1. MASTER THESIS num. 802 ANALYSIS OF ALGORITHMS FOR DETERMINING TRUST AMONG FRIENDS ON SOCIAL NETWORKS Mirjam Šitum Ao. Univ. Prof. Dr. Dieter Merkl Univ. Ass. Mag. Julia Neidhardt Doc. Dr. Sc. Vedran Podobnik

2. Content Introduction Trust Implemented algorithms Application
Evaluation
Results

3. Introduction Recommendation systems Social networks = information
Relations between users

4. Trust Computer science Sociology Psychology Hard definition
Direct trust Peer-to-peer trust
Hard definition
Depends on the goal

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

6. Trust Implemented algorithms: Direct trust algorithm
Direct normalized trust algorithm
Tidal trust algorithm
Mole trust algorithm
Eigen trust algorithm

7. Direct trust algorithm
Interactions(I)
Weights
Friend likes post made by user
𝑤 1
Friend comments on post made by user
𝑤 2
Friend is tagged in post made by user
𝑤 3
Friend commented on a photo of user
𝑤 4
Friend liked photo of user
𝑤 5
Friend is tagged in photo of user
𝑤 6
𝑡𝑟𝑢𝑠𝑡 𝑒𝑔𝑜 𝑢𝑠𝑒𝑟, 𝑓𝑟𝑖𝑒𝑛𝑑 𝑥 = 𝑖∈𝐼 𝑖 𝑥 ∗ 𝑤 𝑖 𝑖∈𝐼 𝑤 𝑖

8. Direct trust normalization
Number of one type of friend x’s interaction with user
Variation of direct algorithm
𝑖𝑤(𝑥)= 𝑖(𝑥) 𝑦∈𝑌 𝑖(𝑦)
𝑡𝑟𝑢𝑠𝑡 𝑒𝑔𝑜 𝑢𝑠𝑒𝑟, 𝑓𝑟𝑖𝑒𝑛𝑑 𝑥 = 𝑖∈𝐼 𝑖𝑤 𝑥 ∗ 𝑤 𝑖 𝑖∈𝐼 𝑤 𝑖
Total number of interactions i of all user’s friends

9. Tidal trust algorithm Sink Threshold =9 8 6 9 9 8 9 10 9 10 8 9 7 8 6
Uses network built by direct trust algorithm
Uses shortest paths to the sink
Favors higher trust values
Sink
Threshold =9 8 6 9 9 8 9 10 9 10 8 9 7 8 6 10 9 8 10
6.95
Source

10. 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

11. Eigen trust algorithm 0.5∗0.2+0.3∗0.4∗0.5=𝟎.𝟏𝟔 0.2 0.5 0.6 0.4 0.5 0.3
Uses network built by direct normalized trust algorithm
Trust values ∈[0,1]
0.2
0.5
0.6
0.4
0.5
0.5
0.3
Sink
0.2
0.5
0.2
0.8
Source
0.3

12. Application Web & Facebook Application Developed in PHP
3 main functionalities:
Collecting & storing user data from Facebook
Computing trust
Survey

13. Application Content 1. Part 2. Part 5 questions
Best friends on Facebook
Best Friends in real life
Music recommendation
Watching over pet
Travel companion
2. Part
User rates algorithm results

14. Application interface

15. Application interface

16. 2 Steps in the research
1. Step - Calibration of weights in direct algorithm
100 users
1 question
2. Step – Evaluation of algorithms
104 users
5 questions + ratings

17. Measures for algorithm evaluation
1. Kendal Tau Distance
user
1. list indexes
2. list indexes A 1 3 B 2 4 C D E 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 indexes
3 > 1
3 > 2
4 > 1
4 > 2
Count - X

18. Measures for algorithm evaluation
2. Rank Difference
Friends
User Perception Ranking
Algorithm Ranking
Difference A 1 53 52 B 2 8 6 C 3 D 4 15 11 E 5
Total Difference = 73

19. Measures for algorithm evaluation
3. Exact (Match) Count
Friend
User Perception Ranking
Algorithm Ranking A 1 20 B 2 C 3 5 D 4 15 E
Match Count = 3
Exact Match Count = 1

20. 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

21. 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, comments, likes , tags
62747 posts, comments, likes and 3618 tags

22. 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

23. Results First question: chose top 5 friends from real life
Direct algorithms - more precise
Eigen trust – highest number of big mistakes
Eigen trust + weighted direct combination – almost precise as direct = interesting for future research

24. Results First question: chose top 5 friends from real life
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%

25. Results For rest of questions: Similar results between algorithms
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

26. Results Direct algorithm
Questions including interaction and socialization – better results
Questions including recommendation, reliance and credence – worse results
Similar results for normalized version

27. 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

28. Results 4 algorithm results shown to user Users graded algorithms
Grades from 1-5
Algorithm
Average 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 algorithm
3.5096
3.3846

29. 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

30. 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