Abstract
The first step in any non linear time series analysis, is to characterize signals in terms of periodicity, stationarity, linearity and predictability. In this work we aim to find if PCG (phonocardiogram) and ECG (electrocardiogram) time series are generated by a deterministic system and not from a random stochastic process. If PCG and ECG are non-linear deterministic systems and they are not very contaminated with noise, data should be confined to a finite dimensional manifold, which means there are structures hidden under the signal that could be used to increase our knowledge in forecasting future values of the time series. A non-linear process can give rise to very complex dynamic behaviours, even though the underlying process is purely deterministic and probably low-dimensional. To test this hypothesis, we have generated 99 surrogates and then we compared the fitting capability of AR (auto-regressive) models on the original and surrogate data. The results show with a 99\% of confidence level that PCG and ECG were generated by a deterministic process. We compared the fitting capability of an ECG and PCG to AR linear models, using a multi-channel approach. We make an assumption that if a signal is more linearly predictable than another one, it may adjust better to these AR linear models. The results showed that ECG is more linearly predictable (for both channels) than PCG, although a filtering step is needed for the first channel. Finally we show that the false nearest neighbour method is insufficient to identify the correct dimension of the attractor in the reconstructed state space for both PCG and ECG signals.

Abstract
In this work, we present a method to extract features from heart sound signals in order to enhance segmentation performance. The approach is data-driven, since the way features are extracted from the recorded signals is adapted to the data itself. The proposed method is based on the extraction of delay vectors, which are modeled with Gaussian mixture model priors, and an information-theoretic dimensionality reduction step which aims to maximize discrimination between delay vectors in different segments of the heart sound signal. We test our approach with heart sounds from the publicly available PhysioNet dataset showing an average F-1 score of 92.6% in detecting S-1 and S-2 sounds.

Abstract
In this paper, deep convolutional neural networks are used to segment heart sounds into their main components. The proposed method is based on the adoption of a novel deep convolutional neural network architecture, which is inspired by similar approaches used for image segmentation. A further post-processing step is applied to the output of the proposed neural network, which induces the output state sequence to be consistent with the natural sequence of states within a heart sound signal (S1, systole, S2, diastole). The proposed approach is tested on heart sound signals longer than 5 seconds from the publicly available PhysioNet dataset, and it is shown to outperform current state-of-the-art segmentation methods by achieving an average sensitivity of 93.4% and an average positive predictive value of 94.5% in detecting S1 and S2 sounds.

Abstract
Automatic and simultaneous electrocardiogram (ECG) and phonocardiogram (PCG) segmentation is a good example of current challenges when designing multi-channel decision support systems for healthcare. In this paper, we implemented and tested a Montazeri coupled hidden Markov model (CHMM), where two HMM's cooperate to recreate the "true" state sequence. To evaluate its performance, we tested different settings (two fully connected and two partially connected channels) on a real dataset annotated by an expert. The fully connected model achieved 71% of positive predictability (P+) on the ECG channel and 67% of P+ on the PCG channel. The partially connected model achieved 90% of P+ on the ECG channel and 80% of P+ in the PCG channel. These results validate the potential of our approach for real world multichannel application systems.

Abstract
In this paper, the topological and dynamical properties of the heart sounds are assessed. The signal is preprocessed and projected into an embedding subspace, which is more suitable to detect the irregularities and the unstable trajectories registered during the cardiac murmurs than the original heart sound signal. We present a method for heart murmur classification divided into five major steps: a) signal is divided into heart beats; b) entropy gradient envelogram is computed from the pre-processed signal; c) the orbital trajectories are reconstructed using the embedding theory; d) n orbits in the embedding subspace are extracted ( per heart beat); e) the median of the n orbits is used as an input to K-Nearest Neighbors ( KNN) classifier. The experimental results achieved are in agreement with the current state of art for heart murmur classification.

Abstract
In this paper we explore a novel feature for the segmentation of heart sounds: the entropy gradient. We are motivated by the fact that auscultations in real environments are highly contaminated by noise and results reinforce our suspicions that the entropy gradient is not only robust to such noise but maintains a high sensitivity to the S1 and S2 components of the signal. Our whole approach consists of three stages, out of which the last two are novel contributions to this field. The first stage consists of typical pre-processing and wavelet reconstruction to obtain the Shannon energy envelogram. On the second stage we use an embedding matrix to track the dynamics of the system, which is formed by delay vectors with higher dimension than the corresponding attractor. On the third stage, we use the eigenvalues and eigenvectors of the embedding matrix to estimate the entropy of the envelogram. Finite differences are used to estimate entropy gradients, in which standard peak picking approaches are used for heart sound segmentation. Experiments are performed on a public dataset of pediatric auscultations obtained in real environments and results show the promising potential of this novel feature for such noisy scenarios.