fusion of heterogeneous social networks for synergistic ...jzhang2/files/prelim_exam_slides.pdf ·...

Fusion of Heterogeneous Social Networks for Synergistic

Knowledge Discovery

Presenter: Jiawei Zhang Date: March 14, 2016

Committee Members: Prof. Philip S. Yu (Chair), Prof. Piotr J. Gmytrasiewicz,

Prof. Xinhua Zhang, Prof. Yuheng Hu,

Prof. Xiangnan Kong

KnowledgeDiscovery

across FusedNetworks

Social Network Alignment

(Prerequisite step)

Inter-NetworkSocial Link Prediction

(Applications)

cross-networkCommunity Detection

(Applications)

inter-networkViral Marketing(Applications)

Future Works Future Works

Outline

1

2

3

4

5

6

Background Knowledge and Basic Concepts

Problem 1: Network Alignment

Problem 2: Social Link Prediction across Networks

Future work 1: Community Detection across Networks

Summary and Selected References

1

Future work 2: Viral Marketing across Networks

• Online Social Networks• Definition: An online social network is a social

structure made up of a set of social actors and a set of ties between these actors[1].

• Example:

...

...

writewrite

write

write

write

contain contain contain contain


attach

attach

attachattach

attach

timestamps posts words locations

Basic Concept Social Networks

[1]: http://en.wikipedia.org/wiki/Social_network

http://en.wikipedia.org/wiki/Social_network

• Representation: Heterogeneous Information Network

where is the sets of various kinds of nodes in the network and is the kind of nodes in G; is the sets of various types of links in the network and is the kind of link in G.

E =S

j Ej

V =S

i Vi

Vi ith

jthEj

Basic Concept Social Networks

...

...

writewrite

write

write

write



attach

attach

attachattach

attach

timestamps posts words locationsV = {user node set, post node set,

word node set, time node set, location node set}

E = {user-user link set, user-post link set, post-word link set, post-time link set, post-location link set}

People are using multiple online social networks simultaneously

[1] Zhang et al. PNA: Partial Network Alignment with Generic Stable Matching, 2015 IEEE IRI. [2] Duggan et al. Social media update 2013.

93% 53% 83%

Locations

Tips

8 AM 12 PM 4 PM 8 PM 11 PM

User Accounts

Temporal Activities

User Accounts

Locationslocate

locate

Tweets

8 AM 12 PM 4 PM 8 PM 11 PM

Temporal Activitiesanchor links

Multiple Aligned Social Networks

anchor users

non-anchor users

Aligned Social Networks

• Multi Aligned Heterogeneous Social Networks

• Definition:

G = (Gset, Aset)

where is the set of Gset = {G(1), G(2), · · · , G(|Gset|)} different heterogeneous information networks;|Gset| is the setAset = {A(1,2), A(1,3), · · · , A(|Gset|,|Gset|�1)}of undirected anchor links among networks.

Multiple Aligned Social Networks

Post

User

Location

Time!stampWord

written atcontain

checkin at

write

follow/follow-1

write-1

checkin at-1

contain-1 written at-1

network schemaNetwork Schema and Intra-Network Social Meta Path

Aligned Network Schema and Inter-Network Social Meta Path

Outline

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4

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Jiawei Zhang and Philip S. Yu. PCT: Partial Co-Alignment of Social Networks. In: Proceedings of the 25th International World Wide Web Conference (WWW ’16), Montreal, Canada, April 11-15, 2016.

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Locations

User Accounts

Locations

Tips

locate

locate

Tweets

anchor links8 AM 12 PM 4 PM 8 PM 11 PM

User Accounts

Temporal Activities

8 AM 12 PM 4 PM 8 PM 11 PM

Temporal Activities

?

?

?

