Phase-based causality analysis with partial mutual information from mixed embedding

Instantaneous phases extracted from multivariate time series can retain information about the relationships between the underlying mechanisms that generate the series. Although phases have been widely used in the study of nondirectional coupling and connectivity, they have not found similar appeal in the study of causality. Herein, we present a new method for phase-based causality analysis, which combines ideas from the mixed embedding technique and the information-theoretic approach to causality in coupled oscillatory systems. We then use the introduced method to investigate causality in simulated datasets of bivariate, unidirectionally paired systems from combinations of Rössler, Lorenz, van der Pol, and Mackey-Glass equations. We observe that causality analysis using the phases can capture the true causal relation for coupling strength smaller than the analysis based on the amplitudes can capture. On the other hand, the causality estimation based on the phases tends to have larger variability, which is attributed more to the phase extraction process than the actual phase-based causality method. In addition, an application on real electroencephalographic data from an experiment on elicited human emotional states reinforces the usefulness of phases in causality identification.

Connectivity Analysis for Multivariate Time Series: Correlation vs. Causality

The study of the interdependence relationships of the variables of an examined system is of great importance and remains a challenging task. There are two distinct cases of interdependence. In the first case, the variables evolve in synchrony, connections are undirected and the connectivity is examined based on symmetric measures, such as correlation. In the second case, a variable drives another one and they are connected with a causal relationship. Therefore, directed connections entail the determination of the interrelationships based on causality measures. The main open question that arises is the following: can symmetric correlation measures or directional causality measures be applied to infer the connectivity network of an examined system? Using simulations, we demonstrate the performance of different connectivity measures in case of contemporaneous or/and temporal dependencies. Results suggest the sensitivity of correlation measures when temporal dependencies exist in the data. On the other hand, causality measures do not spuriously indicate causal effects when data present only contemporaneous dependencies. Finally, the necessity of introducing effective instantaneous causality measures is highlighted since they are able to handle both contemporaneous and causal effects at the same time. Results based on instantaneous causality measures are promising; however, further investigation is required in order to achieve an overall satisfactory performance.

An Experimental Review on Deep Learning Architectures for Time Series Forecasting

In recent years, deep learning techniques have outperformed traditional models in many machine learning tasks. Deep neural networks have successfully been applied to address time series forecasting problems, which is a very important topic in data mining. They have proved to be an effective solution given their capacity to automatically learn the temporal dependencies present in time series. However, selecting the most convenient type of deep neural network and its parametrization is a complex task that requires considerable expertise. Therefore, there is a need for deeper studies on the suitability of all existing architectures for different forecasting tasks. In this work, we face two main challenges: a comprehensive review of the latest works using deep learning for time series forecasting and an experimental study comparing the performance of the most popular architectures. The comparison involves a thorough analysis of seven types of deep learning models in terms of accuracy and efficiency. We evaluate the rankings and distribution of results obtained with the proposed models under many different architecture configurations and training hyperparameters. The datasets used comprise more than 50,000 time series divided into 12 different forecasting problems. By training more than 38,000 models on these data, we provide the most extensive deep learning study for time series forecasting. Among all studied models, the results show that long short-term memory (LSTM) and convolutional networks (CNN) are the best alternatives, with LSTMs obtaining the most accurate forecasts. CNNs achieve comparable performance with less variability of results under different parameter configurations, while also being more efficient.

The Effect of a Hidden Source on the Estimation of Connectivity Networks from Multivariate Time Series

Many methods of Granger causality, or broadly termed connectivity, have been developed to assess the causal relationships between the system variables based only on the information extracted from the time series. The power of these methods to capture the true underlying connectivity structure has been assessed using simulated dynamical systems where the ground truth is known. Here, we consider the presence of an unobserved variable that acts as a hidden source for the observed high-dimensional dynamical system and study the effect of the hidden source on the estimation of the connectivity structure. In particular, the focus is on estimating the direct causality effects in high-dimensional time series (not including the hidden source) of relatively short length. We examine the performance of a linear and a nonlinear connectivity measure using dimension reduction and compare them to a linear measure designed for latent variables. For the simulations, four systems are considered, the coupled Hénon maps system, the coupled Mackey-Glass system, the neural mass model and the vector autoregressive (VAR) process, each comprising 25 subsystems (variables for VAR) at close chain coupling structure and another subsystem (variable for VAR) driving all others acting as the hidden source. The results show that the direct causality measures estimate, in general terms, correctly the existing connectivity in the absence of the source when its driving is zero or weak, yet fail to detect the actual relationships when the driving is strong, with the nonlinear measure of dimension reduction performing best. An example from finance including and excluding the USA index in the global market indices highlights the different performance of the connectivity measures in the presence of hidden source.

