yajun Wang. Scalable influence maximization for prevalent viral marketing in
large-scale social networks. KDD'2010, Washington DC, U.S.A., July 2010.
• Wei Chen, Yifei Yuan, and Li Zhang. Scalable influence maximization in social networks under the linear
threshold model. ICDM'2010, Sydney, Australia, Dec. 2010.
• Kyomin Jung, Wooram Heo, and Wei Chen. IRIE: Scalable and robust influence maximization in social
networks. ICDM'2012, Brussels, Belgium, December, 2012.
• Youze Tang, Xiaokui Xiao, Yanchen Shi:
Influence maximization: near-optimal time complexity meets practical efficiency. SIGMO 2014: 75-86.
• Youze Tang, Yanchen Shi, Xiaokui Xiao:
Influence Maximization in Near-Linear Time: A Martingale Approach. SIGMOD 2015: 1539-1554.
• E. Cohen, D. Delling, T. Pajor, and R.F. Werneck. Sketch-based influence maximization and computation:
scaling up with guarantees. CIKM 2014.
75

References
• Amit Goyal, Francesco Bonchi, and L., A Data-Based approach to Social Influence Maximization. VLDB
2012.
• Amit Goyal, Francesco Bonchi, L., and Suresh Venkatasubramanian, On Minimizing Budget and Time in
Influence Propagation over Social Networks. In Social Network Analysis and Mining, 2012.
• Smriti Bhagat, Amit Goyal, and L., Maximizing Product Adoption in Social Networks. WSDM 2012.
• Wei Lu and L. Profit Maximization over Social Networks. ICDM'12, Brussels, Belgium, December 2012.
• Wei Lu, Francesco Bonchi, Amit Goyal, and L. The Bang for the Buck: Fair Competitive Viral Marketing
from the Host Perspective. KDD'13, Chicago, Illinois, August 2013.
• Cigdem Aslay, Wei Lu, Francesco Bonchi, Amit Goyal, and L. Viral Marketing Meets Social Advertising: Ad
Allocation with Minimum Regret. VLDB 2015, Kohala Coast, Hawaii, August 2015.
• Wei Lu, Wei Chen, and L. From Competition to Complementarity: Comparative Influence Diffusion and
Maximization. To appear in VLDB 2016 conference, New Delhi, India (arXiv version:
http://arxiv.org/abs/1507.00317).
• Amit Goyal, Francesco Bonchi, and L., Learning Influence Probabilities in Social Networks. WSDM 2010,
New York City, 2010.
• Vincent Yun Lou, Smriti Bhagat, L., and Sharan Vaswani:
Modeling non-progressive phenomena for influence propagation. COSN 2014: 131-138.
76

References
• Sharan Vaswani and L.: Influence Maximization with Bandits. CoRR abs/1503.00024 (2015).
• Glenn S. Bevilacqua, Shealen Clare, Amit Goyal, and L.:
Validating Network Value of Influencers by Means of Explanations. ICDM 2013: 967-972.
• Amit Goyal and L.: RecMax: exploiting recommender systems for fun and profit. KDD 2012: 1294-1302.
• Wei Chen, L., and Carlos Castillo. Information and Influence Propagation in Social Networks. Morgan
Claypool, 2013.
77

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