![INSTITUTE OF PHYSICS
BELGRADE Introduction
Network topology
Entropy measures
Temporal patterns
Summary
Network mapping
Weighted bipartite network
Two partitions: Users and
Questions.
Link weight: number of
answers/comments.
Structural properties of
bipartite network and it's
projections to Question and
User partitions.
[M. Mitrovic et al., EPJB 73,
293-301, (2010).]
KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building](https://image.slidesharecdn.com/knowescape2014-thess-mitrovic-141209113040-conversion-gate02/85/Quantitative-Study-of-Innovation-and-Knowledge-Building-in-Questions-Answers-System-with-Math-Tags-11-320.jpg)
![INSTITUTE OF PHYSICS
BELGRADE Introduction
Network topology
Entropy measures
Temporal patterns
Summary
Community structure
2 week activity network.
Community detection
method - Louvain
method. [V. D. Blondel,
JSTAT 2008 (10), P100,
(2008).]
Communities are formed
around few very active
experts.
KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building](https://image.slidesharecdn.com/knowescape2014-thess-mitrovic-141209113040-conversion-gate02/85/Quantitative-Study-of-Innovation-and-Knowledge-Building-in-Questions-Answers-System-with-Math-Tags-13-320.jpg)
![INSTITUTE OF PHYSICS
BELGRADE Introduction
Network topology
Entropy measures
Temporal patterns
Summary
Focus and expertise of users
0 1 2 3 4 5 6 7 8
H
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
number of users
Questions
0 1 2 3 4 5 6 7 8 9
H
0.25
0.20
0.15
0.10
0.05
0.00
numberofusers
Answers+Comments
User activity on separate
tags - Xi = n1; : : : ; nmax;
P
Total activity i =
l ni
User's entropy P
-
Hi =
l
nl
i
Lower Hi higher focus.
[Adamic et al., Proceedings
of WWW'08, (2008).]
KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building](https://image.slidesharecdn.com/knowescape2014-thess-mitrovic-141209113040-conversion-gate02/85/Quantitative-Study-of-Innovation-and-Knowledge-Building-in-Questions-Answers-System-with-Math-Tags-14-320.jpg)
Quantitative Study of Innovation and Knowledge Building in Questions&Answers System with Math Tags
- 1. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Quantitative Study of Innovation and Knowledge Building in Questions&Answers System with Math Tags Marija Mitrovic Dankulov, Bosiljka Tadic Scienti
- 2. c Computing Laboratory, Institute of Physics Belgrade University of Belgrade, Pregrevica 118, 11080 Belgrade
- 3. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Collective Knowledge Building Socio-cultural process which takes place trough self-organized dynamics of interactions among individuals Conditions that support collective knowledge building: (i) Problems as an attempt to understand world/
- 4. eld. (ii) Improving coherence, quality and utility of ideas. (iii) Interaction - participants negotiate
- 5. t between their own ideas and of others. (iv) All participants must contribute. (v) Knowledge-building discourse, more than knowledge sharing;. participants engage in constructing, re
- 6. ning and transforming knowledge. KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 7. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Questions Answers Sites Rich repositories for studying dynamics of collective knowledge building On QA sites: Participants ask, answer and vote for questions. Comment and engage in discussion about questions/answers. All participants contribute trough dierent type of actions: posting and voting for questions, answers, comments. They construct (ask/answer), re
- 8. ne (comment/vote) and transform knowledge. KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 9. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Data: Stack Exchange Stack Exchange: where expert answers to your questions! Network of 130 QA sites where participants answers to informational and factual questions. Mathematics: Data for four year period: since the beginning (July 2010) until April 2014. Rich dataset: 77895 Users posted 269819 Questions, 400511 Answers and 1265445 Comments. High temporal resolution. Tags - list of up to 5 tags is assigned to each question. Overall 1040 tags: calculus, linear algebra, complex analysis, application, : : : KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 10. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Quantitative study of knowledge building: methods Tools and methods from statistical physics and complex network theory. Complex networks - topological structure. Entropy measures of user activity and activity on dierent tags. Time series analysis - power spectrum, avalanches, uctuations. KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 11. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Network mapping Weighted bipartite network Two partitions: Users and Questions. Link weight: number of answers/comments. Structural properties of bipartite network and it's projections to Question and User partitions. [M. Mitrovic et al., EPJB 73, 293-301, (2010).] KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 12. