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A formal model to the routing questions problem in the context of
Cleyton Caetano de Souza
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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
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Introduction
• Web has became essential
– Web, a repository of information
• Search Engines
– Looking answers
• Social Networks
– Waiting answers
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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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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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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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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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The Model
• Each useru has the attributes
– 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠𝑢 that contains all users which follows 𝑢
– 𝐹𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔𝑢 that contains all users which are followed by 𝑢
– 𝑀𝑢 = 𝑚1, … ,𝑚 𝑀 a ordered list that contains all
messages posted for 𝑢
• Each message 𝑚 has the attributes
– 𝑑𝑚- the post date
– 𝑠𝑚- the string posted
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The Problem
Given a query 𝑞 posted by 𝑢,
𝑓 ∈ 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠𝑢 and 𝑝𝑓,𝑞 a function
that tell us the chances of
𝑓 provides a good answer
– Find: 𝑓
– To: 𝑀𝑎𝑥 𝑝𝑓,𝑞
– Over: 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠𝑢
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The problem
• We believe that 𝑝𝑓,𝑞 has a correlation with
three things
– 𝑘𝑓,𝑞 – the knowledge that 𝑓 in relation with 𝑞
– 𝑡𝑢,𝑓 – the trust of 𝑢 has in 𝑓
– 𝑎𝑓 – the level of activity of 𝑓
• That way will actually want to find the best combination of: 𝑘𝑓,𝑞, 𝑡𝑢,𝑓 and 𝑎𝑓
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Knowledge
• Each message 𝑚𝑢 corresponds a fraction of the total expertise of 𝑢
𝑘𝑢 = 𝑘𝑚𝑢𝑚𝑢∈𝑀𝑢
• In IR we represent this fraction as a vector of the words/token contained in 𝑚𝑢
• So the 𝑘𝑢 is a vector where each coordinate represents a token and its value is the frequency of this token in all messages 𝑚𝑢
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Knowledge
• If 𝑡𝑞 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
𝑘𝑓,𝑞 = 𝑡𝑞 ∗ 𝑡𝑘𝑢𝑡∈𝑞
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Trust
• Trust is related to
– Friendship [Schenkel et al 2008]
– Similarity [Kuter and Golbeck 2010]
• So we believe (and simplify) 𝑡𝑢,𝑣 = 𝑓𝑢,𝑣 ∗ 𝑠𝑖𝑚 𝑢, 𝑣
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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
𝑓𝑢,𝑣 =|𝑚𝑒𝑛𝑡𝑖𝑜𝑛𝑠𝑢 𝑣 |
𝑚𝑒𝑛𝑡𝑖𝑜𝑛𝑠𝑢
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Similarity
• The similarity measures how to users are equal under some criterion
• Appears intuitively that the similarity is related to equality among the attributes
𝑠𝑖𝑚1 𝑢, 𝑣 ∝𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠𝑢 ∩ 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠𝑣𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠𝑢 ∪ 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠𝑣
𝑠𝑖𝑚2 𝑢, 𝑣 ∝𝐹𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔𝑢 ∩ 𝐹𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔𝑣𝐹𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔𝑢 ∪ 𝐹𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔𝑣
𝑠𝑖𝑚3 𝑢, 𝑣 ∝ 𝑠𝑖𝑚(𝑘𝑢, 𝑘𝑣)
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Similarity
• Any combination of this equations could be used
• We choose use
𝑠𝑖𝑚 𝑢, 𝑣 =𝑠𝑖𝑚1 𝑢, 𝑣
1 − 𝑠𝑖𝑚1 𝑢, 𝑣∗𝑠𝑖𝑚2 𝑢, 𝑣
1 − 𝑠𝑖𝑚2 𝑢, 𝑣∗𝑠𝑖𝑚3 𝑢, 𝑣
1 − 𝑠𝑖𝑚3 𝑢, 𝑣
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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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Activity
• Activity means the mean time between the messages posted by 𝑢
𝑎𝑢 =𝑡𝑜𝑑𝑎𝑦 − 𝑑𝑚, 𝑀𝑢 + 𝑑𝑚,𝑖+1 − 𝑑𝑚,𝑖
|𝑀|𝑖=1
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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Solving the Model
• Calculate the tuples (𝑘𝑓,𝑞 , 𝑡𝑢,𝑓, 𝑎𝑓) to each
user is a simple task
• But, how decides who is the best?
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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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Solving the Model-Step 1
• The resolution of the model starts calculating the tuple (𝑘𝑓,𝑞 , 𝑡𝑢,𝑓, 𝑎𝑓) to each user
𝑓𝑢 ∈ 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠𝑢
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Solving the Model-Step 2
• The we display this users in a matrix 𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠𝑢 𝑥|𝐹𝑜𝑙𝑙𝑜𝑤𝑒𝑟𝑠𝑢|
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Solving the Model-Step 3
• We create a function 𝑚𝑎𝑝 𝑥 which will map the values of (𝑘𝑓,𝑞 , 𝑡𝑢,𝑓, 𝑎𝑓) in a same scale
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Solving the Model-Step 4
• For each pair 𝑓1, 𝑓2 |𝑓1 ≠ 𝑓2we calculate
𝑝𝑓1,𝑓2 =𝑘𝑓1,𝑞
𝑘𝑓2,𝑞
𝑥
∗𝑡𝑢,𝑓1𝑡𝑢,𝑓2
𝑦
*𝑎𝑓1𝑎𝑓2
𝑧
• 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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Solving the Model-Step 5
• If 𝑝𝑓1,𝑓2 > 0 we put 1 in position (𝑓1, 𝑓2) and 0
in position (𝑓2, 𝑓1)
• If 𝑝𝑓1,𝑓2 < 0 we put 0 in position (𝑓1, 𝑓2) and 1
in position (𝑓2, 𝑓1)
• If 𝑝𝑓1,𝑓2 = 0 we put 1 in position (𝑓1, 𝑓2) and 1
in position (𝑓2, 𝑓1)
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Solving the Model-Step 5
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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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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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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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Thank You
• Any Question?
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