Global Regularity and Individual Variability in Dynamic Behaviors of Human Communication *

Transcription

1 Web Mining Lab Department of Media and Communication City University of Hong Kong Global Regularity and Individual Variability in Dynamic Behaviors of Human Communication * Jonathan J. H. Zhu (j.zhu@cityu.edu.hk) Tai-Quan Peng (taiqpeng@cityu.edu.hk) *This results reported here are preliminary and will be continuously updated. Please contact the authors for the latest findings if you wish to cite the study. Part of the source data comes from Nielsen/NetRatings, copyrighted, all rights reserved. The analyses, interpretations and errors come from the authors. CUC 2009/04/07 1

2 A Fundamental Tension in Social Sciences General Laws Nomothetic Explanation Idiographic Explanation Thick Descriptions 3 Ecological Fallacy Reductionism 2 Individual Variability 1 Personal thoughts: 1. Need sufficient cases to uncover the full range of individual variability; 2. Central tendency and dispersion of individual variability itself is informative; 3. Some general laws may emerge in disjoint from individual variability. CUC 2009/04/07 2

3 Bursts and Heavy-tails of Human Dynamics (Barabάsi, 2005, Nature) P ( ) e P( ) CUC 2009/04/07 3

4 Correspondence Pattern of Darwin & Einstein (Oliveira & Barabάsi, 2005) CUC 2009/04/07 4

5 Poisson versus Power-law Models of Human Dynamics Poisson Distribution (P(K) = e -K ) tasks are executed according to first-come-first-served or to purely random order scheduling rules Uniform pattern of activities Power-law Distribution (P(K) = K - ) decision-based queuing system and priority index A priority list is a dynamic entity, since tasks are removed from it after they are either executed or become irrelevant and new tasks are added continuously. Dense successions of events separated by very long gaps CUC 2009/04/07 5

6 More Empirical Tests of Human Dynamics across Diverse Behavioral Domains Author Year Subject Data Source Exponents ( ) Mobile Phone Usage Gonzalez et al 2008 frequency of visiting different locations 100K anonymous mobile phone users -1 Candia et al 2008 Interevent time distribution for mobile phone calling activity. mobile phone calling record in US -0.9 interevent time distribution between two consecutive SMS 6 person's calling record -2.1 to -1.5 Hong et al 2009 interevent time distribution between consecutive conversations 4 individuals' calling record to Video-on-Demand Crane & Sornette 2008 waiting time between two consecutive viewing behaviors 5 mil time-series of activities on Youtube collected over 8 months -1.4 Webpage Browsing Huberman et al 1998 clicks to each website Web users at an university for 3 weeks -1.5 Dezso et al 2006 time interval between consecutive HTML requests by the same visitor log files of the largest Hungarian news -1.2 and entertainment portal visitation pattern of news documents -0.3 Geczy et al 2008 use of web services in intranet intranet web log data of an organization Evident long tail Goncalves & Ramasco Grabowski & Kosinski Grabowski & Kruszewska Distribution of times between consecutive clicks by the same user to the same URL Distribution of times between consecutive clicks by the same user to the Emory domain Social Network Sites Number of days since the time of an individual was added (invited to the network) to the date of last logging) Logs of the Web server of Emory University. a large social network of an Internet community (Grono) Online Games N of individuals spending time T playing game K individuals in a virtual world of N of individuals whose activity lasted T days MMORPG Games -1 CUC 2009/04/

7 A Classification Scheme of Human Dynamics (Vásquez et al., 2006) Queuing Model I: Assumption: there are no limitations on the number of tasks an individual can handle at any time Results: waiting time of individual tasks follows a heavy tailed distribution with γ = -1.5 Behavioral Domains: surface mails Queuing Model II: Imposing limitations on the queue length Results: heavy tailed waiting time with γ = -1.0 Behavioral Domains: s, web browsing, library visits CUC 2009/04/07 7

8 Power-law Distribution with Varying s (i.e., differential responsiveness or selectivity) 1000 P( Activity) 1000( Activity ) 800 a. X-axis amplified b. X- & Y-axis log transformed Probability of Activity Gamma=-0.5 Gamma=-1 Gamma=-1.5 Gamma= Activity (e.g., duration, waiting time, intensity, etc.) CUC 2009/04/07 8

9 Key Strengths of the Barabάsi Model Widely confirmed (predictive power) One parameter involved (parsimony) Parameter scale free (generaliability) Theoretical explanation offered (heuristic provocativeness) CUC 2009/04/07 9

