An efficient strategy for evaluating similarity between time series based on Wavelet / Karhunen-Loève transforms

The present work aims to present an innovative measure able to efficiently evaluate the similarity between two physiological time series. The proposed methodology combines the Haar wavelet decomposition, in which signals are represented as linear combinations of a set of orthogonal basis, with the Karhunen-Loève transform, that allows for the optimal reduction of that set of basis. The similarity measure is based on the Euclidean distance, but indirectly calculated through the linear combination coefficients of both time series. Moreover, an iterative scheme for computing the referred coefficients significantly decreases the computational complexity of the method that, due to its simplicity and fast execution, can be easily applicable in clinical applications, namely in computational demanding contexts such as telemonitoring environments. This strategy has been successfully implemented and validated inside HeartCycle project, applied to blood pressure signals collected by a telemonitoring platform (TEN-HMS) in the recognition of hypertension episodes.