Apresentação no ICWI 2011

1. A formal model to the routing
questions problem in the context of
twitter
Cleyton Caetano de Souza

2. Schedule
1. Introduction
1. Problem
2. Related Works
3. The model
1. The problem
2. Details
4. A solution to the model
5. Conclusion
6. Future Works Cleyton-UFCG 2

3. Introduction
• Web has became essential
– Web, a repository of information
• Search Engines
– Looking answers
• Social Networks
– Waiting answers
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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?
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 )
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16. Similarity
• Any combination of this equations could be
used
• We choose use
𝑠𝑖𝑚1 𝑢, 𝑣 𝑠𝑖𝑚2 𝑢, 𝑣 𝑠𝑖𝑚3 𝑢, 𝑣
𝑠𝑖𝑚 𝑢, 𝑣 = ∗ ∗
1 − 𝑠𝑖𝑚1 𝑢, 𝑣 1 − 𝑠𝑖𝑚2 𝑢, 𝑣 1 − 𝑠𝑖𝑚3 𝑢, 𝑣
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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
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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
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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?
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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]
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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
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22. Solving the Model-Step 2
• The we display this users in a matrix
𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠 𝑢 𝑥|𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠 𝑢 |
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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
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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 𝑓1
𝑝 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
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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 )
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26. Solving the Model-Step 5
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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
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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
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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
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30. Thank You
• Any Question?
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