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.

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.

Motor Imagery Classification Using Mu and Beta Rhythms of EEG with Strong Uncorrelating Transform Based Complex Common Spatial Patterns.

Recent studies have demonstrated the disassociation between the mu and beta rhythms of electroencephalogram (EEG) during motor imagery tasks. The proposed algorithm in this paper uses a fully data-driven multivariate empirical mode decomposition (MEMD) in order to obtain the mu and beta rhythms from the nonlinear EEG signals. Then, the strong uncorrelating transform complex common spatial patterns (SUTCCSP) algorithm is applied to the rhythms so that the complex data, constructed with the mu and beta rhythms, becomes uncorrelated and its pseudocovariance provides supplementary power difference information between the two rhythms.

Enabling quaternion derivatives: the generalized HR calculus.

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.