Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Predictability of conversation partners

2,400 views

Published on

T. Takaguchi, M. Nakamura, N. Sato, K. Yano, N. Masuda.
Predictability of conversation partners.
Physical Review X, 1, 011008 (2011).

PDF is available free at:

http://prx.aps.org/abstract/PRX/v1/i1/e011008

Published in: Technology, Business
  • Be the first to comment

Predictability of conversation partners

  1. 1. Predictability ofconversation partnersPhys. Rev. X 1, 011008 (2011)1Taro Takaguchi, 1Mitsuhiro Nakamura,2Nobuo Sato, 2Kazuo Yano,and 1,3Naoki Masuda1 Univ. of Tokyo2 Central Research Lab., Hitachi, Ltd.3 JST PRESTO
  2. 2. Conventional assumptions Modeling human behavior such as Mobility patterns Temporal order of in the physical space selecting interaction partners by random (or Lévy) walk by Poisson process Actual behavior: to what degree random / deterministic ?
  3. 3. Predictability of mobility patterns (Song et al., 2010) Mobility patterns are largely predictable. Method: measuring the entropy of the sequence of locations of each cell-phone user How about other components of human behavior?
  4. 4. Predictability of interaction partners interacts with 2 3 2 2 3 1 time discard the timing of events “partner sequence” - Characterize individuals in a social organization - Related to epidemics and information spreading
  5. 5. Data set: face-to-face interaction log in an office Recording from two offices in Japanese companies - subjects: 163 individuals - period: 73 days - total conversation events: 51,879 times We used the data collected by World Signal Center, Hitachi, Ltd., Japan. (株)日立製作所 ワールドシグナルセンタにより収集された データセットを使用した。 Name tag with an infrared module (The Business Microscope system) http://www.hitachi-hitec.com/jyouhou/business-microscope/
  6. 6. Details of data set - A conversation event = communication between close tags - Conversation events: undirected - Time resolution = one minute -Multiple events initiated within the same minute → determine their order at random
  7. 7. Three entropy measures (cf. Song et al., 2010) - for individual who has partners in the recording period, Random entropy: interaction in a totally random manner Uncorrelated entropy: heterogeneity among : the probability to talk with Conditional entropy: second-order correlation : to talk with immediately after with
  8. 8. cf. Entropy “The uncertainty of the random variable” Ex.) coin toss : always tail
  9. 9. Example 1: random 1 Suppose that i 2 3
  10. 10. Example 2: predictable 1 Suppose that i 2 3 (same as example 1)
  11. 11. Quantifying the predictability Mutual information of the partner sequence Interpretation: The information about the NEXT partner that is earned by knowing the PREVIOUS partner rando predictable m
  12. 12. Aim of the study  Examine the predictability of conversation partners - similar to that of mobility patterns  “Predictability” = the mutual information of the partner sequence  Data set: face-to-face interaction log from two offices in Japan i interacts with 2 3 2 2 3 1 events
  13. 13. Histogram of the entropies , regardless of the value of → Partner sequences are predictable to some extent. 40 (a) H i0 (b) number of individuals H i1 4.0 30 H i2 3.5 20 H i2 3.0 10 2.5 0 2.0 1 2 3 4 5 6 7 2.0 2.5 3.0 3.5 4.0 Hi H i1
  14. 14. Significance of Null hypothesis: “ is positive only because of the small data size.” Compare with the value obtained from shuffled partner sequences 3 Error bars: 99% confidential intervals of shuffled sequences (a) 2 ^ Ii Empirical 1 0 1 50 100 150 i in the ascending order of I i
  15. 15. Main cause of the predictability The bursty human activity pattern: characterized by the long-tailed inter-event intervals “ tends to talk with within a short period after talking with .” time of a typical individual
  16. 16. Test 1 (1) Purpose: examine the contribution of the bursty activity Partner sequence in a given day 2 1 3 3 2 1 2 1 3 2 1 3 1 time extract the sequences with each partner 1 with 2 with 3 with
  17. 17. Test 1 (2) Next, shuffle the intervals within each partner 1 with 2 with 3 with merge Calculate of this shuffled sequence 1 2 1 3 1 2 2 3 1 3 2 1 3 1 2 time
