Emergence of Long-Term Memory in Popularity

TL;DR

This paper analyzes long-term memory effects in popularity dynamics using Billboard chart data, revealing how initial popularity and memory strength influence ranking evolution and the emergence of long-term memory.

Contribution

It introduces a model combining logistic growth with power-law long-term memory to explain popularity dynamics and detects the abrupt emergence of long-term memory in popularity evolution.

Findings

Long-term memory emerges abruptly in popularity dynamics.

Initial popularity and memory strength are key factors.

Long-term memory significantly influences popularity spreading and accumulation.

Abstract

Popularity describes the dynamics of mass attention, and is a part of a broader class of population dynamics in ecology and social science literature. Studying accurate model of popularity is important for quantifying spreading of novelty, memes, and influences in human society. Although logistic equation and similar class of nonlinear differential equation formulates traditional population dynamics well, part of the deviation in long-term prediction is stated, yet fully understood. Recently, several studies hinted a long-term memory effect on popularity whose response function follows a power-law, especially that appears on online mass media such as YouTube, Twitter, or Amazon book sales. Here, we investigate the ranking of most popular music, \textit{the Billboard Hot 100 chart}, which is one of the largest popularity dataset spanning several decades. Using a popularity model that comprises logistic growth and a power-law decaying long-term memory, we showed that rank history is mainly characterized by initial popularity and memory strength. With this framework, we investigated temporal development of long-term memory on the whole popularity dynamics. As a result, abrupt emergence of long-term memory and broad initial popularity is illustrated, which was not clearly detected by time-independent measures. We emphasize not only development of the mass media, but also the difference of spreading and accumulated popularity affect dynamics significantly when the popularity has long-term memory.