Challenge 1: Heterogeneity of Social Networks Heterogeneous Link and Attribute Information

• User Anchor Link Inference with Link Information

A

DC

B

36

2

0 1 0 0

1 0 1 1

0 1 0 1

0 1 1 0

A B C DABCDAdjacency Matrix S(1)

0 1 0

1 0 1

0 1 0

2 3 6236

Adjacency Matrix S(2)

0 0 0

1 0 0

0 1 0

0 0 0

ABCD

2 3 6

Transition Matrix P

Assumption: shared users have similar social structures in different networks

Via transition matrix P (i.e., anchor links), we can map the social connections among shared users from network I to network II:

PT S(1) PThe optimal transition matrix P (i.e., anchor links) should minimize the mapping cost

User Anchor Link Inference with Link Information

min

PS(1) S(2)


• User Anchor Link Inference with Attribute Information

A

DC

B

36

2

user profile

8 AM 12 PM 4 PM 8 PM 11 PM

user temporal activity user text usage

cross-network user similarity measures:

Name: Time: Word:

Assumption: shared users have similar attribute information in different networks

User Anchor Link Inference with Attribute Information

0 0 0

1 0 0

0 1 0

0 0 0

ABCD

2 3 6

Transition Matrix P

1/3 2/3 1

1 1/3 0

2/3 1 0

0 1/3 2/3

ABCD

2 3 6

Similarity Matrix P

Vuser similarity = (name_sim + time_sim + text_sim)/3

The optimal transition matrix P (i.e., anchor links) should maximize the mapped user similarities

max


• User Anchor Link Inference with Link and Attribute information

• Hard 0-1 non-linear integer programming problem, very challenging to address

• Relax the hard 0-1 constraint, P can take real values in range [0, 1] • These introduced redundant anchor links will be pruned with a

network matching post-processing step

One-to-One Constraint

Challenge 2: Redundant Link Pruning with Network Flow based Social Network Matching

0.1

0.7

0.9

0.2

0.3

0.3

0.1

0.2

0.1

User Preference Bipartite Graphs Network Flow Graph

S T

GF = (NF ,LF ,W)

Challenge 2: Redundant Link Pruning with Network Flow based Social Network Matching

introduced network flow variable for user anchor links

user anchor link existence con- fidence scores (previous step)

variable bound constraintsmass balance constraints

s.t. 0 F (u, v) 1, 8(u, v) 2 {S}⇥ U (1) [ U (2) ⇥ {T}.

Multiple Aligned Network Datasetanchor links based upon the ranking scores of the classifier.Our solution is motivated by the stable marriage problem [8]in mathematics.

We first use a toy example in Figure 2 to illustrate themain idea of our solution. Suppose in Figure 2(a) we aregiven the ranking scores from the classifiers. We can see inFigure 2(b) that link prediction methods with a fixed thresh-old may not be able to predict well, because the predictedlinks do not satisfy the constraint of one-to-one relationship.Thus one user account in the source network can be linkedwith multiple accounts in the target network. In Figure 2(c),weighted maximium matching methods can find a set of linkswith maximum sum of weights. However, it is worth notingthat the input scores are uncalibrated, so maximum weightmatching may not be a good solution for anchor link predic-tion problems. The input scores only indicate the ranking ofdi↵erent user pairs, i.e., the preference relationship amongdi↵erent user pairs.

Here we say ‘node x prefers node y over node z’, if thescore of pair (x, y) is larger than the score of pair (x, z). Forexample, in Figure 2(c), the weight of pair a, i.e., Score(a) =0.8, is larger than Score(c) = 0.6. It shows that user u

s1

(thefirst user in the source network) prefers u

t1

over u

t2

. Theproblem with the prediction result in Figure 2(c) is that,the pair (us

1

, u

t1

) should be more likely to be an anchor linkdue to the following reasons: (1) u

s1

prefers u

t1

over u

t2

; (2)u

t1

also prefers u

s1

over u

s2

.Definition (Blocking Pair): A pair (us

i , utj) is a blocking

pair i↵ u

si and u

tj both prefer each other over their current

assignments respectively in the predicted set of anchor linksA0.Definition (Stable Matching): An inferred anchor link setA0 is stable if there is no blocking pair.

