MASTER THESIS num. 802

ANALYSIS OF ALGORITHMS FOR DETERMINING TRUST AMONG

FRIENDS ON SOCIAL NETWORKS

Mirjam Šitum

Ao. Univ. Prof. Dr. Dieter MerklUniv. Ass. Mag. Julia NeidhardtDoc. Dr. Sc. Vedran Podobnik

Content

• Introduction• Trust• Implemented algorithms• Application• Evaluation• Results

Introduction

• Recommendation systems• Social networks = information• Relations between users

Trust

• Sociology• Psychology

• Computer science

Direct trust Peer-to-peer trust

Hard definition

Depends on the goal

Trust

Trust can have these properties:• Context specific• Dynamic• Propagative• Aggregative• Asymetric

Trust

Implemented algorithms:

• Direct trust algorithm• Direct normalized trust algorithm• Tidal trust algorithm• Mole trust algorithm• Eigen trust algorithm

Direct trust algorithmInteractions(I) Weights

Friend likes post made by user

Friend comments on post made by user

Friend is tagged in post made by user

Friend commented on a photo of user

Friend liked photo of user

Friend is tagged in photo of user

𝑡𝑟𝑢𝑠𝑡 (𝑒𝑔𝑜𝑢𝑠𝑒𝑟 , 𝑓𝑟𝑖𝑒𝑛𝑑𝑥 )=∑𝑖∈ 𝐼

𝑖 (𝑥 )∗𝑤𝑖

∑𝑖 ∈𝐼

𝑤 𝑖

Direct trust normalization• Variation of direct algorithm

Number of one type of friend x’s interaction with user

Total number of interactions i of all user’s friends

Tidal trust algorithm• Uses network built by

direct trust algorithm• Uses shortest paths

to the sink• Favors higher trust

values

Source

Sink

9 8 10

9 108

10 9

8 6

9 8 10

9 9

Threshold =9

8 7 6

6.95

Mole trust algorithm

• Similar to tidal trust

Differences:• Doesn’t stop when sink is found• Stops at depth d • Treshold = 60% of highest trust value towards the

sink

Eigen trust algorithm

• Uses network built by direct normalized trust algorithm

• Trust values

Source

Sink0.3

0.5

0.2

0.6

0.4

0.2

0.8

0.5

0.5

0.2

0.3

0.5∗0.2+0.3∗0.4∗0.5=𝟎 .𝟏𝟔

Application

• Web & Facebook Application• Developed in PHP

3 main functionalities:• Collecting & storing user data from Facebook• Computing trust• Survey

Application Content

1. Part• 5 questions o Best friends on Facebooko Best Friends in real lifeo Music recommendation o Watching over pet o Travel companion

2. Part• User rates algorithm results

Application interface

Application interface

2 Steps in the research

1. Step - Calibration of weights in direct algorithmo 100 userso 1 question

2. Step – Evaluation of algorithmso 104 userso 5 questions + ratings

Measures for algorithm evaluation1. Kendal Tau Distance

user 1. list indexes 2. list indexes

A 1 3

B 2 4

C 3 1

D 4 2

E 5 5

Pair (A,B) (A,C) (A,D) (A,E) (B,C) (B.D) (B,E) (C,D) (C,E) (D,E)First list indexes

1 < 2 1 < 3 1 < 4 1 < 5 2 < 3 2 < 4 2 < 5 3 < 4 3 < 5 4 < 5

Second list

indexes3 < 4 3 > 1 3 > 2 3 < 5 4 > 1 4 > 2 4 < 5 1 < 2 1 < 5 2 < 5

Count - X X - X X - - - -

Measures for algorithm evaluation2. Rank Difference

Friends User Perception Ranking Algorithm Ranking Difference

A 1 53 52

B 2 8 6

C 3 1 2

D 4 15 11

E 5 3 2

Total Difference = 73

Measures for algorithm evaluation3. Exact (Match) Count

Friend User Perception Ranking Algorithm Ranking

A 1 20

B 2 2

C 3 5

D 4 15

E 5 3

Match Count = 3

Exact Match Count = 1

Calibrating the weights• 100 users chose top 5 friends from real life• combination of weight values from 1 to 20, step 0.5• for every combination -> average rank difference per user was

calculated• weight combination with lowest average rank difference was chosen

Weight Description Value

W1 Likes on user posts 2.5

W2 Comments on user posts 5

W3 Tags on user posts 10.5

W4 Likes on user photos 1

W5 Comments on user photos 12

W6 Tags on user photos 2

Statistics

• 100 users – 1. part for calibration

• 104 users – filled survey

• 215 users – in the database

• 108 users – female

• 107 users – male

• 83864 friendships (42403 have direct trust value)