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Topology Broad distributions of degree for both partitions stable over time and tags. 100 10-1 10-2 10-3 10-4 10-5 10-6 100 101 102 s 10-7 P(s) 1st year 2nd year 3rd year 4th year 101 100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 100 101 102 103 104 s 10-8 P(s) Users 1st year 2nd year 3rd year 4th year 101 100 10-1 10-2 10-3 10-4 10-5 100 101 q 10-6 P(q) homework calculus real-analysis linear-algebra 101 100 10-1 10-2 10-3 10-4 10-5 10-6 100 101 102 103 q 10-7 P(q) homework calculus real-analysis linear-algebra KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 13. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Community structure 2 week activity network. Community detection method - Louvain method. [V. D. Blondel, JSTAT 2008 (10), P100, (2008).] Communities are formed around few very active experts. KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 14. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Focus and expertise of users 0 1 2 3 4 5 6 7 8 H 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 number of users Questions 0 1 2 3 4 5 6 7 8 9 H 0.25 0.20 0.15 0.10 0.05 0.00 numberofusers Answers+Comments User activity on separate tags - Xi = n1; : : : ; nmax; P Total activity i = l ni User's entropy P - Hi = l nl i Lower Hi higher focus. [Adamic et al., Proceedings of WWW'08, (2008).] KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 15. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Zipf's and Heap's law Heap's law 105 104 103 102 101 100 101 102 103 104 105 106 107 N 100 D(N) Tags Combination of Tags D(N) N
- 16. ;
- 17. 1 sublinear growth (
- 18. = 0:27 (Tags)
- 19. = 0:92 (Combination of Tags) Zipfs's law 106 105 104 103 102 101 100 101 102 103 104 105 R 100 f(R) Tags Combination of Tags f(R) R; = 1:47 (Tags) = 1 (Combination of Tags) KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 20. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Entropy of events associated to Tag 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 100 101 102 103 104 105 106 K 0.2 S/log(K) data reshuffle K - number of occurrence of Tag. - sequence of events divide into K equal intervals; fl is the number of occurrence of Tag in interval l; PS = K l=1 flK log( flK ) S = 0 all events are in one interval; Smax = log(K) events are equally distributed. KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 21. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Power spectrum Power spectrum is of type 1 f for small frequencies - long term correlations. 109 108 107 106 105 104 103 102 101 100 100 101 102 103 104 s 10-1 P(s) p(t) binned 1011 1010 109 108 107 106 105 104 103 102 101 100 101 102 103 104 s 100 P(s) Na(t) binned 109 108 107 106 105 104 103 102 101 100 100 101 102 103 104 q 10-1 P(q) homework binned 108 107 106 105 104 103 102 101 100 100 101 102 103 104 q 10-1 P(q) calculus binned 25 20 15 10 5 0 10000 20000 30000 40000 50000 60000 t[10min] 0 p(t) New users 25 20 15 10 5 0 10000 20000 30000 40000 50000 60000 t[10min] 0 Na(t) all 25 20 15 10 5 0 10000 20000 30000 40000 50000 60000 t[10min] 0 N(t) homework 25 20 15 10 5 0 10000 20000 30000 40000 50000 60000 t[10min] 0 N(t) calculus [M. Mitrovic et al., JSTAT 2011, P02005, (2011).] KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 22. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Avalanche distribution Time series of events N(t) ) time series of avalanches Si. 14 12 10 8 6 4 78000 78500 79000 79500 80000 101 100 10-1 10-2 10-3 10-4 10-5 10-6 100 101 102 103 S 10-7 P(S) all homework calculus 101 100 10-1 10-2 10-3 10-4 10-5 100 101 102 T 10-6 P(T) all homework calculus t 2 N(t) time series of events Broad distributions of avalanche sizes and duration ) self-organized criticality (SOC). KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 23. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Avalanche size returns 100 10-1 10-2 10-3 10-4 10-5 −20 −15 −10 −5 0 5 10 15 20 d/σ 10-6 P(d) homework calculus Return di=Si+1 Si+ P(d) = P0(1(1q)( d )2) 1 1q SOC ) peaked distribution with fat tail. KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building
- 24. INSTITUTE OF PHYSICS BELGRADE Introduction Network topology Entropy measures Temporal patterns Summary Summary Collective knowledge building can be studied by applying methods of complex networks and statistical physics: Complex networks - QA sites can be used for studying of dynamics of collective knowledge building process. Entropy measures - most of the users focus on few categories (expertise); tag speci
- 25. c dynamics is highly cooperative process. Time series analysis - self-organized criticality mechanism with long-range correlations is at the origin of collective knowledge building. KnowEscape 2014j M. Mitrovic Dankulov: Quantitative study of knowledge building