Segment Parameter Labelling in MCMC Mean-Shift Change Detection

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. This work proposes a Bayesian mean-shift change point detection algorithm that makes use of repetition in segment parameters, by introducing segment class labels that utilise a Dirichlet process prior. The performance of the proposed approach was assessed on both synthetic and real world data, highlighting the enhanced performance when using parameter labelling

Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing

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 in a variety of applications, the non-commutative nature of the quaternion product has been prohibitive to the development of quaternion uncorrelating transforms. To this end, we introduce novel techniques for a simultaneous decomposition of the covariance and complementary covariance matrices in the quaternion domain, whereby the quaternion version of the Takagi factorisation is explored to diagonalise symmetric quaternion-valued matrices. This gives new insights into the quaternion uncorrelating transform (QUT) and forms a basis for the proposed quaternion approximate uncorrelating transform (QAUT) which simultaneously diagonalises all four covariance matrices associated with improper quaternion signals. The effectiveness of the proposed uncorrelating transforms is validated by simulations on both synthetic and real-world quaternion-valued signals.Comment: 41 pages, single column, 10 figure

A regularised EEG informed Kalman filtering algorithm

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 an extrinsic data channel carrying information about the system’s future state. Thus, each state can be represented with a corresponding process noise covariance, i.e. the Kalman gain is automatically adjusted according to the detected state. As a real-world application, we demonstrate for the first time how the analysis of electroencephalogram (EEG) can be used to predict the voluntary body movement and inform the tracking Kalman algorithm about a possible state transition. Furthermore, we provide a rigorous analysis to establish a relationship between the Kalman performance and the detection accuracy. Simulations on both synthetic and real-world data support our analysis

Machine learning methods for detecting urinary tract infection and analysing daily living activities in people with dementia

Dementia is a neurological and cognitive condition that affects millions of people around the world. At any given time in the United Kingdom, 1 in 4 hospital beds are occupied by a person with dementia, while about 22% of these hospital admissions are due to preventable causes. In this paper we discuss using Internet of Things (IoT) technologies and in-home sensory devices in combination with machine learning techniques to monitor health and well-being of people with dementia. This will allow us to provide more effective and preventative care and reduce preventable hospital admissions. One of the unique aspects of this work is combining environmental data with physiological data collected via low cost in-home sensory devices to extract actionable information regarding the health and well-being of people with dementia in their own home environment. We have worked with clinicians to design our machine learning algorithms where we focused on developing solutions for real-world settings. In our solutions, we avoid generating too many alerts/alarms to prevent increasing the monitoring and support workload. We have designed an algorithm to detect Urinary Tract Infections (UTI) which is one of the top five reasons of hospital admissions for people with dementia (around 9% of hospital admissions for people with dementia in the UK). To develop the UTI detection algorithm, we have used a Non-negative Matrix Factorisation (NMF) technique to extract latent factors from raw observation and use them for clustering and identifying the possible UTI cases. In addition, we have designed an algorithm for detecting changes in activity patterns to identify early symptoms of cognitive decline or health decline in order to provide personalised and preventative care services. For this purpose, we have used an Isolation Forest (iForest) technique to create a holistic view of the daily activity patterns. This paper describes the algorithms and discusses the evaluation of the work using a large set of real-world data collected from a trial with people with dementia and their caregivers

Eigen-based machine learning techniques for complex and hyper-complex processing.

One of the earlier works on eigen-based techniques for the hyper-complex domain of quaternions was on “quaternion principal component analysis of colour images”. The results of this work are still instructive in many aspects. First, it showed how naturally the quaternion domain accounts for the coupling between the dimensions of red, blue and green of an image, hence its suitability for multichannel processing. Second, it was clear that there was a lack of eigen-based techniques for such a domain, which explains the non-trivial gap in the literature. Third, the lack of such eigen-based quaternion tools meant that the scope and the applications of quaternion signal processing were quite limited, especially in the field of biomedicine. And fourth, quaternion principal component analysis made use of complex matrix algebra, which reminds us that the complex domain lays the building blocks of the quaternion domain, and therefore any research endeavour in quaternion signal processing should start with the complex domain. As such, the first contribution of this thesis lies in the proposition of complex singular spectrum analysis. That research provided a deep understanding and an appreciation of the intricacies of the complex domain and its impact on the quaternion domain. As the complex domain offers one degree of freedom over the real domain, the statistics of a complex variable x has to be augmented with its complex conjugate x*, which led to the term augmented statistics. This recent advancement in complex statistics was exploited in the proposed complex singular spectrum analysis. The same statistical notion was used in proposing novel quaternion eigen-based techniques such as the quaternion singular spectrum analysis, the quaternion uncorrelating transform, and the quaternion common spatial patterns. The latter two methods highlighted an important gap in the literature – there were no algebraic methods that solved the simultaneous diagonalisation of quaternion matrices. To address this issue, this thesis also presents new fundamental results on quaternion matrix factorisations and explores the depth of quaternion algebra. To demonstrate the efficacy of these methods, real-world problems mainly in biomedical engineering were considered. First, the proposed complex singular spectrum analysis successfully addressed an examination of schizophrenic data through the estimation of the event-related potential of P300. Second, the automated detection of the different stages of sleep was made possible using the proposed quaternion singular spectrum analysis. Third, the proposed quaternion common spatial patterns facilitated the discrimination of Parkinsonian patients from healthy subjects. To illustrate the breadth of the proposed eigen-based techniques, other areas of applications were also presented, such as in wind and financial forecasting, and Alamouti-based communication problems. Finally, a preliminary work is made available to suggest that the next step from this thesis is to move from static models (eigen-based models) to dynamic models (such as tracking models)

Eigen-based machine learning techniques for complex and hyper-complex processing.

