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A formal model to the routing questions problem

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Apresentação no ICWI 2011

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A formal model to the routing questions problem

1. 1. A formal model to the routingquestions problem in the context of twitter Cleyton Caetano de Souza
2. 2. Schedule1. Introduction 1. Problem2. Related Works3. The model 1. The problem 2. Details4. A solution to the model5. Conclusion6. Future Works Cleyton-UFCG 2
3. 3. Introduction• Web has became essential – Web, a repository of information• Search Engines – Looking answers• Social Networks – Waiting answers Cleyton-UFCG 3
4. 4. Problem• Could occurs problems when you publish your question – None answer – None see – Many answers• Direct the answer to someone – You ensure a answer, but will be a good one? Cleyton-UFCG 4
5. 5. Problem• Informally, the problem that we proposes to solve is given a question posted by a user (asker) in Twitter, find among his followers that user with the characteristics: – (1) knows the answer – (2) has the trust of the questioner – (3) provide the answer quickly Cleyton-UFCG 5
6. 6. Related Works• (Morris, Teevan e Panovich 2010a) – 93.5% of users received answers to their question after post them and these responses – in 90.1% of cases, were provided within one day• Applications – Aardvark (Horowitz and Kamvar 2010) – Q-Sabe (Andrade et al 2003)• The differential of our research Cleyton-UFCG 6
7. 7. The Model• The twitter is defined by the tuple 𝑇 = {𝑈, 𝑅}• Where 𝑈 = {𝑢1 , … , 𝑢 𝑈 } is a set of users• And 𝑅 is the set of all relationships 𝑟𝑖,𝑗 between two users 𝑖 and 𝑗. – The existence of 𝑟𝑖,𝑗 means that i follows j, this way 𝑟𝑖,𝑗 ≠ 𝑟𝑗,𝑖 Cleyton-UFCG 7
8. 8. The Model• Each useru has the attributes – 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠 𝑢 that contains all users which follows 𝑢 – 𝐹𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑢 that contains all users which are followed by 𝑢 – 𝑀 𝑢 = 𝑚1 , … , 𝑚 𝑀 a ordered list that contains all messages posted for 𝑢• Each message 𝑚 has the attributes – 𝑑 𝑚 - the post date – 𝑠 𝑚 - the string posted Cleyton-UFCG 8
9. 9. The Problem Given a query 𝑞 posted by 𝑢, 𝑓 ∈ 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠 𝑢 and 𝑝 𝑓,𝑞 a function that tell us the chances of 𝑓 provides a good answer– Find: 𝑓– To: 𝑀𝑎𝑥 𝑝 𝑓,𝑞– Over: 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠 𝑢 Cleyton-UFCG 9
10. 10. The problem• We believe that 𝑝 𝑓,𝑞 has a correlation with three things – 𝑘 𝑓,𝑞 – the knowledge that 𝑓 in relation with 𝑞 – 𝑡 𝑢,𝑓 – the trust of 𝑢 has in 𝑓 – 𝑎 𝑓 – the level of activity of 𝑓• That way will actually want to find the best combination of: 𝑘 𝑓,𝑞 , 𝑡 𝑢,𝑓 and 𝑎 𝑓 Cleyton-UFCG 10
11. 11. Knowledge• Each message 𝑚 𝑢 corresponds a fraction of the total expertise of 𝑢 𝑘𝑢 = 𝑘 𝑚𝑢 𝑚 𝑢 ∈𝑀 𝑢• In IR we represent this fraction as a vector of the words/token contained in 𝑚 𝑢• So the 𝑘 𝑢 is a vector where each coordinate represents a token and its value is the frequency of this token in all messages 𝑚 𝑢 Cleyton-UFCG 11
12. 12. Knowledge• If 𝑡 𝑞 is the frequency of the token 𝑡 in 𝑞, the knowledge needed to answer satisfactorily the question is calculated as a inner product between the vector that represent the follower and the vector that represent the question 𝑘 𝑓,𝑞 = 𝑡𝑞 ∗ 𝑡𝑘𝑢 𝑡∈𝑞 Cleyton-UFCG 12
13. 13. Trust• Trust is related to – Friendship [Schenkel et al 2008] – Similarity [Kuter and Golbeck 2010]• So we believe (and simplify) 𝑡 𝑢,𝑣 = 𝑓 𝑢,𝑣 ∗ 𝑠𝑖𝑚 𝑢, 𝑣 Cleyton-UFCG 13
