Clive Cheong Took

• PhD
• Royal Holloway University of London

This paper analyses the centralized fusion linear estimation problem in multi-sensor systems with multiple packet dropouts and correlated noises. Packet dropouts are modeled by independent Bernoulli distributed random variables. This problem is addressed in the tessarine domain under conditions of T1 and T2-properness, which entails a reduction in...

Learning machines for vector sensor data are naturally developed in the quaternion domain and are underpinned by quaternion statistics. To this end, we revisit the “augmented” representation basis for discrete quaternion random variables (RVs) ${\bf{q}}^{a}[n]$ , i.e., ${[}{\bf{q}}{[}{n}{]}\;{\bf{q}}^{\imath}{[}{n}{]}\;{\bf{q}}^{\jmath}{[}{n}{]}...

Since the recent emergence of Sars-CoV2 virus, the whole academic community shifted dramatically towards online, distance or blended type learning. This has meant that academics and teachers have had to learn new pedagogic and technologically enhanced learning techniques in a short space of time. Moreover, it has led to an increased reliance on rem...

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 treatmen...

This paper analyses the centralized fusion linear estimation problem in multi-sensor systems with multiple packet dropouts and correlated noises. Packet dropouts are modeled by independent Bernoulli distributed random variables. This problem is addressed in the tessarine domain under conditions of T1 and T2-properness, which entails a reduction in...

The quaternion-based least mean square (QLMS) algorithm has found more and more applications since its design in 2009. However, its deployment on edge devices still does not meet the real-time constraints nor the complex design methodology requirements (e.g., parallel computations). We address these issues by proposing a reconfigurable hardware arc...

Matlab files for paper on "Weight sharing for LMS algorithms: Convolutional Neural Networks Inspired Multichannel Adaptive Filtering"

Weight sharing has been a key to the success of convolutional neural networks, as it forces a neural network to detect common ‘local’ features across an image by applying the same weights across all input samples (pixels). This has been shown to resolve both the computational and performance issues as less data are required for training and there i...

Weight sharing has been a key to the success of convolutional neural networks, as it forces a neural network to detect common `local' features across an image by applying the same weights across all input samples (pixels). This has been shown to resolve both the computational and performance issues as less data are required for training and there i...

The roll-out of the new generation smart meter with artificial intelligence (AI)-based data mining algorithms causes serious privacy issues for consumers. By detecting appliance usages, an adversary can easily monitor the behaviour patterns of residents. In this paper, a privacy-preserving smart metering model is proposed; the system utilizes a dat...

Digital signal processing (DSP) education has traditionally employed more demanding mathematics than most topics found among courses in electrical/electronic/computer engineering. In some cases, the technical challenges posed by some courses have made it difficult for students to complete those courses successfully. Here, we advocate for creativity...

Deep neural networks (NNs) have been proved to be efficient learning systems for supervised and unsupervised tasks. However, learning complex data representations using deep NNs can be difficult due to problems such as lack of data, exploding or vanishing gradients, high computational cost, or incorrect parameter initialization, among others. Deep...

Presents information on the 2019 ICASSP Conference.

This is a rebuttal on the correspondence article on “Comments on The Quaternion LMS Algorithm for Adaptive Filtering of Hypercomplex Processes”, T-SP-23558-2018.

Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool i...

The advancement of Internet-of-Things (IoT) edge devices with various types of sensors enables us to harness diverse information with Mobile Crowd-Sensing applications (MCS). This highly dynamic setting entails the collection of ubiquitous data traces, originating from sensors carried by people, introducing new information security challenges; one...

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...

This work addresses the problem of segmentation in time series data with respect to a statistical parameter of interest in Bayesian models. It is common to assume that the parameters are distinct within each segment. As such, many Bayesian change point detection models do not exploit the segment parameter patterns, which can improve performance. Th...

Detection algorithms for electroencephalography (EEG) data, especially in the field of interictal epileptiform discharge (IED) detection, have traditionally employed handcrafted features which utilised specific characteristics of neural responses. Although these algorithms achieve high accuracy, mere detection of an IED holds little clinical signif...

This work develops a class of techniques for the sequential detection of transient changes in the variance of time series data. In particular, we introduce a class of change detection algorithms based on the windowed volatility filter. The first method detects changes by employing a convex combination of two such filters with differing window sizes...

