David G. Márquez

A new algorithm for wavelet-based heart rate variability analysis

Abstract One of the most promising non-invasive markers of the activity of the autonomic nervous system is heart rate variability (HRV). HRV analysis toolkits often provide spectral analysis techniques using the Fourier transform, which assumes that the heart rate series is stationary. To overcome this issue, the Short Time Fourier Transform (STFT) is often used. However, the wavelet transform is thought to be a more suitable tool for analyzing non-stationary signals than the STFT. Given the lack of support for wavelet-based analysis in HRV toolkits, such analysis must be implemented by the researcher. This has made this technique underutilized. This paper presents a new algorithm to perform HRV power spectrum analysis based on the Maximal Overlap Discrete Wavelet Packet Transform (MODWPT). The algorithm calculates the power in any spectral band with a given tolerance for the bands boundaries. The MODWPT decomposition tree is pruned to avoid calculating unnecessary wavelet coefficients, thereby optimizing execution time. The center of energy shift correction is applied to achieve optimum alignment of the wavelet coefficients. This algorithm has been implemented in RHRV, an open-source package for HRV analysis. To the best of our knowledge, RHRV is the first HRV toolkit with support for wavelet-based spectral analysis.

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes

The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.

A study on the representation of QRS complexes with the optimum number of Hermite functions

Abstract When choosing a representation for the classification of heartbeats a common solution is using the coefficients of a linear combination of basis functions, such as Hermite functions. Among the advantages of this representation is the possibility of using model selection criteria for choosing the optimal representation, a property that is missing in other heartbeat representation schemes. However, to date none of the authors who have used basis functions has studied what is the optimal model length (number of functions in the linear combination). This length is usually chosen using ad hoc techniques such as the visual inspection of the reconstruction obtained for a few beats. This has led to such different choices as representing the QRS of the beats by as few as 3 or as much as 20 Hermite functions. This paper studies what is the optimal number of Hermite functions to be used when representing the QRS. The Hermite characterization of the QRS complex was calculated using from 2 to 30 functions. To determine the optimal number of functions AIC and BIC were calculated for all the heartbeats in the MIT-BIH database, obtaining for each QRS the optimum model length. The features of the Hermite characterization have been studied using feature selection techniques. Data about the impact of the length of the representation chosen on the computational resources is also presented. Using this information, we have developed a clustering algorithm based on mixture models that has a misclassification rate of 0.96% and 0.36% over the MIT-BIH database and the AHA database, respectively.

A novel and simple strategy for evolving prototype based clustering

Abstract In this paper, we present a novel strategy for evolving prototype based clusters that uses a weighting scheme to “progressively forget” old samples. The rate of forgetfulness can be controlled by a single intuitive memory parameter. This weighting scheme can be used to create efficient dynamic summaries, such as mean or covariance, of data streams. Using this weighting scheme we have developed evolving versions of the K-means and Gaussian Mixture models algorithms. They can analyze the incoming data in an online manner and they are specially geared towards dealing with concept drift originated by changes in the underlying data distribution. The algorithms were validated over a simulated database where a wide variety of concept drift situations occur and over real data related to property sales, showing their capability to follow changes in data.

Low-Power, Low-Latency Hermite Polynomial Characterization of Heartbeats Using a Field-Programmable Gate Array

The characterization of the heartbeat is one of the first and most important steps in the processing of the electrocardiogram (ECG) given that the results of the subsequent analysis depend on the outcome of this step. This characterization is computationally intensive, and both off-line and on-line (real-time) solutions to this problem are of great interest. Typically, one uses either multi-core processors or graphics processing units which can use a large number of parallel threads to reduce the computational time needed for the task. In this paper, we consider an alternative approach, based on the use of a dedicated hardware implementation (using a field-programmable gate-array (FPGA)) to solve a critical component of this problem, namely, the best-fit Hermite approximation of a heartbeat. The resulting hardware implementation is characterized using an off-the-shelf FPGA card. The single beat best-fit computation latency when using six Hermite basis polynomials is under \(0.5\,ms\) with a power dissipation of 3.1 W, demonstrating the possibility of true real-time characterization of heartbeats for online patient monitoring.

Introducing Negative Evidence in Ensemble Clustering Application in Automatic ECG Analysis

Ensemble clustering generates data partitions by using different data representations and/or clustering algorithms. Each partition provides independent evidence to generate the final partition: two instances falling in the same cluster provide evidence towards them belonging to the same final partition.