14. 14. Friendship• Friendship measures the importance of a user to another• In Twitter a good estimative of friendship should consider the mentions (connections) between 𝑢 and 𝑣, so |𝑚𝑒𝑛𝑡𝑖𝑜𝑛𝑠 𝑢 𝑣 | 𝑓 𝑢,𝑣 = 𝑚𝑒𝑛𝑡𝑖𝑜𝑛𝑠 𝑢 Cleyton-UFCG 14
15. 15. Similarity• The similarity measures how to users are equal under some criterion• Appears intuitively that the similarity is related to equality among the attributes 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠 𝑢 ∩ 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠 𝑣 𝑠𝑖𝑚1 𝑢, 𝑣 ∝ 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠 𝑢 ∪ 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠 𝑣 𝐹𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑢 ∩ 𝐹𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑣 𝑠𝑖𝑚2 𝑢, 𝑣 ∝ 𝐹𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑢 ∪ 𝐹𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑣 𝑠𝑖𝑚3 𝑢, 𝑣 ∝ 𝑠𝑖𝑚(𝑘 𝑢 , 𝑘 𝑣 ) Cleyton-UFCG 15
16. 16. Similarity• Any combination of this equations could be used• We choose use 𝑠𝑖𝑚1 𝑢, 𝑣 𝑠𝑖𝑚2 𝑢, 𝑣 𝑠𝑖𝑚3 𝑢, 𝑣𝑠𝑖𝑚 𝑢, 𝑣 = ∗ ∗ 1 − 𝑠𝑖𝑚1 𝑢, 𝑣 1 − 𝑠𝑖𝑚2 𝑢, 𝑣 1 − 𝑠𝑖𝑚3 𝑢, 𝑣 Cleyton-UFCG 16
17. 17. Activity• Users not interact with the same intensity• It seems intuitive that the activity level of a user depends on the frequency with he/she post new tweets Cleyton-UFCG 17
18. 18. Activity• Activity means the mean time between the messages posted by 𝑢 |𝑀| 𝑡𝑜𝑑𝑎𝑦 − 𝑑 𝑚, 𝑀 𝑢 + 𝑖=1 𝑑 𝑚,𝑖+1 − 𝑑 𝑚,𝑖 𝑎𝑢 = 𝑀𝑢 +1• As lower this value, most active is the user and bigger the chances of him give a answer quickly Cleyton-UFCG 18
19. 19. Solving the Model• Calculate the tuples (𝑘 𝑓,𝑞 , 𝑡 𝑢,𝑓 , 𝑎 𝑓 ) to each user is a simple task• But, how decides who is the best? Cleyton-UFCG 19
20. 20. Solving the Model• We consider this is a problem of decision making with multiple criteria• We decide to use the Weight Product Model to solve based on [Triantaphyllou and Mann 1989] Cleyton-UFCG 20
21. 21. Solving the Model-Step 1• The resolution of the model starts calculating the tuple (𝑘 𝑓,𝑞 , 𝑡 𝑢,𝑓 , 𝑎 𝑓 ) to each user 𝑓 𝑢 ∈ 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠 𝑢 Cleyton-UFCG 21
22. 22. Solving the Model-Step 2• The we display this users in a matrix 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠 𝑢 𝑥|𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠 𝑢 | Cleyton-UFCG 22
23. 23. Solving the Model-Step 3• We create a function 𝑚𝑎𝑝 𝑥 which will map the values of (𝑘 𝑓,𝑞 , 𝑡 𝑢,𝑓 , 𝑎 𝑓 ) in a same scale Cleyton-UFCG 23
24. 24. Solving the Model-Step 4• For each pair 𝑓1 , 𝑓2 |𝑓1 ≠ 𝑓2 we calculate 𝑥 𝑦 𝑧 𝑘 𝑓1 ,𝑞 𝑡 𝑢,𝑓1 𝑎 𝑓1𝑝 𝑓1,𝑓2 = ∗ * 𝑘 𝑓2 ,𝑞 𝑡 𝑢,𝑓2 𝑎 𝑓2• The values 𝑥,𝑦 and 𝑧 are factors of importance and must be between 0 and 1, besides that 𝑥+ 𝑦+ 𝑧=1 Cleyton-UFCG 24
25. 25. Solving the Model-Step 5• If 𝑝 𝑓1,𝑓2 > 0 we put 1 in position (𝑓1 , 𝑓2 ) and 0 in position (𝑓2 , 𝑓1 )• If 𝑝 𝑓1,𝑓2 < 0 we put 0 in position (𝑓1 , 𝑓2 ) and 1 in position (𝑓2 , 𝑓1 )• If 𝑝 𝑓1,𝑓2 = 0 we put 1 in position (𝑓1 , 𝑓2 ) and 1 in position (𝑓2 , 𝑓1 ) Cleyton-UFCG 25
26. 26. Solving the Model-Step 5 Cleyton-UFCG 26
27. 27. Solving the Model-Step 6 (End)• We calculate the sum of each line of the matrix, this number represents the number of victories of each user• In the end we have• The question will be routed to the user with more victories Cleyton-UFCG 27
28. 28. Conclusion• The differential of our research – We focus in a successful network – We treat the problem over a new perspective – We lead with a recent and interesting problem Cleyton-UFCG 28
29. 29. Future Works• The model was already implemented• We are investigating if our heuristics are coherent• We will investigating – If the indications of the model are accurate – If direct questions is more effective – What factor of importance is most important Cleyton-UFCG 29
30. 30. Thank You• Any Question? Cleyton-UFCG 30