Widely linear estimation plays an important role in quaternion signal processing, as it caters for both proper and improper quaternion signals. However, widely linear algorithms are computationally expensive owing to the use of augmented variables and statistics. To reduce the computation cost while maintaining the performance level, we propose a f...

Recent developments in quaternion-valued widely linear processing have illustrated that the exploitation of complete second-order statistics requires consideration of both the covariance and complementary covariance matrices. Such matrices have a tremendous amount of structure, and their decomposition is a powerful tool in a variety of applications...

Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool i...

Artificial neural networks suffer from prolonged training times, this is intensified when the volume of data is big. Mini-batching has become the standard in training neural networks. By reducing the number of data used to train each iteration the training time greatly shortens; even in a big data environment. A number of techniques such as paralle...

A novel quaternion-valued common spatial patterns (QCSP) algorithm is introduced to model co-channel coupling of multi-dimensional processes. To cater for the generality of quaternion-valued non-circular data, we propose a generalised QCSP (G-QCSP) which incorporates the information on power difference between the real and imaginary parts of data c...

Detection algorithms for electroencephalography (EEG) data typically employ handcrafted features that take advantage of the signal's specific properties. In the field of interictal epileptic discharge (IED) detection, the feature representation that provides optimal classification performance is still an unresolved issue. In this paper, we consider...

The conventional Kalman filter assumes a constant process noise covariance according to the system's dynamics. However, in practice, the dynamics might alter and the initial model for the process noise may not be adequate to adapt to abrupt dynamics of the system. In this paper, we provide a novel informed Kalman filter (IKF) which is informed by a...

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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 uncor...

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 involv...

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...

Complex tensor factorisation of correlated brain sources is addressed in this paper. The electrical brain responses due to motory, sensory, or cognitive stimuli, i.e. event related potentials (ERPs), particularly P300, have been used for cognitive information processing. P300 has two subcomponents, P3a and P3b which are correlated and therefore, th...

MATLAB code simulation

MATLAB simulation for QLMS

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...

Quaternion derivatives in the mathematical literature are typically defined only for analytic (regular) functions. However, in engineering problems, functions of interest are often real-valued and thus not analytic, such as the standard cost function. The HR calculus is a convenient way to calculate formal derivatives of both analytic and non-analy...

With the advent of the emerging field of big data, it is becoming increasingly important to equip machine learning algorithms to cope with volume, variety, and velocity of data. In this work, we employ the MapRe-duce paradigm to address these issues as an enabling technology for the well-known support vector machine to perform distributed classific...

A solution to the problem of intraference is obtained by recognising that the current diagonalisation schemes for the complex symmetric pseudocovariance matrix are not adequate to preserve its intrinsic complex-valued nature. To this end, we propose the correlation preserving transform (CPT), which both maintains the degree of the intrinsic correla...

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...

Forecasting one step ahead is generally straightforward. Forecasting two steps ahead a little more challenging. Forecasting further into the horizon may require prior forecasted samples, as the availability of historical data may not be adequate to do so. It is in this motivational context that we proposed an eigen-based approach for complex-valued...

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...

We introduce the concept of intra-ference in order to quantify the degree to which the integrity of bivariate (or complex) sources is preserved in applications based on matrix decompositions of bivariate data. This is achieved by examining the pseudocovariance matrix of noncircular complex sources, and by recognising that the pseudocovariance is in...

An efficient widely linear prediction algorithm is introduced for the class of wide-sense stationary quaternion signals. Specifically, using second order statistics information in the quaternion domain, a multivariate Durbin-Levison-like algorithm is derived. The proposed solution can be applied under a very general formulation of the problem, allo...

The strictly linear quaternion valued affine projection algorithm (QAPA) and its widely linear counterpart (WLQAPA) are introduced, in order to provide fast converging stochastic gradient learning in the quaternion domain, for the processing of both second order circular (proper) and second order noncircular (improper) signals. This is achieved bas...

The so called “augmented” statistics of complex random variables has established that both the covariance and pseudocovariance are necessary to fully describe second order properties of noncircular complex signals. To jointly decorrelate the covariance and pseudocovariance matrix, the recently proposed strong uncorrelating transform (SUT) requires...

A novel way to calculate the gradient of real functions of quaternion variables, typical cost functions in quaternion signal processing, is proposed. This is achieved by revisiting quaternion involutions and by simplifying the existing HR derivatives. This has allowed us to express the class of quaternion least mean square (QLMS) algorithms in a mo...