One of the earlier works on eigen-based techniques for the hyper-complex domain of quaternions was on “quaternion principal component analysis of colour images”. The results of this work are still instructive in many aspects. First, it showed how naturally the quaternion domain accounts for the coupling between the dimensions of red, blue and green of an image, hence its suitability for multichannel processing. Second, it was clear that there was a lack of eigen-based techniques for such a domain, which explains the non-trivial gap in the literature. Third, the lack of such eigen-based quaternion tools meant that the scope and the applications of quaternion signal processing were quite limited, especially in the field of biomedicine. And fourth, quaternion principal component analysis made use of complex matrix algebra, which reminds us that the complex domain lays the building blocks of the quaternion domain, and therefore any research endeavour in quaternion signal processing should start with the complex domain. As such, the first contribution of this thesis lies in the proposition of complex singular spectrum analysis. That research provided a deep understanding and an appreciation of the intricacies of the complex domain and its impact on the quaternion domain. As the complex domain offers one degree of freedom over the real domain, the statistics of a complex variable x has to be augmented with its complex conjugate x*, which led to the term augmented statistics. This recent advancement in complex statistics was exploited in the proposed complex singular spectrum analysis. The same statistical notion was used in proposing novel quaternion eigen-based techniques such as the quaternion singular spectrum analysis, the quaternion uncorrelating transform, and the quaternion common spatial patterns. The latter two methods highlighted an important gap in the literature – there were no algebraic methods that solved the simultaneous diagonalisation of quaternion matrices. To address this issue, this thesis also presents new fundamental results on quaternion matrix factorisations and explores the depth of quaternion algebra. To demonstrate the efficacy of these methods, real-world problems mainly in biomedical engineering were considered. First, the proposed complex singular spectrum analysis successfully addressed an examination of schizophrenic data through the estimation of the event-related potential of P300. Second, the automated detection of the different stages of sleep was made possible using the proposed quaternion singular spectrum analysis. Third, the proposed quaternion common spatial patterns facilitated the discrimination of Parkinsonian patients from healthy subjects. To illustrate the breadth of the proposed eigen-based techniques, other areas of applications were also presented, such as in wind and financial forecasting, and Alamouti-based communication problems. Finally, a preliminary work is made available to suggest that the next step from this thesis is to move from static models (eigen-based models) to dynamic models (such as tracking models)

A New Pattern Representation Method for Time-series Data

The rapid growth of Internet of Things (IoT) and sensing technologies has led to an increasing interest in time-series data analysis. In many domains, detecting patterns of IoT data and interpreting these patterns are challenging issues. There are several methods in time-series analysis that deal with issues such as volume and velocity of IoT data streams. However, analysing the content of the data streams and extracting insights from dynamic IoT data is still a challenging task. In this paper, we propose a pattern representation method which represents time-series frames as vectors by first applying Piecewise Aggregate Approximation (PAA) and then applying Lagrangian Multipliers. This method allows representing continuous data as a series of patterns that can be used and processed by various higher-level methods. We introduce a new change point detection method which uses the constructed patterns in its analysis. We evaluate and compare our representation method with Blocks of Eigenvalues Algorithm (BEATS) and Symbolic Aggregate approXimation (SAX) methods to cluster various datasets. We have also evaluated our proposed change detection method. We have evaluated our algorithm using UCR time-series datasets and also a healthcare dataset. The evaluation results show significant improvements in analysing time-series data in our proposed method

Lagrangian-based Pattern Extraction for Edge Computing in the Internet of Things

Edge computing can improve the scalability and efficiency of IoT systems by performing some of the analysis and operations on the nodes or on intermediary edge devices. This will reduce the energy consumption, data transmission load and latency by shifting some of the processes to the edge devices. In this paper, we introduce a pattern extraction method which uses both the Lagrangian Multiplier and the Principal Component Analysis (PCA) to create patterns from raw sensory data. We have evaluated our method by applying a clustering method on constructed patterns. The results show that by using our proposed Lagrangian-based pattern extraction method, the existing clustering algorithms perform more accurately - by up to 20% higher compared with the state-of-the-art methods, especially in dealing with dynamic real-world data. We have conducted our evaluations based on synthetic and real-world data sets and have compared the results to the existing state-of-the-art approaches. We also discuss how the proposed methods can be embedded into the edge computing devices in IoT systems and applications