  18. 18. Result of Test 1 Generate 100 shuffled sequence Contribution of burstiness 3 (a) bars: mean ± sd for the shuffled sequences Error 2 I iburst Empirical 1 0 1 50 100 150 i in the ascending order of I i
  19. 19. Test 2 Purpose: examine the predictability after omitting the burstiness 2 3 2 2 2 3 3 1 events merge into one Calculate of the merged sequence
  20. 20. Result of Test 2 Shuffle the merged sequence with replacement conditioned that no partner ID appears successively is significantly large. → Predictability remains without the effect of the burstiness. 3 Error bars: 99% confidential intervals of shuffled sequences (b) 2 ^merge Ii Original 1 0 1 50 100 150 merge i in the ascending order of Ii
  21. 21. Summary so far  Partner sequence: predictable to some extent  Main cause of predictability: the bursty activity pattern - Predictability remains after omitting the burstiness. 4.0 (b) 3.5 H i2 3.0 2.5 2.0 2.0 2.5 3.0 3.5 4.0 H i1
  22. 22. Predictability depends on individuals Depends on ’s position in the social network? Histogram of 40 number of individuals 30 20 10 0 0.5 1.0 1.5 2.0 Ii
  23. 23. Conversation network Undirected and weighted network Node : individual Link : a pair of individuals having at least one event Link weight : The total number of events for the pair Node attributions Degree Strength Mean weight
  24. 24. Correlation between and node attributions No correlation Negative Negative
  25. 25. Hypotheses - Fix , small → abundance of weak links (with small weights) □ Hypothesis about links - “Strength of weak ties” (Granovetter, 1973) □ Hypothesis about nodes
  26. 26. Strength of weak ties (Granovetter, 1973) Weak links offer non-redundant contacts. Weak links tend to connect different communities. “bridge”
  27. 27. Hypotheses - Fix , small → abundance of weak links (with small weights) □ Hypothesis about links - Weak links connect different communities. □ Hypothesis about nodes • Individuals connecting different communities → large • Individuals concealed in a community → small
  28. 28. Hypothesis about links Purpose: quantify the degree of being concealed in a community Relative neighborhood overlap of a link (Onnela et al., 2007)
  29. 29. Hypothesis about links “Strength of weak ties” hypothesis; a link with large tends to have a large → increases with : averaged over the links with 0.45 (a) 0.40 <O>w 0.35 Consistent with the hypothesis 0.30 0.2 0.4 0.6 0.8 1.0 P cum(w ) fraction of the links with
  30. 30. Hypotheses - Fix , small → abundance of weak links (with small weights) □ Hypothesis about links - Weak links connect different communities. □ Hypothesis about nodes • Individuals connecting different communities → large • Individuals concealed in a community → small
  31. 31. Hypothesis about nodes Purpose: quantify the degree of being concealed in a community Clustering coefficient of a node (Watts and Strogatz, 1998)
  32. 32. Abundance of triangles - 3-clique percolation community (Palla et al., 2005) - Hierarchical structure (Ravász and Barabási, 2003) Nodes connecting communities → small
  33. 33. Clustering coefficient with link-weight threshold : after eliminating the links with Original CN 10 1 3 1 5 2 7 12 5 Expectation: triangles persist around individuals with small for a fixed
  34. 34. Hypothesis about nodes ■: Pearson correlation coefficient between and ○: Partial correlation coefficient and between with and fixed
  35. 35. Hypotheses - Fix , small → abundance of weak links (with small weights) □ Hypothesis about links - Weak links connect different communities. □ Hypothesis about nodes • Individuals connecting different communities → large • Individuals concealed in a community → small 0.45 (a) 0.40 <O>w 0.35 0.30 0.2 0.4 0.6 0.8 1.0 P cum(w )
  36. 36. Conclusions  Predictability of partner sequence - Face-to-face interaction log in offices in Japanese companies  Conversation partners: predictable to some extent - A main cause: the bursty activity pattern - Significant predictability after omitting the burstiness  Dependence on the individual’s position in the conversation network - “Strength of weak ties” - INTER-community individuals → large - INTRA-community individuals → small Full paper is available Taro Takaguchi, Mitsuhiro Nakamura, Nobuo Sato, Kazuo Yano, and Naoki Masuda, “Predictability of conversation partners”, Phys. Rev. X 1, 011008 (2011).

×