Kernel archetypal analysis for clustering web search frequency time series

We analyze time series which indicate how collective attention to social media services or Web-based businesses evolves over time. Data was gathered from Goolge Trends and consists of discrete time series of varying duration. Following the related literature, we fit Weibull distributions to the data. Given the two parameters of its fitted model, we embed each time series in a low-dimensional space and apply kernel archetypal analysis based on the Kullback-Leibler divergence for clustering. Our results reveal strong regularities in the dynamics of collective attention to social media and thus illustrate the potential of advanced pattern recognition techniques in the emerging area of Web science.