We propose to formulate the anchor link prediction prob-lem as a stable matching problem between user accounts insource network and accounts in target network. Assume thatwe have two sets of unlabeled user accounts, i.e., Us = {u

si }i

in source network and U t = {u

tj}j in target network. Each

u

si has a ranking list or preference list P (us

i ) over all the useraccounts in target network (ut

j 2 U t) based upon the inputscores of di↵erent pairs. For example, in Figure 2(a), thepreference list of node u

s1

is P (us1

) = (ut1

> u

t2

), indicatingthat node u

t1

is preferred by u

s1

over u

t2

. The preference listof node u

s2

is also P (us2

) = (ut1

> u

t2

). Similarly, we alsobuild a preference list for each user account in the targetnetwork. In Figure 2(a), P (ut

1

) = P (ut2

) = (us1

> u

s2

).The proposed Mna method for anchor link prediction is

shown in Algorithm 1. In each iteration, we first randomlyselect a free user account u

si from the source network. Then

we get the most prefered user node u

tj by u

si in its preference

list P (usi ). We then remove u

tj from the preference list, i.e.,

P (usi ) = P (us

i ) � u

tj .

If u

tj is also a free account, we add the pair of accounts

(usi , u

tj) into the current solution set A0. Otherwise, u

tj is

already occupied with u

sp in A0. We then examine the pref-

erence of u

tj . If u

tj also prefers u

si over u

sp, it means that the

pair (usi , u

tj) is a blocking pair. We remove the blocking pair

by replacing the pair (usp, u

tj) in the solution set A0 with the

pair (usi , u

tj). Otherwise, if u

tj prefers u

sp over u

si , we start

the next iteration to reach out the next free node in thesource network. The algorithm stops when all the users inthe source network are occupied, or all the preference listsof free accounts in the source network are empty.

Table 2: Properties of the Heterogeneous SocialNetworks

network

property Twitter Foursquare

# nodeuser 5,223 5,392tweet/tip 9,490,707 48,756location 297,182 38,921

# linkfriend/follow 164,920 31,312write 9,490,707 48,756locate 615,515 48,756

4. EXPERIMENTS

4.1 Data PreparationIn order to evaluate the performance of the proposed ap-

proach for anchor link prediction, we tested our algorithm ontwo real-world social networks as summarized in Table 2. Wechose Twitter and Foursquare as our data sources becausepublic tweets and Foursquare tips can be easily collected bytheir APIs.

1) Foursquare: the first network we crawled is the Foursquarewebsite, a representative location-based social network(LBSN). We collected a dataset consisting of 5,392users and 94,187 tips. For each tip, the location data(latitude and longitude) as well as the timestamp areavailable. Moreover, Foursquare network also providesdata about whether one user is following or a friendof another user. These links can indicate the socialrelationship among the users.

2) Twitter: The second network we crawled is Twitter,an online social microblogging network. We collected5,223 users and 9,490,707 tweets. In Twitter network,all tweets include time data, and some tweets includelocation data. In total, we have 615,515 tweets withlocation data (latitude and longitude), which is about6.5% of all the tweets we collected.

In order to conduct experiments, we pre-process these rawdata to obtain the ground-truth of users’ anchor links. InFoursquare network, we can collect some users’ Twitter IDsin their account pages. We use these information to build theground-truth of anchor links between user accounts acrossthe two networks. If a Foursquare user has shown his/herTwitter ID in the website, we treat it as an anchor linkbetween this user’s Foursquare account and Twitter account.

4.2 Comparative MethodsIn order to study the e↵ectiveness of the proposed ap-

proach, we compare our method with eight baseline meth-ods, which are commonly used baselines including both su-pervised and unsupervised link prediction approaches. Thecompared methods are summarized as follows:

• Multi-Network Anchoring(Mna): the proposed methodin this paper. Mna can explicitly exploit four types ofinformation from both networks to infer anchor links,i.e., social, spatial, temporal and text data. In ad-dition, Mna incorporates the one-to-one constraint inthe inference process. We argue that by combining the

Anchor Links: 3,388

Detailed Experiment Settings• Comparison Methods

• UNICOAT: Model proposed in this paper, involves link inference and post-pruning steps.

• BigAlign: Bipartite Network Alignment with Link Information [12] • BigAlignExt: Bipartite Network Alignment + Matching • ISO: User Anchor Link Inference with Link Information [12] • ISOExt: User Anchor Link Inference + Matching • RDD: a unsupervised anchor link inference method

[12] D. Koutra, H. Tong, and D. Lubensky. Big-align: Fast bipartite graph alignment. In ICDM, 2013

UNICOAT Big-A Big-A-E ISO ISO-Eprediction √ √

(Bipartite)√

(Bipartite)√

(user anchor link)√

(user anchor link)

matching √ √ √Link Info. √ √ √ √ √

Attribute Info. √

• Evaluation Metrics • AUC, Precision@100

Experiment ResultsAlignment Ratio: θ = 1: full alignment settingθ = 5: 20% alignment setting

Outline

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Jiawei Zhang, Philip S. Yu and Zhi-Hua Zhou. Meta-path based Multi-network Collective Link Prediction. In: Proceedings of the 20th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD ’14 ), New York City, NY, August 24-27, 2014.

