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A new method for continuous ECG analysis using geometric algebra and fuzzy clustering

The aim of this paper is to describe a group of new and original algorithms to achieve robust and reliable analysis of long term ECG recorded in difficult situations (as in epileptic patients). To achieve robustness even when the signal is corrupted, available data from different leads (electrodes) are combined using some tools of recent mathematical methods based on Geometric Algebra and Calculus (GA and GC) and backed by an original Fuzzy Clustering (FC) algorithm. Some geometric constructions of GA make it possible to quantify multi dimensional geometric characteristic of signals which pertain to time correlation of different projections of heart electric activity. Moreover these geometric characteristics help highlighting notable ECG waves (P, QRS, T). Fuzzy clustering algorithm we present here is used in event detection as well as in a sophisticated data smoothing algorithm and outlier elimination. Isoelectric curve of ECG, is calculated with a high degree of reliability and besides classic parameters, some spatio-temporal characteristics of ECG are also defined and computed which use original methods in this work. These parameters can be related to fine characteristics of heart electric activity and its spatiotemporal synchrony. A number of ECG recordings in epileptic patients has been analyzed by this method.