Clustering of functional boxplots for multiple streaming time series

In this paper we introduce a micro-clustering strategy for Functional Boxplots. The aim is to summarize a set of streaming time series splitted in non overlapping windows. It is a two step strategy which performs at first, an on-line summarization by means of functional data structures, named Functional Boxplot micro-clusters; then it reveals the final summarization by processing, off-line, the functional data structures. Our main contribute consists in providing a new definition of micro-cluster based on Functional Boxplots and, in defining a proximity measure which allows to compare and update them. This allows to get a finer graphical summarization of the streaming time series by five functional basic statistics of data. The obtained synthesis will be able to keep track of the dynamic evolution of the multiple streams.