Finding Topic-sensitive Influential Twitterers

Presenter 吴伟涛

TwitterRank:

Outline

1. Introduction

2. Dataset

3. Topic modeling and Homophily in Twitter

4. TwitterRank

5. Experiment and results

6. Conclusions

Introduction

MotivationThe number of followers is the main metric to identify

influential twitterers. Twitterer’s influence may vary with

different topics.

SolutionIdentify influential twitterers taking both the topical

similarity between users and the link structure into

account.

Introduction

Two contributions of this paper:

1.First to report homophily in Twitter

2.Introduce TwitterRank to measure the

topic-sensitive influence of the twitterers.

Outline

Introduction

Dataset

Topic modeling and Homophily in Twitter

TwitterRank

Experiment and results

Conclusions

Twitter Dataset

1. Obtain a set of top-1000 Singapore-based twitterers. Denote the set as S, |S|=996.

2. Crawled all the followers and the friends of each s ∈ S and stored them in set S’.

3. Let S’’= S ∪ S’, and S* = {s|s ∈ S’’, and s is from Singapore}.|S*| = 6748. For each s ∈ S*, crawled all the tweets she had published so far. Denote it as T. |T|=1,021,039.

Tweet Distribution

Tweet Distribution

Reciprocity in Following Relationships

Reciprocity in Following Relationships

72.4% of the twitterers follow more than 80% of their followers

80.5% of the twitterers have 80% of their friends follow them back

Casual following or homophily?

Outline

Introduction

Dataset

Topic modeling and Homophily in Twitter

TwitterRank

Experiment and results

Conclusions

Homophily in Twitter

Q1: Are twitterers with “following” relationships

more similar than those without according to

the topics they are interested in?

Q2: Are twitterers with reciprocal “following”

relationships more similar than those without

according to the topics they are interested in?

Topic modeling

定义距离：Dist(i,j)

计算平均距离

验证：

?

验证： ?

follow nofollow计算平均距离

asymsym

follow nofollow sym asym

结论：homophily

Topic Modeling

Goal:

Automatically identify the topics that twitterers are

interested in based on the tweets they published.

Latent Dirichlet Allocation (LDA) model is applied

Topic Modeling

LDA-based generative process for generating a doc:

1.For each document, pick a topic from its

distribution over topic,

2.Sample a word from the distribution over the words

associated with the chosen topic.

3.The process is repeated for all the words in the

document.

Topic Modeling Results

1. DT — D×T matrix

D: the number of users

T: the number of topics

DTij : the number of times a word in user si’s

tweets has been assigned to topic tj.

Topic Modeling

we first row normalize the DT matrix as DT’ such

that ||DT’i ·||1=1 for each row DT’i · . Thus each row

of matrix DT’ is basically the probability distribution

of twitterer si’s interest over the T topics, i.e. each

element DT’i j captures the probability that twitterer

si is interested in topic tj.

Topic Difference

Definition 1: the topical difference between two

twitterers si and sj can be calculated as:

( , ) 2* ( , )JSdist i j D i j

DJS(i,j) is the Jensen-Shannon Divergence between the two probability distributions DT’i · and DT’j ·

which is defined as:' '1

( , ) ( ( || ) ( || ))2JS KL i KL jD i j D DT M D DT M

Topic Difference

M is the average of the two probability distibutions,

i.e.

DKL is the Kullback-Leibler Divergence which defines

the divergence from distribution Q to P as:

' '1( )2 i jM DT DT

( )( || ) ( ) log

( )KLi

P iD P Q P i

Q i

Hypothesis Testing

* Note that, this part of work, hypothesis testing,

and topic distillation as well, is applied on a set of

twitterers who publish more than 10 tweets in total.

We denote this set as , and | | = 4050.

*uS

*uS

Hypothesis Testing (I)

Formalize Q1 as a two-sample t-tet:

: the mean topical difference of the pairs of

users with “following” relationship.

: the mea topical difference of those without.

follow

nofollow

0 : follow nofollowH

1 : follow nofollowH

Hypothesis Testing (I)

Result:

The null-hypothesis H0 is rejected at significant

level .

0.01

Hypothesis Testing (II)

Formalize Q2 as a two-sample t-tet:

: the mean topical difference of the pairs of

users with reciprocal following relationship.

: the mea topical difference of pairs of users

with only one-direction relationship.

0 : sym asymH

1 : sym asymH

sym

asym

Hypothesis Testing (II)

Result:

The null-hypothesis H0 is rejected at significant

level .

0.01

Implication

Homophily phenomenon does exist:

-The answer to Q1 is yes.

-The answer to Q2 is also yes.

-There are twitterers who are serious in following others.

Outline

Introduction

Dataset

Topic modeling and Homophily in Twitter

TwitterRank

Experiment and results

Conclusions

Topic-specific TwitterRank

A topic-specific random walk model is applied to calculate the user’s influential score.

The transition matrix for topic t, denoted as Pt . The transition probability of surfer from follower si to friend sj is:

:

| |( , ) * ( , )

| |i a

jt t

aa s s

Tp i j sim i j

T

' '( , ) 1 | |t it jtsim i j DT DT

Topic-specific TwitterRank

Topic-specific teleportation:

The influence scores of twitters are calculated iteratively:

Aggregation of topic-specific TwitterRank:

''t tE DT

(1 )t t t tTR P TR E

t tt

TR r TR

Outline

Introduction

Dataset

Topic modeling and Homophily in Twitter

TwitterRank

Experiment and results

Conclusions

Comparison with other Algorithms

Comparison to:

In-degree

PageRank

Topic-sensitive PageRank

Comparison in recommendation scenario.

Recommendation task

St

Recommendation task

s0

sf

L

Evaluation

Assume A is a ranked list recommended by any of the algorithms. Let A(si) to be

the rank of si in A. The quality of the recommendation Q(A) is measured as Q(A)=|{si|si ∈St, and A(si)<A(sf)}|. The

lower the value of Q(A) is, the higher the quality of corresponding algorithm is.

Criteria to generate L set

The number of followers that sf has.

The number of tweets that sf published.

Topical difference between s0 and sf .

Whether reciprocal relationship between s0 and sf .

Experiment Results

Experiment Results

All performs better in Ldf than in Ldh:

- There are twitterers who “follow” because of the

topical similarity between them and their friends.

This support the homophily phenomenon. TR is outperformed in Lfh, Ltl and Ldh:

- InD perform the best in Lfh. This is because

twitterers “following” benaviors have already been

biased toward those with more followers.

Experiment Results

- TR performs the worst in Ltl, because LDA-based

topic distillation needs more contents to achieve

reasonable accuracy.

- TR outperforms all the other algorithms except InD

in Ldh. There still exist some twitters who do not

“follow” based on topical similarity, although homophily is observed.

Outline

Introduction

Dataset

Topic modeling and Homophily in Twitter

TwitterRank

Experiment and results

Conclusions

Conclusion and future work Homophily does exist:

- Not all users just randomly “follows”.

Future work:- To make the algorithm more robust to manipulation, e.g

purposely publish large number of tweets.

- To classify different categories of users by studying their

following behaviors more closely.

- Incremental topic distillation/ event detection.

Thank you