A review of signal processing and machine learning techniques for interictal epileptiform discharge detection.

Brain interictal epileptiform discharges (IEDs), as one of the hallmarks of epileptic brain, are transient events captured by electroencephalogram (EEG). IEDs are generated by seizure networks, and they occur between seizures (interictal periods). The development of a robust method for IED detection could be highly informative for clinical treatment procedures and epileptic patient management. Since 1972, different machine learning techniques, from template matching to deep learning, have been developed to automatically detect IEDs from scalp EEG (scEEG) and intracranial EEG (iEEG). While the scEEG signals suffer from low information details and high attenuation of IEDs due to the high skull electrical impedance, the iEEG signals recorded using implanted electrodes enjoy higher details and are more suitable for identifying the IEDs. In this review paper, we group IED detection techniques into six categories: (1) template matching, (2) feature representation (mimetic, time-frequency, and nonlinear features), (3) matrix decomposition, (4) tensor factorization, (5) neural networks, and (6) estimation of the iEEG from the concurrent scEEG followed by detection and classification. The methods are compared quantitatively (e.g., in terms of accuracy, sensitivity, and specificity), and their general advantages and limitations are described. Finally, current limitations and possible future research paths related to this field are mentioned.

Deep Neural Architectures for Mapping Scalp to Intracranial EEG.

Data is often plagued by noise which encumbers machine learning of clinically useful biomarkers and electroencephalogram (EEG) data is no exemption. Intracranial EEG (iEEG) data enhances the training of deep learning models of the human brain, yet is often prohibitive due to the invasive recording process. A more convenient alternative is to record brain activity using scalp electrodes. However, the inherent noise associated with scalp EEG data often impedes the learning process of neural models, achieving substandard performance. Here, an ensemble deep learning architecture for nonlinearly mapping scalp to iEEG data is proposed. The proposed architecture exploits the information from a limited number of joint scalp-intracranial recording to establish a novel methodology for detecting the epileptic discharges from the sEEG of a general population of subjects. Statistical tests and qualitative analysis have revealed that the generated pseudo-intracranial data are highly correlated with the true intracranial data. This facilitated the detection of IEDs from the scalp recordings where such waveforms are not often visible. As a real-world clinical application, these pseudo-iEEGs are then used by a convolutional neural network for the automated classification of intracranial epileptic discharges (IEDs) and non-IED of trials in the context of epilepsy analysis. Although the aim of this work was to circumvent the unavailability of iEEG and the limitations of sEEG, we have achieved a classification accuracy of 68% an increase of 6% over the previously proposed linear regression mapping.

Quaternion Singular Spectrum Analysis of Electroencephalogram With Application in Sleep Analysis.

A novel quaternion-valued singular spectrum analysis (SSA) is introduced for multichannel analysis of electroencephalogram (EEG). The analysis of EEG typically requires the decomposition of data channels into meaningful components despite the notoriously noisy nature of EEG--which is the aim of SSA. However, the singular value decomposition involved in SSA implies the strict orthogonality of the decomposed components, which may not reflect accurately the sources which exhibit similar neural activities. To allow for the modelling of such co-channel coupling, the quaternion domain is considered for the first time to formulate the SSA using the augmented statistics. As an application, we demonstrate how the augmented quaternion-valued SSA (AQSSA) can be used to extract the sources, even at a signal-to-noise ratio as low as -10 dB. To illustrate the usefulness of our quaternion-valued SSA in a rehabilitation setting, we employ the proposed SSA for sleep analysis to extract statistical descriptors for five-stage classification (Awake, N1, N2, N3 and REM). The level of agreement using these descriptors was 74% as quantified by the Cohen's kappa.

Maintaining the integrity of sources in complex learning systems: intraference and the correlation preserving transform.

The correlation preserving transform (CPT) is introduced to perform bivariate component analysis via decorrelating matrix decompositions, while at the same time preserving the integrity of original bivariate sources. Specifically, unlike existing bivariate uncorrelating matrix decomposition techniques, CPT is designed to preserve both the order of the data channels within every bivariate source and their mutual correlation properties. We introduce the notion of intraference to quantify the effects of interchannel mixing artifacts within recovered bivariate sources, and show that the integrity of separated sources is compromised when not accounting for the intrinsic correlations within bivariate sources, as is the case with current bivariate matrix decompositions. The CPT is based on augmented complex statistics and involves finding the correct conjugate eigenvectors associated with the pseudocovariance matrix, making it possible to maintain the physical meaning of the separated sources. The benefits of CPT are illustrated in the source separation and clustering scenarios, for both synthetic and real-world data.

Adaptive convex combination approach for the identification of improper quaternion processes.

Data-adaptive optimal modeling and identification of real-world vector sensor data is provided by combining the fractional tap-length (FT) approach with model order selection in the quaternion domain. To account rigorously for the generality of such processes, both second-order circular (proper) and noncircular (improper), the proposed approach in this paper combines the FT length optimization with both the strictly linear quaternion least mean square (QLMS) and widely linear QLMS (WL-QLMS). A collaborative approach based on QLMS and WL-QLMS is shown to both identify the type of processes (proper or improper) and to track their optimal parameters in real time. Analysis shows that monitoring the evolution of the convex mixing parameter within the collaborative approach allows us to track the improperness in real time. Further insight into the properties of those algorithms is provided by establishing a relationship between the steady-state error and optimal model order. The approach is supported by simulations on model order selection and identification of both strictly linear and widely linear quaternion-valued systems, such as those routinely used in renewable energy (wind) and human-centered computing (biomechanics).

Augmented Complex Common Spatial Patterns for Classification of Noncircular EEG From Motor Imagery Tasks.

