Distance Metrics for Classification of Arbitrarily Sampled Patterns - an ECG Example

Compression, Compressed Sensing and Arbitrary Sampling (AS) all are data reduction techniques challenging the general sampling theorem and investigated how to combine efficiency of storage and preservation of original information. In general, AS assumes the use of given irregular sampling grid according to limitations of signal source, however in domains such as geology, astronomy, meteorology or medicine data appear in not a priori known irregular intervals. The representative of more predictable category is the ECG: (1) the local bandwidth of the signal is modulated by properties of conducting tissue, (2) the bandwidth is related to wave borders which may be precisely delineated with existing methods, and (3) there is strong need for storage efficiency since all recorders worldwide produce daily ca. 600TB of data with expected average storage time of order of 40 years. Unfortunately direct processing of non-uniformly sampled time series is rarely applied due to lack of appropriate methods. In this paper we propose a distance metric and demonstrate its utility to minimum-distance classification of 1-D non-uniform signal strips such as heart beats. The method is based on graph representation of data sequence and does not require inputs other than detection point witnessing the beat occurrence. The classification error and computational complexity both are greater than in the case of uniform patterns, however the proposed algorithm is sampling model independent and may also be applied to uniform data.