arXiv subjects

Danilo P. Mandic

Publications and source records attributed to Danilo P. Mandic.

At least 37 records · Page 2Linked to original sources

arXiv2023

A Deep Matched Filter For R-Peak Detection in Ear-ECG

The Ear-ECG provides a continuous Lead I electrocardiogram (ECG) by measuring the potential difference related to heart activity using electrodes that can be embedded within earphones. The significant increase in wearability and comfort afforded by Ear-ECG is often accompanied by a corresponding degradation in signal quality - a common obstacle that is shared by most wearable technologies. We aim to resolve this issue by introducing a Deep Matched Filter (Deep-MF) for the highly accurate detection of R-peaks in wearable ECG, thus enhancing the utility of Ear-ECG in real-world scenarios. The Deep-MF consists of an encoder stage (trained as part of an encoder-decoder module to reproduce ground truth ECG), and an R-peak classifier stage. Through its operation as a Matched Filter, the encoder searches for matches with an ECG template pattern in the input signal, prior to filtering the matches with the subsequent convolutional layers and selecting peaks corresponding to true ECG matches. The so condensed latent representation of R-peak information is then fed into a simple R-peak classifier, of which the output provides precise R-peak locations. The proposed Deep Matched Filter is evaluated using leave-one-subject-out cross validation over 36 subjects with an age range of 18-75, with the Deep-MF outperforming existing algorithms for R-peak detection in noisy ECG. The Deep-MF achieves a median R-peak recall of 94.9\%, a median precision of 91.2\% and an (AUC) value of 0.97. Furthermore, we demonstrate that the Deep Matched Filter algorithm not only retains the initialised ECG kernel structure during the training process, but also amplifies portions of the ECG which it deems most valuable. Overall, the Deep Matched Filter serves as a valuable step forward for the real-world functionality of Ear-ECG and, through its explainable operation, the acceptance of deep learning models in e-health.

eess.SP↗

arXiv2023

Convex Quaternion Optimization for Signal Processing: Theory and Applications

Convex optimization methods have been extensively used in the fields of communications and signal processing. However, the theory of quaternion optimization is currently not as fully developed and systematic as that of complex and real optimization. To this end, we establish an essential theory of convex quaternion optimization for signal processing based on the generalized Hamilton-real (GHR) calculus. This is achieved in a way which conforms with traditional complex and real optimization theory. For rigorous, We present five discriminant theorems for convex quaternion functions, and four discriminant criteria for strongly convex quaternion functions. Furthermore, we provide a fundamental theorem for the optimality of convex quaternion optimization problems, and demonstrate its utility through three applications in quaternion signal processing. These results provide a solid theoretical foundation for convex quaternion optimization and open avenues for further developments in signal processing applications.

math.OC↗

arXiv2023

UAdam: Unified Adam-Type Algorithmic Framework for Non-Convex Stochastic Optimization

Adam-type algorithms have become a preferred choice for optimisation in the deep learning setting, however, despite success, their convergence is still not well understood. To this end, we introduce a unified framework for Adam-type algorithms (called UAdam). This is equipped with a general form of the second-order moment, which makes it possible to include Adam and its variants as special cases, such as NAdam, AMSGrad, AdaBound, AdaFom, and Adan. This is supported by a rigorous convergence analysis of UAdam in the non-convex stochastic setting, showing that UAdam converges to the neighborhood of stationary points with the rate of $\mathcal{O}(1/T)$. Furthermore, the size of neighborhood decreases as $β$ increases. Importantly, our analysis only requires the first-order momentum factor to be close enough to 1, without any restrictions on the second-order momentum factor. Theoretical results also show that vanilla Adam can converge by selecting appropriate hyperparameters, which provides a theoretical guarantee for the analysis, applications, and further developments of the whole class of Adam-type algorithms.

cs.LG↗

arXiv2023

Graph Tensor Networks: An Intuitive Framework for Designing Large-Scale Neural Learning Systems on Multiple Domains

Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we introduce the Graph Tensor Network (GTN) framework, an intuitive yet rigorous graphical framework for systematically designing and implementing large-scale neural learning systems on both regular and irregular domains. The proposed framework is shown to be general enough to include many popular architectures as special cases, and flexible enough to handle data on any and many data domains. The power and flexibility of the proposed framework is demonstrated through real-data experiments, resulting in improved performance at a drastically lower complexity costs, by virtue of tensor algebra.

