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

Content Introduction Trust Implemented algorithms Application Evaluation Results

Introduction Recommendation systems Social networks = information Relations between users

Trust Computer science Sociology Psychology Hard definition 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 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

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

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

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 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

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

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

Application interface

Application interface

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

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

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

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

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 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

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%

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

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

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 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

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