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The problem to accurately and parsimoniously characterize random series ofevents (RSEs) present in the Web, such as e-mail conversations or Twitterhashtags, is not trivial. Reports found in the literature reveal two apparentconflicting visions of how RSEs should be modeled. From one side, thePoissonian processes, of which consecutive events follow each other at arelatively regular time and should not be correlated. On the other side, theself-exciting processes, which are able to generate bursts of correlated eventsand periods of inactivities. The existence of many and sometimes conflictingapproaches to model RSEs is a consequence of the unpredictability of theaggregated dynamics of our individual and routine activities, which sometimesshow simple patterns, but sometimes results in irregular rising and fallingtrends. In this paper we propose a highly parsimonious way to characterizegeneral RSEs, namely the Burstiness Scale (BuSca) model. BuSca views each RSEas a mix of two independent process: a Poissonian and a self-exciting one. Herewe describe a fast method to extract the two parameters of BuSca that,together, gives the burstyness scale, which represents how much of the RSE isdue to bursty and viral effects. We validated our method in eight diverse andlarge datasets containing real random series of events seen in Twitter, Yelp,e-mail conversations, Digg, and online forums. Results showed that, even usingonly two parameters, BuSca is able to accurately describe RSEs seen in thesediverse systems, what can leverage many applications.

Burstiness Scale: a highly parsimonious model for characterizing random series of events