A characterization of electrocardiogram signals through optimal allocation of information granularity

We propose and develop a concept of a granular representation of a collection of signals (patterns) where a prototype (representative) of such numeric signals is formed as a certain information granule (say, a set, fuzzy set, rough set, and alike) instead of a single numeric entity. As being more abstract, the granular format of the representative of the family of signals is more in rapport with the nature of the representation task itself. It is instrumental in quantifying the diversity of data and capture their inherent distribution characteristics.

In the realization of the granular representation of the signals, we introduce a certain level of granularity (supplied in advance), which in the construction of the granular representative is regarded as an essential important modeling asset. A two-phase design is developed whose ultimate goal is to optimally allocate (distribute) the predefined level of granularity to the individual elements of the universe of discourse over which the signals are described. Given the nature of the required optimization, the ensuing optimization problem is solved by engaging a machinery of population-based optimization, namely Particle Swarm Optimization (PSO). Furthermore a number of information granularity distribution protocols are proposed. The numerical experiments completed for synthetic data and ECG MIT-BIH database signals are used to demonstrate the performance of the overall optimization algorithm and quantify the effectiveness of the allocation of information granularity realized by the PSO. An area under curve (AUC) criterion is proposed as a measure to express the quality of the overall optimization framework.

For both synthetic as well as ECG signals, it is shown that the method endowed with the PSO identifies the best prototype and spans the lower and upper bounds of its granular counterpart. In addition to the numeric quantification of the best (optimized) granular prototype, the method helps visualizing its bounds. The relative difference in mapping performance between the best and the weakest granular prototypes is in the range of 18% (for normal ECG complexes) and over 26% in case of complexes of premature ventricular contraction.

A complete algorithm of the construction of granular prototypes is presented. Treating the granular prototype as a template of a given class of electrocardiogram (ECG) signals, a matching process is facilitated and used as a basis for the design of signal classification algorithms. Various realizations of granular prototypes can be completed with the use of fuzzy sets or rough sets.