Structual Trend Analysis for Online Social Networks

Ceren Budak Divyakant Agrawal Amr El AbbadiScience,UCSB SantaBarbara,USA

Reporter: Qi Liu

What to do?

Trend

traditional

structural

coordinate

uncoordinate

What’s new?

• Structural trend definition• Reducing to local triangles counting• Sampling tech for online detection

From where?

• A temporal view• Using spatial properties• Counting, streaming and semi-streaming

Define it!

• Directed G=(N,E)• ejiϵE => ni is one neighbor of nj

• ni mentions Tx => <ni, Tx>

Traditional:Coordinate: Uncoordinate:

High scores for coordinated trend

• Large number of pairs of connected nodes• Large number of mentions• For a complete graph, favors a uniform

distribution• In a power law graph, biased toward

influential nodes

Example for complete graph

f(Tx) = f(Ty) = 2Ng(Tx) = 3N(N-1) g(Ty) = 4N(N-1)

1

N+1

2

2

2 2

Tx Ty

1

1

Example for power law graph

f(Tx) = f(Ty) = K+N-1g(Tx) = 2K(N-1) g(Ty) = 2K+2N-4

Tx

Ty

K

111

1

11K

Significance Validation

• Model-Based Validation– Independent Trend Formation Model• pi,x: external influence

• qi,j,x: internal influence

– Nearest Neighbor model• u: probability from 2 to 1• k: pairs of connected nodes per step

• Analysis-Based Validation

Coordinated differs from traditional

• Spearman rank correlation coefficient(SRCC)– – [-1, +1]

• Average precision–

• difference

What topics detected?

• Vary p and q• Using different score functions• Results:

App: Sybil Attack Detection

• Ranking of Ty: co>tr>un• Breakpoints may means attack• Small p,q and few Sybil nodes, big effect

Analysis-Based Validation

• Twitter data: 467 million posts, 20 million users, spanning 7 months

• 230m posts, 2.7m users, 2960495 hashtags

Extraction

Tr vs Co vs Un

Something new about twitter data

• Choose 60th to 100th topics• Findings: – coordinated trend: 7694 users, 21.5 edges on

average; – uncoordinated trend: 21114 users, 8.6 edges

Prefuse

Hashtag categories effect

• 7 categories: political, technology, celebrity, games, idioms, movies, music and none

Incremental Counting Algorithm

• For a coming <nl,Tx>

•

Reducing to count local triangles

• A directed multi-graph G’ = (N’,E’)• N’ = T U N, E’ = Et U Ef

Sampling tech

• How to work?• Correctness:–

– Xx = Countx / (ps)^2, : triangles sharing edges

Conclusion

• Two trend definitons• A reduction• Sampling tech

THE ENDTHANKS!