A novel augmented complex-valued common spatial pattern (CSP) algorithm is introduced in order to cater for general complex signals with noncircular probability distributions. This is a typical case in multichannel electroencephalogram (EEG), due to the power difference or correlation between the data channels, yet current methods only cater for a very restrictive class of circular data. The proposed complex-valued CSP algorithms account for the generality of complex noncircular data, by virtue of the use of augmented complex statistics and the strong-uncorrelating transform (SUT). Depending on the degree of power difference of complex signals, the analysis and simulations show that the SUT based algorithm maximizes the inter-class difference between two motor imagery tasks. Simulations on both synthetic noncircular sources and motor imagery experiments using real-world EEG support the approach.

Fast independent component analysis algorithm for quaternion valued signals.

An extension of the fast independent component analysis algorithm is proposed for the blind separation of both Q-proper and Q-improper quaternion-valued signals. This is achieved by maximizing a negentropy-based cost function, and is derived rigorously using the recently developed HR calculus in order to implement Newton optimization in the augmented quaternion statistics framework. It is shown that the use of augmented statistics and the associated widely linear modeling provides theoretical and practical advantages when dealing with general quaternion signals with noncircular (rotation-dependent) distributions. Simulations using both benchmark and real-world quaternion-valued signals support the approach.

Quaternion-valued nonlinear adaptive filtering.

A class of nonlinear quaternion-valued adaptive filtering algorithms is proposed based on locally analytic nonlinear activation functions. To circumvent the stringent standard analyticity conditions which are prohibitive to the development of nonlinear adaptive quaternion-valued estimation models, we use the fact that stochastic gradient learning algorithms require only local analyticity at the operating point in the estimation space. It is shown that the quaternion-valued exponential function is locally analytic, and, since local analyticity extends to polynomials, products, and ratios, we show that a class of transcendental nonlinear functions can serve as activation functions in nonlinear and neural adaptive models. This provides a unifying framework for the derivation of gradient-based learning algorithms in the quaternion domain, and the derived algorithms are shown to have the same generic form as their real- and complex-valued counterparts. To make such models second-order optimal for the generality of quaternion signals (both circular and noncircular), we use recent developments in augmented quaternion statistics to introduce widely linear versions of the proposed nonlinear adaptive quaternion valued filters. This allows full exploitation of second-order information in the data, contained both in the covariance and pseudocovariances to cater rigorously for second-order noncircularity (improperness), and the corresponding power mismatch in the signal components. Simulations over a range of circular and noncircular synthetic processes and a real world 3-D noncircular wind signal support the approach.

Kurtosis-based blind source extraction of complex non-circular signals with application in EEG artifact removal in real-time.

A new class of complex domain blind source extraction algorithms suitable for the extraction of both circular and non-circular complex signals is proposed. This is achieved through sequential extraction based on the degree of kurtosis and in the presence of non-circular measurement noise. The existence and uniqueness analysis of the solution is followed by a study of fast converging variants of the algorithm. The performance is first assessed through simulations on well understood benchmark signals, followed by a case study on real-time artifact removal from EEG signals, verified using both qualitative and quantitative metrics. The results illustrate the power of the proposed approach in real-time blind extraction of general complex-valued sources.

Split quaternion nonlinear adaptive filtering.

A split quaternion learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of three- and four-dimensional signals is proposed. The derivation takes into account the non-commutativity of the quaternion product, an aspect neglected in the derivation of the existing learning algorithms. It is shown that the additional information taken into account by a rigorous treatment of quaternion algebra provides improved performance on hypercomplex processes. A rigorous analysis of the convergence of the proposed algorithms is also provided. Simulations on both benchmark and real-world signals support the approach.

Fractional delay estimation for blind source separation and localization of temporomandibular joint sounds.

Temporomandibular joint (TMJ) sound sources are generated from the two joints connecting the lower jaw to the temporal bone. Such sounds are important diagnostic signs in patients suffering from temporomandibular disorder (TMD). In this study, we address the problem of source separation of the TMJ sounds. In particular, we examine patients with only one TMJ generating "clicks". Thereafter, we consider the TMJ sounds recorded from the two auditory canals as mixtures of clicks from the TMD joint and the noise produced by the other healthy/normal TMJ. We next exploit the statistical nonstationary nature of the TMJ signals by employing the degenerate unmixing estimation technique (DUET) algorithm, a time-frequency (T-F) approach to separate the sources. As the DUET algorithm requires the sensors to be closely spaced, which is not satisfied by our recording setup, we have to estimate the delay between the recorded TMJ sounds to perform an alignment of the mixtures. Thus, the proposed extension of DUET enables an essentially arbitrary separation of the sensors. It is also shown that DUET outperforms the convolutive Infomax algorithm in this particular TMJ source separation scenario. The spectra of both separated TMJ sources with our method are comparable to those available in existing literature. Examination of both spectra suggests that the click source has a better audible prominence than the healthy TMJ source. Furthermore, we address the problem of source localization. This can be achieved automatically by detecting the sign of our proposed mutual information estimator which exhibits a maximum at the delay between the two mixtures. As a result, the localized separated TMJ sources can be of great clinical value to dental specialists.

Underdetermined blind source separation of temporomandibular joint sounds.

The underdetermined blind source separation problem using a filtering approach is addressed. An extension of the FastICA algorithm is devised which exploits the disparity in the kurtoses of the underlying sources to estimate the mixing matrix and thereafter achieves source recovery by employing the ll-norm algorithm. Besides, we demonstrate how promising FastICA can be to extract the sources. Furthermore, we illustrate how this scenario is particularly appropriate for the separation of temporomandibular joint (TMJ) sounds.