The strict Cauchy-Riemann-Fueter (CRF) analyticity conditions establish that only linear quaternion-valued functions are analytic, prohibiting the development of quaternion-valued nonlinear adaptive filters for the recurrent neural network architecture (RNN). In this work, the requirement of local analyticity in gradient based learning is exercised...

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 augment...

We propose a unitary diagonalisation of a special class of quaternion matrices, the so-called η-Hermitian matrices A=AηH,η∈{ı,j,κ} arising in widely linear modelling. In 1915, Autonne exploited the symmetric structure of a matrix A=AT to propose its corresponding factorisation (also known as the Takagi factorisation) in the complex domain C. Simila...

The recently proposed HR-calculus has enabled rigorous derivation of quaternion-valued adaptive filtering algorithms, and has also introduced several equivalent forms of the quaternion least mean square (QLMS). This work aims to address the uniqueness of the solutions to the stochastic gradient optimisation problems, and to provide a unified framew...

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 fol...

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 a...

We introduce a class of gradient adaptive stepsize algorithms for quaternion valued adaptive filtering based on three- and four-dimensional vector sensors. This equips the recently introduced quaternion least mean square (QLMS) algorithm with enhanced tracking ability and enables it to be more responsive to dynamically changing environments, while...

Blind extraction of quaternion-valued latent sources is addressed based on their local temporal properties. The extraction criterion is based on the minimum mean square widely linear prediction error, thus allowing for the extraction of both proper and improper quaternion sources. The use of the widely linear adaptive predictor is justified by the...

Augmented quaternion statistics Widely linear quaternion least mean square (WL-QLMS) Fusion of atmospheric parameters Data fusion via vector spaces a b s t r a c t This work introduces novel methodology for the simultaneous modelling and forecasting of three-dimensional wind field. This is achieved based on a quaternion wind model, which by virtue...

Second order statistics of quaternion random variables and signals are revisited in order to exploit the complete second order statistical information available. The conditions for Q‐proper (second order circular) random processes are presented, and to cater for the non-vanishing pseudocovariance of such processes, the use of ı‐j‐κ‐covariances is i...

Real functions of quaternion variables are typical cost functions in quaternion valued statistical signal processing, however, standard differentiability conditions in the quaternion domain do not permit direct calculation of their gradients. To this end, based on the isomorphism with real vectors and the use of quaternion involutions, we introduce...

A quaternion widely linear (QWL) model for quaternion valued mean-square-error (MSE) estimation is proposed. The augmented statistics are first introduced into the field of quaternions, and it is demonstrated that this allows for capturing the complete second order statistics available. The QWL model is next incorporated into the quaternion least m...

Variable tap-length is introduced into complex-valued adaptive filters in order to provide an additional degree of freedom, enhance tracking ability, and provide data-adaptive optimal modelling. This is achieved by extending the fractional tap-length (FT) algorithm from the real domain ℝ and by accounting for some special properties of the complex...

Short term forecasting of wind field in the quaternion domain is addressed. This is achieved by casting the three components of wind speed (two horizontal and a vertical) into a pure quaternion and adding air temperature as a scalar component, to form the full quaternion. First, HR calculus is introduced in order to provide a unifying framework for...

This work presents novel methodology for the simultaneous modelling and forecasting of three-dimensional (3D) wind fields. This is achieved based on a quaternion domain wind model, which naturally accounts for the coupling between the dimensions of the 3D wind field. The proposed quaternion valued processing also facilitates the fusion of external...

A learning algorithm for the training of quaternion valued adaptive infinite impulse (IIR) filters is introduced. This is achieved by taking into account specific properties of stochastic gradient approximation in the quaternion domain and the recursive nature of the sensitivities within the IIR filter updates, to give the quaternion-valued stochas...

A quaternion valued recursive least squares algorithm for the processing of the generality of quaternion valued random processes (both circular and noncircular) is introduced. This is achieved by extending the widely linear model from the complex domain, and accounting for the specific properties of quaternion algebra. Firstly, the widely linear qu...

An augmented affine projection adaptive filtering algorithm (AAPA), utilising the full second order statistical information in the complex domain is proposed. This is achieved based on the widely linear model and the joint optimisation of the direct and conjugate data channel parameters. The analysis illustrates that the use of augmented complex st...