cs.LG↗

arXiv2023

Hearables: Ear EEG Based Driver Fatigue Detection

Ear EEG based driver fatigue monitoring systems have the potential to provide a seamless, efficient, and feasibly deployable alternative to existing scalp EEG based systems, which are often cumbersome and impractical. However, the feasibility of detecting the relevant delta, theta, alpha, and beta band EEG activity through the ear EEG is yet to be investigated. Through measurements of scalp and ear EEG on ten subjects during a simulated, monotonous driving experiment, this study provides statistical analysis of characteristic ear EEG changes that are associated with the transition from alert to mentally fatigued states, and subsequent testing of a machine learning based automatic fatigue detection model. Novel numerical evidence is provided to support the feasibility of detection of mental fatigue with ear EEG that is in agreement with widely reported scalp EEG findings. This study paves the way for the development of ultra-wearable and readily deployable hearables based driver fatigue monitoring systems.

eess.SP↗

arXiv2023

Hearables: Feasibility of Recording Cardiac Rhythms from Single Ear Locations

Wearable technologies are envisaged to provide critical support to future healthcare systems. Hearables - devices worn in the ear - are of particular interest due to their ability to provide health monitoring in an efficient, reliable and unobtrusive way. Despite the considerable potential of these devices, the ECG signal that can be acquired through a hearable device worn on a single ear is still relatively unexplored. Biophysics modelling of ECG volume conduction was used to establish principles behind the single ear ECG signal, and measurements of cardiac rhythms from 10 subjects were found to be in good correspondence with simulated equivalents. Additionally, the viability of the single ear ECG in real-world environments was determined through one hour duration measurements during a simulated driving task on 5 subjects. Results demonstrated that the single ear ECG resembles the Lead I signal, the most widely used ECG signal in the identification of heart conditions such as myocardial infarction and atrial fibrillation, and was robust against real-world measurement noise, even after prolonged measurements. This study conclusively demonstrates that hearables can enable continuous monitoring of vital signs in an unobtrusive and seamless way, with the potential for reliable identification and management of heart conditions such as myocardial infarction and atrial fibrillation.

physics.med-ph↗

arXiv2022

Rapid Extraction of Respiratory Waveforms from Photoplethysmography: A Deep Encoder Approach

Much of the information of breathing is contained within the photoplethysmography (PPG) signal, through changes in venous blood flow, heart rate and stroke volume. We aim to leverage this fact, by employing a novel deep learning framework which is a based on a repurposed convolutional autoencoder. Our model aims to encode all of the relevant respiratory information contained within photoplethysmography waveform, and decode it into a waveform that is similar to a gold standard respiratory reference. The model is employed on two photoplethysmography data sets, namely Capnobase and BIDMC. We show that the model is capable of producing respiratory waveforms that approach the gold standard, while in turn producing state of the art respiratory rate estimates. We also show that when it comes to capturing more advanced respiratory waveform characteristics such as duty cycle, our model is for the most part unsuccessful. A suggested reason for this, in light of a previous study on in-ear PPG, is that the respiratory variations in finger-PPG are far weaker compared with other recording locations. Importantly, our model can perform these waveform estimates in a fraction of a millisecond, giving it the capacity to produce over 6 hours of respiratory waveforms in a single second. Moreover, we attempt to interpret the behaviour of the kernel weights within the model, showing that in part our model intuitively selects different breathing frequencies. The model proposed in this work could help to improve the usefulness of consumer PPG-based wearables for medical applications, where detailed respiratory information is required.

eess.IV↗

arXiv2022

Complexity-based Financial Stress Evaluation

Financial markets typically exhibit dynamically complex properties as they undergo continuous interactions with economic and environmental factors. The Efficient Market Hypothesis indicates a rich difference in the structural complexity of security prices between normal (stable markets) and abnormal (financial crises) situations. Considering the analogy between market undulation of price time series and physical stress of bio-signals, we investigate whether stress indices in bio-systems can be adopted and modified so as to measure 'standard stress' in financial markets. This is achieved by employing structural complexity analysis, based on variants of univariate and multivariate sample entropy, to estimate the stress level of both financial markets on the whole and the performance of the individual financial indices. Further, we propose a novel graphical framework to establish the sensitivity of individual assets and stock markets to financial crises. This is achieved through Catastrophe Theory and entropy-based stress evaluations indicating the unique performance of each index/individual stock in response to different crises. Four major indices and four individual equities with gold prices are considered over the past 32 years from 1991-2021. Our findings based on nonlinear analyses and the proposed framework support the Efficient Market Hypothesis and reveal the relations among economic indices and within each price time series.

eess.SP↗

arXiv2022

Graph-Regularized Tensor Regression: A Domain-Aware Framework for Interpretable Multi-Way Financial Modelling

