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 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.

Continual learning models allow them to learn and adapt to new changes and tasks over time. However, in continual and sequential learning scenarios, in which the models are trained using different data with various distributions, neural networks (NNs) tend to forget the previously learned knowledge. This phenomenon is often referred to as catastrophic forgetting. The catastrophic forgetting is an inevitable problem in continual learning models for dynamic environments. To address this issue, we propose a method, called continual Bayesian learning networks (CBLNs), which enables the networks to allocate additional resources to adapt to new tasks without forgetting the previously learned tasks. Using a Bayesian NN, CBLN maintains a mixture of Gaussian posterior distributions that are associated with different tasks. The proposed method tries to optimize the number of resources that are needed to learn each task and avoids an exponential increase in the number of resources that are involved in learning multiple tasks. The proposed method does not need to access the past training data and can choose suitable weights to classify the data points during the test time automatically based on an uncertainty criterion. We have evaluated the method on the MNIST and UCR time-series data sets. The evaluation results show that the method can address the catastrophic forgetting problem at a promising rate compared to the state-of-the-art models.

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.

Quaternion adaptive line enhancer (QALE) has been proposed recently for the recovery of two- (2-D) or three-dimensional (3-D) periodic signals from their noisy mixtures [1] with the help of quaternion-valued adaptive filtering theory. Similar to the traditionall-D [2] version, QALE, relies mainly on the second order similarity between the signal and its delayed version and is more effective when the signal is narrowband. Here, quaternion-valued singular spectrum analysis (QSSA) [3] is used to develop a robust 3-D ALE system where in the reconstruction stage of QSSA the eigentriples are adaptively selected (filtered) using the delayed version of the data. Unlike the QALE where (second) order statistics are taken into account, in the proposed QSSA-QALE the full eigen-spectrum of the embedding matrix is exploited. Consequently, the system works for non-Gaussian noise and wideband 3-D periodic signals. The two systems have been implemented and their results compared. It is shown that the QSSA-QALE significantly outperformed QALE when the noise is not Gaussian.

The advent of Internet of Things, has resulted in the development of infrastructure for capturing and storing data from domains ranging from smart devices (e.g. smartphones) to smart cities. This data is often available publicly and has enabled a wider range of data consumers to utilise such data sets for applications ranging from scientific experimentation to enhancing commercial activity for businesses. Accordingly this has resulted in the need for the development data analysis tools that are both simple to use and provide the most effective tools for a given data set. To this end, we introduce data analysis tools as web service, that enables the data consumer to make a simple HTTP request for processing data over the internet. By providing such tools as a web service, we demonstrate the potential of such a system to aid both the advanced and novice data consumer. Furthermore, this work provides an use case example of the proposed tool on publicly available data extracted from the smart city CityPulse IoT project.

The recent introduction of η-Hermitian matrices A = AηHhas opened a new avenue of research in quaternion signal processing. However, the exploitation of this matrix structure has been limited, perhaps due to the lack of joint diagonalisation methodologies of these matrices. As such, we propose novel decompositions of η-Hermitian matrices to address this shortcoming in the literature. As an application, we consider a blind source separation problem in the form of an Alamouti-based communication system. Simulation studies demonstrate the effectiveness of our proposed joint diago-nalisation technique and indicate that our approach is particularly useful when the sources are correlated.

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 multiple-step ahead forecasting. Here we establish an augmented complex-domain singular spectrum analysis framework to perform prediction beyond 50 step ahead. It is shown that other prediction algorithms such as the least mean square, though useful and adaptive, cannot use the predicted samples to predict further. In some cases, they may diverge from the trend. Simulations on real-world data support our approach.

In this work, we introduce a complex-valued singular spectrum analysis for the analysis of electroencephalogram (EEG), which typically exhibits noncircular probability distribution. To exploit such prior knowledge, our technique makes use of recent advances in complex-valued statistics to exploit the power difference or the correlation between the data channels, in contrast to current methods which cater only for the restrictive class of circular data. In particular, the principal component analysis-like technique was employed to detect the onset of P300, and tracked this event-related potential. In this way, the classification of EEG can be made possible to differentiate between a healthy subject and a schizophrenic patient. In particular, we illuminate how features such as P3a and P3b can be used to perform such classification.