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Predicting social links across multiple aligned networks simultaneously

Net

wor

k 1

Net

wor

k 2

existing social linksanchor link social links to be predicted?

?

?

?

?

?

?

Disadvantages of Supervised Link Prediction Setting

？

u1u2

u3

u4link features label

(u1, u2) +1

u5

(u3, u5) +1… … …

(u3, u4) -1… … …

(u4, u2) -1

information used to extract feature vectors for these links

(u5, u4) supervised learning model

network structure

link to be predictedlabel/score

existinglinks

non-existinglinks

non-existing links!=

negative links

non-existing linksshould be

unlabeled links

PU Learning: How to find reliable negative links?

Supervised link prediction ==> Positive Unlabeled (PU) link

prediction

class imbalance problemnegative instances >>

positive instances

Reliable Negative Links Extraction

+ + ++

+++

—— —— —

——

++ ++ +

++

Spy Positive Links Unlabeled Links

Reliable Negative Links

classification boundary

Feature Space

{Existing-Spy {U{Spy

P’ N’

P N{RN✏

{Spy{U

training set

test set

classification results

UP

reliablenegative

links

PU Link Prediction Setting

？

u1u2

u3

u4link features label

(u1, u2) +1

u5

(u3, u5) +1… … …

(ux, uy) -1

… … …

(ux, uy) -1

information used to extract feature vectors for these links

(u5, u4) supervised learning model

network structure

link to be predictedscores

existinglinks

what kind of informationare there in the network?

Post

User

Location

Time!stampWord

written atcontain

checkin at

write

follow/follow-1

write-1

checkin at-1

contain-1 written at-1

network schemaNetwork Schema and Intra-Network Social Meta Path

count the # meta pathinstances in the networkconnecting certain user

pairs (u, v)

Multi-Network Collective Link Prediction Framework

Network 1

Network N

…

y(P1), y(U1)y(L1)

update network

Network 2

update network

update network

build predict

build predictP1,U1 L1

build predict

L2P2,U2y(P2), y(U2)

y(L2)

y(Ln)Pn,Un Ln

feature extraction

… …

p(Ln)

p(L2)

p(L1)x�(P1),x�(U1)

x�(P2),x�(U2)

x�(Pn),x�(Un)

x (Pn),x (Un)

x (P2),x (U2)

x (P1),x (U1)x (L1)

x (L2)

x (Ln)

x�(Ln)

x�(L2)

x�(L1)

y(Pn), y(Un)

M1,MS1

M2,MS2

Mn,MSn

Experiment Settings

• Ground truth: existing social link among users• hide part of the existing links in the test set• build model to discover these links

• Comparison Methods• MLI (Multi-network Link Identifier)• LI (Link Identifier): predict links in each network independently• SCAN(Supervised Cross-Aligned-Network link prediction):

supervised link prediction • SCAN_s (SCAN with source network): features are extracted

based on inter-network meta paths• SCAN_t (SCAN with target network): features are extracted

based on intra-network meta paths

• Evaluation Metrics• AUC, Accuracy, F1

Experiment Results

simultaneous link prediction is better than independent link prediction

PU link prediction setting can improve the results

using features based on intra-network meta paths and inter-network meta paths simultaneously can achieve better results

Outline

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4


New Social Networks Emerge Every Year

2010200920082007200620052004 2011launch year

http://en.wikipedia.org/wiki/List_of_social_networking_websites

http://en.wikipedia.org/wiki/List_of_social_networking_websites

Emerging Networks Attract Limited Usages

Locations

Tips

8 AM 12 PM 4 PM 8 PM 11 PM

User Accounts

Temporal Activities

Emerging Networks Contains Sparse Information

Hard to calculate effective closeness measures among users

due to the sparse information

Emerging Network Community Detection

closeness measures among users:Intimacy

Challenge: Information Sparsity Problem• Solution: use both Link and Attribute information