The Automatic Detection of Seizure Based on Tensor Distance And Bayesian Linear Discriminant Analysis

Electroencephalogram (EEG) plays an important role in recording brain activity to diagnose epilepsy. However, it is not only laborious, but also not very cost effective for medical experts to manually identify the features on EEG. Therefore, automatic seizure detection in accordance with the EEG recordings is significant for the diagnosis and treatment of epilepsy. Here, a new method for detecting seizures using tensor distance (TD) is proposed. First, the time-frequency characteristics of EEG signals are obtained by wavelet transformation, and the tensor representation of EEG signals is then obtained. Tucker decomposition is used to obtain the principal components of the EEG tensor. After, the distances between different categories of EEG tensors are calculated as the EEG features. Finally, the TD features are classified through the Bayesian Linear Discriminant Analysis (Bayesian LDA) classifier. The performance of this method is measured by the sensitivity, specificity, and recognition accuracy. Results indicate 95.12% sensitivity, 97.60% specificity, 97.60% recognition accuracy, and a false detection rate of 0.76 per hour in the invasive EEG dataset, which included 566.57[Formula: see text]h of EEG recording data from 21 patients. Taken together, the results show that TD has a good detection effect for seizure classification and that this method has high computational speed and great potential for real-time diagnosis.

Detection of Epileptic Seizure Using Pretrained Deep Convolutional Neural Network and Transfer Learning

INTRODUCTION

The diagnosis of epilepsy takes a certain process, depending entirely on the attending physician. However, the human factor may cause erroneous diagnosis in the analysis of the EEG signal. In the past 2 decades, many advanced signal processing and machine learning methods have been developed for the detection of epileptic seizures. However, many of these methods require large data sets and complex operations.

METHODS

In this study, an end-to-end machine learning model is presented for detection of epileptic seizure using the pretrained deep two-dimensional convolutional neural network (CNN) and the concept of transfer learning. The EEG signal is converted directly into visual data with a spectrogram and used directly as input data.

RESULTS

The authors analyzed the results of the training of the proposed pretrained AlexNet CNN model. Both binary and ternary classifications were performed without any extra procedure such as feature extraction. By performing data set creation from short-term spectrogram graphic images, the authors were able to achieve 100% accuracy for binary classification for epileptic seizure detection and 100% for ternary classification.

DISCUSSION/CONCLUSION

The proposed automatic identification and classification model can help in the early diagnosis of epilepsy, thus providing the opportunity for effective early treatment.

Comparison of Causality Network Estimation in the Sensor and Source Space: Simulation and Application on EEG

The usage of methods for the estimation of the true underlying connectivity among the observed variables of a system is increasing, especially in the domain of neuroscience. Granger causality and similar concepts are employed for the estimation of the brain network from electroencephalogram (EEG) data. Also source localization techniques, such as the standardized low resolution electromagnetic tomography (sLORETA), are widely used for obtaining more reliable data in the source space. In this work, connectivity structures are estimated in the sensor and in the source space making use of the sLORETA transformation for simulated and for EEG data with episodes of spontaneous epileptiform discharges (ED). From the comparative simulation study on high-dimensional coupled stochastic and deterministic systems originating in the sensor space, we conclude that the structure of the estimated causality networks differs in the sensor space and in the source space. Moreover, different network types, such as random, small-world and scale-free, can be better discriminated on the basis of the data in the original sensor space than on the transformed data in the source space. Similarly, in EEG epochs containing epileptiform discharges, the discriminative ability of network topological indices was significantly better in the sensor compared to the source level. In conclusion, causality networks constructed at the sensor and source level, for both simulated and empirical data, exhibit significant structural differences. These observations indicate that further studies are warranted in order to clarify the exact relationship between data registered in the sensor and source space.

Roles of Very Fast Ripple (500-1000[Formula: see text]Hz) in the Hippocampal Network During Status Epilepticus

Very fast ripples (VFRs, 500-1000[Formula: see text]Hz) are considered more specific than high-frequency oscillations (80-500[Formula: see text]Hz) as biomarkers of epileptogenic zones. Although VFRs are frequent abnormal phenomena in epileptic seizures, their functional roles remain unclear. Here, we detected the VFRs in the hippocampal network and tracked their roles during status epilepticus (SE) in rats with pilocarpine-induced temporal lobe epilepsy (TLE). All regions in the hippocampal network exhibited VFRs in the baseline, preictal, ictal and postictal states, with the ictal state containing the most VFRs. Moreover, strong phase-locking couplings existed between VFRs and slow oscillations (1-12[Formula: see text]Hz) in the ictal and postictal states for all regions. Further investigation indicated that during VFRs, the build-up of slow oscillations in the ictal state began from the temporal lobe and then spread through the whole hippocampal network via two different pathways, which might be associated with the underlying propagation of epileptiform discharges in the hippocampal network. Overall, we provide a functional description of the emergence of VFRs in the hippocampal network during SE, and we also establish that VFRs may be the physiological representation of the pathological alterations in hippocampal network activity during SE in TLE.

