Source-linked AI summary
Role of Activity in Human Dynamics
Tao Zhou, Hoang Anh Tuan Kiet, Beom Jun Kim, Bing-Hong Wang, Petter Holme
TL;DR
The paper investigates how power-law interevent times arise in human activity, focusing on movie ratings and related communication data. It empirically analyzes activity and interevent-time distributions, finding that more active individuals and groups have larger power-law exponents and narrower distributions. The results identify activity as a significant feature of interest-driven human dynamics, while individual movie-rating records remain too short to establish power laws for typical users.
Problem
The paper asks how power-law interevent times arise in human activity, especially in interest-driven systems not characterized by waiting task lists.
Method
The study analyzes Netflix movie-rating records by measuring interevent times and activity at population, group, and individual levels, with supporting evidence from text-message data.
Results
Activity correlates positively with group and individual power-law exponents, while individual distribution width correlates negatively with activity; text-message data show similar patterns.
Takeaways & Limitations
Activity is a significant feature of aggregate and individual temporal patterns in interest-driven human dynamics, distinct from task-driven universality classes.
Takeaways & Limitations
Typical individual movie-rating records are too short to establish that users’ interevent-time distributions follow power laws.
Abstract
from arXiv · showhide
The human society is a very complex system; still, there are several non-trivial, general features. One type of them is the presence of power-law distributed quantities in temporal statistics. In this Letter, we focus on the origin of power-laws in rating of movies. We present a systematic empirical exploration of the time between two consecutive ratings of movies (the interevent time). At an aggregate level, we find a monotonous relation between the activity of individuals and the power-law exponent of the interevent-time distribution. At an individual level, we observe a heavy-tailed distribution for each user, as well as a negative correlation between the activity and the width of the distribution. We support these findings by a similar data set from mobile phone text-message communication. Our results demonstrate a significant role of the activity of individuals on the society-level patterns of human behavior. We believe this is a common character in the interest-driven human dynamics, corresponding to (but different from) the universality classes of task-driven dynamics.
Introduction. –
The paper asks how power-law interevent times arise in human activity and examines movie-rating behavior as an interest-driven system. It contrasts this setting with queuing explanations developed for task-driven communication.
- Introduction. –: Large digital datasets reveal power-law interevent times at both population and individual levels, patterns not explained by independent uniformly random interactions.Such patterns matter for understanding communication, technology impacts, computer-virus spread, and human travel.
- Introduction. –: Barabási’s queuing model explains some heavy-tailed response times through highest-priority-first task selection and predicts universality classes with exponents 1 and 1.5.These classes were observed in e-mail and surface-mail communication, respectively.
- Introduction. –: Movie rating provides an interest-driven system for testing power-law interevent times where users are not necessarily following task lists.The study measures τ, the time between consecutive movie ratings, and reports an aggregated power law spanning more than two orders of magnitude.
T. Zhou et al.
The study identifies a monotonic relationship between group activity and interevent-time power-law exponents. This suggests that individual activity is a key ingredient in aggregate temporal behavior.
- T. Zhou et al.: Group power-law exponents increase monotonically with mean activity, indicating that activity helps determine aggregate interevent-time distributions.The analysis divides the population into groups ordered by mean activity.
- T. Zhou et al.: Activity is therefore implicated as a key ingredient in the society-level emergence of interevent-time patterns.
Data source. –
The dataset comes from Netflix’s public movie-rating records, collected to support personalized recommendations and released through a recommender-system competition. Each record links a user, movie, rating, and timestamp.
- Data source. –: The Netflix dataset contains 17,770 movies, 447,139 users, and approximately 9.67 × 10^7 records.
- Data source. –: Each record includes a user ID, movie ID, rating viα from 1 to 5, and rating time tiα.For a user with ki movie records, the data yield ki − 1 interevent times at one-day resolution.
Interevent time distribution for the whole population. –
Aggregated movie-rating interevent times follow a power law with exponent γ ≈ 2.08 over more than two orders of magnitude. The analysis removes weekly oscillation bias, and the resulting scaling cannot be explained by aggregating Poissonian agents.
- Interevent time distribution for the whole population. –: γ ≈ 2.08 describes the aggregated interevent-time power law over more than two orders of magnitude.The exponent is estimated by maximum likelihood.
- Interevent time distribution for the whole population. –: Weekly oscillations are present, so the exponent calculation uses only interevent times separated by one week.The retained points are F(7), F(14), F(21), and so on.
- Interevent time distribution for the whole population. –: The observed group- and individual-level statistics show that the aggregate scaling cannot result from combining Poissonian agents with different characteristic times.
Interevent time distribution for groups. –
Grouping users by activity reveals a monotonic increase of the interevent-time power-law exponent with mean activity, while activity distributions rule out homogeneous Poissonian individuals as the source of the group-level heavy tails.
- Activity is defined as each user’s event frequency, Ai = ni/Ti, where Ti spans the first to last recorded event.The mean activity across users is ⟨A⟩= 0.812.
- The interevent-time exponent increases monotonically with group mean activity, indicating that individual activity shapes aggregate temporal behavior.Users are sorted by activity into twenty groups, whose mean activities decrease from group 1 to group 20.
- The population activity distribution is intermediate between exponential and power-law rather than uniform, whereas group 4 and group 17 can each show approximately uniform activity distributions.
- Because groups with similar uniform activity distributions have substantially different exponents, group-level heavy tails cannot originate from homogeneous Poissonian individuals.
Interevent time distribution for individuals. –
At the individual level, less-active users have broader, smaller-exponent interevent-time distributions, while finite records limit statistical confirmation of credible power-law scaling.
- Less-active individuals have broader interevent-time distributions and smaller power-law exponents, paralleling the group-level relation.
- Individual distributions appear heavy-tailed but fail the Kolmogorov–Smirnov test, plausibly because individual records span only months to years.
T. Zhou et al.
Individual movie-rating and text-message records show broad interevent-time distributions whose width decreases with activity, while text-message users consistently exhibit power-law behavior.
- Almost every user has a heavy-tailed interevent-time distribution broader than a Poisson distribution with the same average interval.
- The second moment ⟨τ 2⟩ is negatively correlated with activity, indicating narrower individual interevent-time distributions among more active users.
- All mobile-phone users show power-law interevent-time distributions passing the Kolmogorov–Smirnov test, whereas the two illustrated Netflix distributions do not pass at threshold quantile 0.9.
- Figure 6 compares the observed second moment with the Poisson expectation, whose expected value is the inverse of activity.
- At the individual level, activity and the power-law exponent have an almost monotonous relation, with only two users showing slight deviations.
Conclusions. –
The paper argues that activity is a common organizing feature of heavy-tailed timing in interest-driven systems, distinct from queuing-based universality classes in task-driven systems.
- Interest-driven systems show power-law exponents varying widely and strongly positively correlated with individual activity.
- This activity-centered pattern contrasts with earlier queuing explanations developed for task-driven communication such as e-mail and surface mail.
- A power-law distribution of activity might also contribute to the dynamics of task-driven systems.