• 34656 photos, 71806 comments, 186827 likes ,

111777 tags

• 62747 posts, 46873 comments, 158183 likes

and 3618 tags

Evaluation

Algorithms:• Direct • Normalized Direct• Tidal• Mole• Eigen

Combinations:• Direct + Mole• Direct +Tidal• Norm. Direct + Eigen

Measures:• Kendal Tau Distance• Rank Difference• Match Count• Direct Match Count

Results

• Direct algorithms - more precise

• Eigen trust – highest number of big mistakes

• Eigen trust + weighted direct combination – almost precise as direct = interesting for future research

First question: chose top 5 friends from real life

Direct

Norm. D

irect

MoleEig

enTid

al

Mole+Dire

ct

Eigen

+Norm

.Direct

Tidal+

Direct

0

10

20

30

40

50

60

Rank DifferenceRank Difference Filtered

Results

• Peer-to-peer algorithms - better ordering of top 5 friends

• Less precise because of sparse network

• Can be used when• No direct connection between

nodes

• In combination with direct algorithms for more information

• Direct algorithms – average top 5 guess: more than 40%

First question: chose top 5 friends from real life

Direct

Norm. D

irect

MoleEig

enTid

al

Mole+Dire

ct

Eigen

+Norm

.Direct

Tidal+

Direct

00.5

11.5

22.5

33.5

44.5

5

Kendal Tau Distance

Direct

Norm. D

irect

MoleEig

enTid

al

Mole+Dire

ct

Eigen

+Norm

.Direct

Tidal+

Direct

0

0.5

1

1.5

2

2.5

Match CountExact Count

Results

• For rest of questions:• 2nd question: „best friends from Facebook”• Three context questions

• Similar results between algorithms• Worse results than for first question, for all algorithms

• Weights calibrated for first question

Results• Direct algorithm

• Questions including interaction and socialization – better results• Questions including recommendation, reliance and credence – worse

results• Similar results for normalized version

1 2 3 4 50

5

10

15

20

25

30

35

Rank differenceRank Difference Fil-tered

1 2 3 4 50

0.5

1

1.5

2

2.5

Match CountExact Count

Results• Peer-to-peer algorithms

• Hard to say which algorithms best for which context• Every algorithm has similar results for every

question• Eigen most precise with question about „friends to

go with on a trip”• Mole and Tidal most precise with question about

music recommendation

Results

• 4 algorithm results shown to user• Users graded algorithms• Grades from 1-5

AlgorithmAverage grade for sentence Your best friends from real

life

Average grade for sentence Your best friends from

Facebook

Direct trust algorithm 3.2885 3.3269

Combination of Mole trust and direct trust algorithm

2.5384 2.6731

Combination of Tidal trust and direct trust algorithm

2.6154 2.5962

Combination of Eigen trust and norm. Direct trust

algorithm3.5096 3.3846

Results

• Last part of the survey• Users feedback on algorithms

• Mostly friends from school/college

• Direct algorithm -> 35 users said: friends from school/college

• Trust computed from user interactions =>interactions in real life are translated to the social network setting

• People transfer socialization from real life to social networks

Conclusion

• Direct trust algorithms show better result• Normalized direct algorithm was better variant

• Peer-to-peer algorithms:• were less precise due to sparse network• showed better ordering for top 5 friends

• Weakness: sparse network, Advantage: direct user feedback

• People have need to transfer real life socializing to social networks

• Future work:• Test peer-to-peer algorithms with less sparse networks• Research ways of algorithm combination