Transfer entropies within dynamical effects framework

Transfer entropy (TE) is widely used in time-series analysis to detect causal couplings between temporally evolving objects. As a coupling strength quantifier, the TE alone often seems insufficient, raising the question of its further interpretations. Here the TE is related to dynamical causal effects (DCEs) which quantify long-term responses of a coupling recipient to variations in a coupling source or in a coupling itself: Detailed relationships are established for a paradigmatic stochastic dynamical system of bidirectionally coupled linear overdamped oscillators, their practical applications and possible extensions are discussed. It is shown that two widely used versions of the TE (original and infinite-history) can become qualitatively distinct, diverging to different long-term DCEs.

EEG Connectivity Analysis Using Denoising Autoencoders for the Detection of Dyslexia

The Temporal Sampling Framework (TSF) theorizes that the characteristic phonological difficulties of dyslexia are caused by an atypical oscillatory sampling at one or more temporal rates. The LEEDUCA study conducted a series of Electroencephalography (EEG) experiments on children listening to amplitude modulated (AM) noise with slow-rythmic prosodic (0.5-1[Formula: see text]Hz), syllabic (4-8[Formula: see text]Hz) or the phoneme (12-40[Formula: see text]Hz) rates, aimed at detecting differences in perception of oscillatory sampling that could be associated with dyslexia. The purpose of this work is to check whether these differences exist and how they are related to children's performance in different language and cognitive tasks commonly used to detect dyslexia. To this purpose, temporal and spectral inter-channel EEG connectivity was estimated, and a denoising autoencoder (DAE) was trained to learn a low-dimensional representation of the connectivity matrices. This representation was studied via correlation and classification analysis, which revealed ability in detecting dyslexic subjects with an accuracy higher than 0.8, and balanced accuracy around 0.7. Some features of the DAE representation were significantly correlated ([Formula: see text]) with children's performance in language and cognitive tasks of the phonological hypothesis category such as phonological awareness and rapid symbolic naming, as well as reading efficiency and reading comprehension. Finally, a deeper analysis of the adjacency matrix revealed a reduced bilateral connection between electrodes of the temporal lobe (roughly the primary auditory cortex) in DD subjects, as well as an increased connectivity of the F7 electrode, placed roughly on Broca's area. These results pave the way for a complementary assessment of dyslexia using more objective methodologies such as EEG.

Rhythmic Network Modulation to Thalamocortical Couplings in Epilepsy

Thalamus interacts with cortical areas, generating oscillations characterized by their rhythm and levels of synchrony. However, little is known of what function the rhythmic dynamic may serve in thalamocortical couplings. This work introduced a general approach to investigate the modulatory contribution of rhythmic scalp network to the thalamo-frontal couplings in juvenile myoclonic epilepsy (JME) and frontal lobe epilepsy (FLE). Here, time-varying rhythmic network was constructed using the adapted directed transfer function between EEG electrodes, and then was applied as a modulator in fMRI-based thalamocortical functional couplings. Furthermore, the relationship between corticocortical connectivity and rhythm-dependent thalamocortical coupling was examined. The results revealed thalamocortical couplings modulated by EEG scalp network have frequency-dependent characteristics. Increased thalamus- sensorimotor network (SMN) and thalamus-default mode network (DMN) couplings in JME were strongly modulated by alpha band. These thalamus-SMN couplings demonstrated enhanced association with SMN-related corticocortical connectivity. In addition, altered theta-dependent and beta-dependent thalamus-frontoparietal network (FPN) couplings were found in FLE. The reduced theta-dependent thalamus-FPN couplings were associated with the decreased FPN-related corticocortical connectivity. This study proposed interactive links between the rhythmic modulation and thalamocortical coupling. The crucial role of SMN and FPN in subcortical-cortical circuit may have implications for intervention in generalized and focal epilepsy.

Reorganization of Large-Scale Functional Networks During Low-Frequency Electrical Stimulation of the Cortical Surface

We investigated the functional network reorganization caused by low-frequency electrical stimulation (LFES) of human brain cortical surface. Intracranial EEG data from subdural grid positions were analyzed in 16 pre-surgery epileptic patients. LFES was performed by injecting current pulses (10[Formula: see text]mA, 0.2[Formula: see text]ms pulse width, 0.5[Formula: see text]Hz, 25 trials) into all adjacent electrode contacts. Dynamic functional connectivity analysis was carried out on two frequency bands (low: 1–4[Formula: see text]Hz; high: 10–40[Formula: see text]Hz) to investigate the early, high frequency and late, low frequency responses elicited by the stimulation. The centralization increased in early compared to late responses, suggesting a more prominent role of direct neural links between primarily activated areas and distant brain regions. Injecting the current into the seizure onset zone (SOZ) evoked a more integrated functional topology during the early (N1) period of the response, whereas during the late (N2) period — regardless of the stimulation site — the connectedness of the SOZ was elevated compared to the non-SOZ tissue. The abnormal behavior of the epileptic sub-network during both part of the responses supports the idea of the pathogenic role of impaired inhibition and excitation mechanisms in epilepsy.