Dichotomy Between Clustering Performance and Minimum Distortion in Piecewise-Dependent-Data (PDD) Clustering

In many signal such speech, bio-signals, protein chains, etc. there is a dependency between consecutive vectors. As the dependency is limited in duration such data can be called as Piecewise-Dependent- Data (PDD). In clustering it is frequently needed to minimize a given distance function. In this paper 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 distortion), i.e. meaningful clustering