Granular representation schemes of time series: A study in an optimal allocation of information granularity

Information granularity augments a variety of schemes of representation of time series, helps quantify the quality of models of the series and supports a thorough analysis of their parameters. This study introduces a concept of a granular representation of time series. We show that information granules formed on a basis of a given original numeric representation of the series can be optimized through a process of allocation (distribution) of information granularity being regarded here as an essential design asset. We formulate an optimization criterion and utilize a Particle Swarm Optimization (PSO) as an optimization vehicle to distribute a predefined level of information granularity. An optimization criterion used in the formation of the granular representation scheme is concerned with expressing and maximizing coverage of available temporal data by their granular representation. Experimental results in which we focus on the Piecewise Aggregate Approximation (PAA) offer details of the optimization of the allocation of granularity completed for some synthetic and real-world time series and quantify the performance of the resulting granular schemes of representation of time series.