Intimacy Calculation with both Connection and Attribute Information

user

user time loc word

time

loc

wor

d

0

network transitional matrix

weighted normalized adjacency matrices(1) among users(2) between users and attributes

Locations

Tips

8 AM 12 PM 4 PM 8 PM 11 PM

User Accounts

Temporal Activities

User Accounts

Locationslocate

locate

Tweets

8 AM 12 PM 4 PM 8 PM 11 PM

Temporal Activities

Users use multiple social networks simultaneously

Intimacy Calculation with Information across Aligned Networks

00

00 network transitional matrixof Twitter

network transitional matrixof Foursquare

anchor transitional matrix

weighted aligned network transitional matrix

Intimacy Calculation with Information across Aligned Networks

high-dimensional stationary aligned

network transitional matrix

we only care about the intimacy matrix among users (lower dimension)

sub-matrix at the upper left corner

intimacy matrix among users in Foursquare

00

00

Outline

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5 Future work 2: Viral Marketing across Networks

Future Work 1: Viral Marketing across Aligned Networks

• Viral Marketing Background Knowledge

Linear Threshold (LT) Model

• A node v has threshold θv ~ U[0,1] • A node v is influenced by each neighbor w

according to a weight bvw such that

• A node v becomes active when at least

• It will stop if no other nodes can be activated

, active neighbor of

v w vw v

b θ≥∑

, neighbor of

1v ww v

b ≤∑

Details in Propagation

• Diffusion weight

• Activation Probability:

• Aggregation: logistic function

Aligned Heterogeneous Network Influence Maximization 1. The problem is NP-hard.

2. Based on our diffusion model, influence function is monotone.

3. Based on our diffusion model, influence function is submodular.

4. Algorithm: Step-wise greedy algorithm achieves a (1-1/e)-approximation.

Outline

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6 Summary and Selected References6



KnowledgeDiscovery

across FusedNetworks

Social Network Alignment

Inter-NetworkSocial Link Prediction

cross-networkcommunity detection

inter-networkViral Marketing

Summary of problems across aligned networks• Social Network Alignment: to

identify shared users across aligned networks;

• Social Link Prediction: to infer the friendship among users across aligned networks;

• Community Detection: to detect the community structure formed by users across aligned networks;

• Viral Marketing: viral marketing across aligned social networks to achieve broader influence.

ReferencesNetwork Alignment and Anchor Link Inference[1] Jiawei Zhang and Philip S. Yu. PCT: Partial Co-Alignment of Social Networks. In: Proceedings of the 25th International World Wide Web Conference (WWW ’16), Montreal, Canada, April 11-15, 2016. [2] Jiawei Zhang and Philip S. Yu. Multiple Anonymized Social Networks Alignment. In: Proceedings of the IEEE International Conference on Data Mining (ICDM ’15), Atlantic City, NJ, USA, November 14-17, 2015. [3] Jiawei Zhang and Philip S. Yu. Integrated Anchor and Social Link Predictions across Partially Aligned Social Networks. In: Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI ’15), Buenos Aires, Argentinean, July 25-31, 2015. [4] Jiawei Zhang, Weixiang Shao, Senzhang Wang, Xiangnan Kong and Philip S. Yu. PNA: Partial Network Alignment with Generic Stable Matching. In: Proceedings of the 16th IEEE International Conference on Information Reuse and Integration (IEEE IRI '15), San Francisco, CA, USA, August 13-15, 2015. [5] Xiangnan Kong, Jiawei Zhang and Philip S. Yu. Inferring Anchor Links across Heterogeneous Social Networks. In: Proceedings of the 22nd ACM International Conference on Information and Knowledge Management (CIKM ’13), San Francisco, CA, October 27-November 1, 2013.

