the age of a submission in digg hours at a given time t, we measure how many diggs were received on the portal between t and the promotion time of the story, divided by 5,478 diggs.

Similar hourly activity plots were not possible for YouTube in 2008, given that video view counts were provided by the API approximately only once a day, in contrast to all the diggs received by a Digg story. Moreover, we were able to capture only a fraction of the large amount of traffic the YouTube site handled by monitoring only the selected videos in our sample.

Predicting the future

Here, we cover the process we used to model and predict the future popularity of individual content and measure the performance of the predictions: First, we performed a logarithmic transformation on the popularities of submissions. The transformed variables exhibit strong correlations between early and later time periods; on this scale, the naturally random fluctuations can be expressed as an additive noise term. We call reference time tr the time at which we intend to predict the popularity of a submission whose age with respect to its upload ( promotion) time is tr. By indicator time ti we mean when in the life cycle of the submission we performed the prediction, or how long we can observe submission history in order to extrapolate for future popularity (ti < tr).

To help determine whether the popularity of submissions early on is a predictor of later popularity, see Figures 3 and 4, which show the popularity counts for submissions at the reference time tr = 30 days both for Digg and YouTube vs. the popularity measured at the indicator times ti = 1 digg hour and ti = 7 days for the two portals, respectively. We measured the popularity of You Tube videos at the end of the seventh day, so the view counts at that time ranged from 101 to 104, similar to Digg in this measurement. We logarithmically rescaled the horizontal and vertical axes in the figures due to the large variances present among the popularity of different submissions, which span three decades.

Observing the Digg data, we noted the popularity of about 11% of the stories (lighter blue in Figure 3) grew much

While Digg
stories saturate
fairly quickly
(about a day)
to their respective
reference
popularities,
you Tube videos
keep attracting
views throughout
their lifetimes.

more slowly than the popularity of the majority of submissions; by the end of the first hour of their lifetimes, they had received most of the diggs they will ever receive. The difference in popularity growth of the two clusters is perceivable until approximately the seventh digg hour, after which the separation vanishes due to digg counts of stories mostly saturating to their respective maximum values, as in Figure 1.

A Bayesian network analysis of submission features (day of the week/hour of the day of submission/promotion, category of submission, number of diggs in the upcoming phase) reveals no obvious reason for the presence of clustering; we assumed it arises when the Digg promotion algorithm misjudged the expected future popularity of stories, promoting stories from the “upcoming” phase unlikely to sustain user interest. Users lose interest much sooner in them than in stories in the upper cluster. We used k-means clustering, with k = 2 and cosine distance measure to separate the two clusters, as in Figure 3, and discarded the stories in the lower cluster.

Trends and randomness. Our in-depth analysis of the data found strong linear correlations between early and later times of the logarithmically transformed submission popularities, with correlation coefficients between early and later times exceeding 0.9. Such a strong correlation suggests the more popular submissions are at the beginning, the more popular they will also be later on. The connection can be described by a linear model: ln N (tr) = ln [r(ti, tr)N(ti)] + ξ(ti, tr)