A formal model to the routing questions problem

A formal model to the routing questions problem in the context of

twitter

Cleyton Caetano de Souza

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

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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