Link Prediction and Recommendation[6] Jiawei Zhang, Philip S. Yu and Zhi-Hua Zhou. Meta-path based Multi-network Collective Link Prediction. In: Proceedings of the 20th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD ’14 ), New York City, NY, August 24-27, 2014. [7] Jiawei Zhang, Xiangnan Kong and Philip S. Yu. Transferring Heterogeneous Links across Location-Based Social Networks. In: Proceedings of the 7th International ACM Conference on Web Search and Data Mining (WSDM ’14), New York City, NY, February 24-28, 2014. [8] Jiawei Zhang, Xiangnan Kong and Philip S. Yu. Predicting Social Links for New Users across Aligned Heterogeneous Social Networks. In: Proceedings of the 13th IEEE International Conference on Data Mining (ICDM ’13), Dallas, Texas, December 7-10, 2013.

ReferencesClustering and Community Detection[9] Jiawei Zhang and Philip S. Yu. Community Detection for Emerging Networks. In: Proceedings of the 15th SIAM International Conference on Data Mining (SDM ’15), Vancouver, British Columbia, Canada, Apr 30-May 2, 2015. [10] Jiawei Zhang and Philip S. Yu. MCD: Mutual Clustering across Multiple Heterogeneous Networks. In: Proceedings of IEEE BigData Congress (IEEE BigData Congress ’15), New York City, NY, June 27-July 2, 2015. [11] Weixiang Shao, Jiawei Zhang, Lifang He and Philip S. Yu. Multi-Source Multi-View Clustering via Discrepancy Penalty. In: Proceedings of the International Joint Conference on Neural Networks (IJCNN '16), Vancouver, Canada, July 24-29, 2016. [12] Songchang Jin, Jiawei Zhang, Philip S. Yu, Shuqiang Yang and Aiping Li. Synergistic Partitioning in Multiple Large Scale Social Networks. In: Proceedings of the 2014 IEEE International Conference on Big Data (IEEE BigData ’14), Washington, DC, October 27-30, 2014

Information Diffusion and Viral Marketing[13] Qianyi Zhan, Jiawei Zhang, Senzhang Wang, Philip S. Yu and Junyuan Xie. Influence Maximization across Partially Aligned Heterogenous Social Networks. In: Proceedings of the 19th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD ’15), Ho Chi Minh City, Vietnam, May 19-22, 2015. [14] Jiawei Zhang, Philip S. Yu, Yuanhua Lv, and Qianyi Zhan. Information Propagation at Workplace via Diffusion Channel Aggregation. Submitted to the Proceedings of the 22nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD).

ReferencesEnterprise and Professional Social Networks Knowledge Discovery[15] Jiawei Zhang, Philip S. Yu and Yuanhua Lv. Organizational Chart Inference. In: Proceedings of the 21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD ’15), Sydney, Australia, August 10-13, 2015. [16] Jiawei Zhang, Yuanhua Lv and Philip S. Yu. Enterprise Social Link Prediction. In: Proceedings of the 24th ACM International Conference on Information and Knowledge Management (CIKM ’15), Melbourne, Australia, October 19-23, 2015. [17] Qingbo Hu, Sihong Xie, Jiawei Zhang, Qiang Zhu and Philip S. Yu. HeteroSales: Utilizing Heterogeneous Social Networks to Identify the Next Enterprise Customer. In: Proceedings of the 25th International World Wide Web Conference (WWW ’16), Montreal, Canada, April 11-15, 2016.

Geo-spatial Information Fusion and Mining[18] Jiawei Zhang, Xiao Pan, Moyin Li and Philip S. Yu. Bicycle-Sharing System Analysis and Trip Prediction. In: Proceedings of the 17th International Conference on Mobile Data Management (MDM '16), Porto, Portugal, June 13-16, 2016.

Other Correlated Papers[19] Senzhang Wang, Honghui Zhang, Jiawei Zhang, Philip S. Yu and Zhoujun Li. Inferring Diffusion Networks with Structure Transfer. In: Proceedings of the 20th International Conference on Database Systems for Advanced Applications (DASFAA ’15), Hanoi, Vietnam, April 20-23, 2015. [20] Jiawei Zhang, Qianyi Zhan, and Philip S. Yu. Concurrent Alignment of Multiple Anonymized Social Networks with Generic Stable Matching. Submitted to the Springer Advances in Intelligent Systems and Computing (AISC) Journal.

Fusion of Heterogeneous Social Networks for Synergistic Knowledge Discovery

Jiawei Zhang [email protected]

Q & A

mailto:[email protected]

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