10 Remaining Issues in the Barabάsi Model Ecological fallacy: the power-law regularity has been observed at the aggregate level without systematic confirmation at the individual level (Robinson, 1950) Falsifiability: the priority-based model is an ad hoc explanation with challenges from many other alternative hypotheses (e.g., automaticity, flow, etc.) CUC 2009/04/07 10

11 Research Questions Is the Power-law distribution uniform (i.e., with the same decision making mechanism) across all individuals? If not, how much the individuals differ and what the differences look like? What factor accounts for the individual variability? CUC 2009/04/07 11

12 Data Source Web Browsing Data A panel of 3,703 Internet users randomly sampled in Hong Kong from 2002 to 2004 A client log file of their webpage browsing behaviors at home in four weeks spread out in or mil entries in the dataset, i.e., 1,300+ visits per user over 4 weeks or 46 visits per user per day P2P Usage Data A server log file of users downloading documents from each other on through the Maze system from Nov 2008-Feb 2009 Total users = 229,000, total number of document transferred = 37 mil, or 165 documents per user in the 4 months CUC 2009/04/07 12

13 Measurement of Human Dynamic Behaviors Webpage Browsing a. Inter-event Time: time intervals between two consecutive webpage requests b. Preference of Websites: Time Duration/Website/Day/User c. Stickiness to Website: Number of Requests/Website/Day/User d. Diversity of Behaviors: Number of Websites/Day/User P2P Usage e. In-degree: Number of documents downloaded by others/day f. Out-degree: Number of documents downloaded from others/day CUC 2009/04/07 13

14 Global Regularity of Human Dynamics in Web Browsing & P2P Usage CUC 2009/04/07 14

15 Global Regularity in Web Browsing CUC 2009/04/07 15

16 Global Regularity in P2P Usage CUC 2009/04/07 16

17 Are Human Behaviors Uniform? -- Individual Variability on γ CUC 2009/04/07 17

18 Individual Variability in Web Browsing CUC 2009/04/07 18

19 Individual Variability on P2P Usage CUC 2009/04/07 19

20 Possible Distribution of individual γ s (P-P Plot Results) CUC 2009/04/07 20

21 Conditions for Emergence of Global Regularity from Individual Behaviors Self-similarity Principle: If and only if individual behaviors follow the same distribution as the global behavior does (e.g., power-law at both levels), the latter is a linear accumulation of the former. As such, we can draw safely inferences about individuals from the global parameter. Emergence Principle: If individual behaviors follow a distribution (e.g., normal) different from a well-established global behavior (e.g., powerlaw), the latter still holds (i.e., not necessarily an ecological fallacy), emerged from complex interactions among individuals (i.e., > 2). See Hidalgo (2006), Physica A, pp CUC 2009/04/07 21

22 What Accounts for the Variability? An Explanatory Model CUC 2009/04/07 22

23 Determinants of Individual s (HLM Level-2 Parameter Coefficients) Five variables are included as explanatory variables to explain the variance of in webpage browsing behavior Demographics (age, gender, occupation, and education level) Lifestyles The models produce satisfactory explanatory power, which explained 50% of the variance of in inter-event time model. Lifestyle accounts far more variance than demographic variables Age is the most important among four demographic variables Who deviates from the norm? Decision-based queuing mechanism is NOT unconditionally applicable across individuals Not all individuals will rationally assign priorities to all arriving tasks Alternative mechanism (e.g., random/fcfs or automaticity) will take place when the conditions for queuing mechanism are not met (e.g., motivation, capacity, or need) The strength of priority index DOES vary across individuals CUC 2009/04/07 23

24 Three Individuals as Illustration CUC 2009/04/07 24

25 Conclusions The study contributes the following to human dynamics research: Confirms the robust and ubiquitous global regularity of human communication behavior as a power-law distribution at the aggregate level. Finds a considerable amount of variability at the individual level, with a substantial number of individuals deviating from the power-law pattern. Uncovers that the individual variability is not randomly generated, but follows several well-known families of distributions (e.g., normal, lognormal, and Weibull). Explains the individual variability, up to 50%, by lifestyle and other personal characteristics. CUC 2009/04/07 25

26 Future Work Uncover the causal mechanism underlying the power-law distribution of human behavior at both individual and global levels: Priority-based hypothesis Automaticity hypothesis Play/flow hypothesis Anything else? Identify conditions/boundaries of power-law human behavior: Stability and/or change within individuals over time Stability and/or change within individual across content domains Explore the conditions for the emergence of global regularity from individual variability Self-similarity Disjoint CUC 2009/04/07 26