Dichotomy between clustering performance and minimum distortion in piecewise-dependent-data (PDD) clustering

In many time-series such as speech, biosignals, protein chains, etc. there is a dependency between consecutive vectors. As the dependency is limited in duration, such data can be referred to as piecewise-dependent data (PDD). In clustering, it is frequently needed to minimize a given distance function. In this letter, we will show that in PDD clustering there is a contradiction between the desire for high resolution (short segments and low distance) and high accuracy (long segments and high distance), i.e., meaningful clustering.