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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
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
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
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