Analytics of financial data is inherently a Big Data paradigm, as such data are collected over many assets, asset classes, countries, and time periods. This represents a challenge for modern machine learning models, as the number of model parameters needed to process such data grows exponentially with the data dimensions; an effect known as the Curse-of-Dimensionality. Recently, Tensor Decomposition (TD) techniques have shown promising results in reducing the computational costs associated with large-dimensional financial models while achieving comparable performance. However, tensor models are often unable to incorporate the underlying economic domain knowledge. To this end, we develop a novel Graph-Regularized Tensor Regression (GRTR) framework, whereby knowledge about cross-asset relations is incorporated into the model in the form of a graph Laplacian matrix. This is then used as a regularization tool to promote an economically meaningful structure within the model parameters. By virtue of tensor algebra, the proposed framework is shown to be fully interpretable, both coefficient-wise and dimension-wise. The GRTR model is validated in a multi-way financial forecasting setting and compared against competing models, and is shown to achieve improved performance at reduced computational costs. Detailed visualizations are provided to help the reader gain an intuitive understanding of the employed tensor operations.

q-fin.CP↗

arXiv2022

An Apparatus for the Simulation of Breathing Disorders: Physically Meaningful Generation of Surrogate Data

The rapidly increasing prevalence of debilitating breathing disorders, such as chronic obstructive pulmonary disease (COPD), calls for a meaningful integration of artificial intelligence (AI) into healthcare. While this promises improved detection and monitoring of breathing disorders, AI techniques are almost invariably "data hungry" which highlights the importance of generating physically meaningful surrogate data. Indeed, domain aware surrogates would enable both an improved understanding of respiratory waveform changes with different breathing disorders, and enhance the training of machine learning algorithms. To this end, we introduce an apparatus comprising of PVC tubes and 3D printed parts as a simple yet effective method of simulating both obstructive and restrictive respiratory waveforms in healthy subjects. Independent control over both inspiratory and expiratory resistances allows for the simulation of obstructive breathing disorders through the whole spectrum of FEV1/FVC spirometry ratios (used to classify COPD), ranging from healthy values to values seen in severe chronic obstructive pulmonary disease. Moreover, waveform characteristics of breathing disorders, such as a change in inspiratory duty cycle or peak flow are also observed in the waveforms resulting from use of the artificial breathing disorder simulation apparatus. Overall, the proposed apparatus provides us with a simple, effective and physically meaningful way to generate faithful surrogate breathing disorder waveforms, a prerequisite for the use of artificial intelligence in respiratory health.

physics.med-ph↗

arXiv2022

Pearl: Parallel Evolutionary and Reinforcement Learning Library

Reinforcement learning is increasingly finding success across domains where the problem can be represented as a Markov decision process. Evolutionary computation algorithms have also proven successful in this domain, exhibiting similar performance to the generally more complex reinforcement learning. Whilst there exist many open-source reinforcement learning and evolutionary computation libraries, no publicly available library combines the two approaches for enhanced comparison, cooperation, or visualization. To this end, we have created Pearl (https://github.com/LondonNode/Pearl), an open source Python library designed to allow researchers to rapidly and conveniently perform optimized reinforcement learning, evolutionary computation and combinations of the two. The key features within Pearl include: modular and expandable components, opinionated module settings, Tensorboard integration, custom callbacks and comprehensive visualizations.

cs.LG↗

arXiv2021

HOTTBOX: Higher Order Tensor ToolBOX

HOTTBOX is a Python library for exploratory analysis and visualisation of multi-dimensional arrays of data, also known as tensors. The library includes methods ranging from standard multi-way operations and data manipulation through to multi-linear algebra based tensor decompositions. HOTTBOX also comprises sophisticated algorithms for generalised multi-linear classification and data fusion, such as Support Tensor Machine (STM) and Tensor Ensemble Learning (TEL). For user convenience, HOTTBOX offers a unifying API which establishes a self-sufficient ecosystem for various forms of efficient representation of multi-way data and the corresponding decomposition and association algorithms. Particular emphasis is placed on scalability and interactive visualisation, to support multidisciplinary data analysis communities working on big data and tensors. HOTTBOX also provides means for integration with other popular data science libraries for visualisation and data manipulation. The source code, examples and documentation ca be found at https://github.com/hottbox/hottbox.

cs.MS↗

arXiv2021

A Full Second-Order Analysis of the Widely Linear MVDR Beamformer for Noncircular Signals

A full performance analysis of the widely linear (WL) minimum variance distortionless response (MVDR) beamformer is introduced. While the WL MVDR is known to outperform its strictly linear counterpart, the Capon beamformer, for noncircular complex signals, the existing approaches provide limited physical insights, since they explicitly or implicitly omit the complementary second-order (SO) statistics of the output interferences and noise (IN). To this end, we exploit the full SO statistics of the output IN to introduce a full SO performance analysis framework for the WL MVDR beamformer. This makes it possible to separate the overall signal-to-interference plus noise ratio (SINR) gain of the WL MVDR beamformer w.r.t. the Capon one into the individual contributions along the in-phase (I) and quadrature (Q) channels. Next, by considering the reception of the unknown signal of interest (SOI) corrupted by an arbitrary number of orthogonal noncircular interferences, we further unveil the distribution of SINR gains in both the I and Q channels, and show that in almost all the spatial cases, these performance advantages are more pronounced when the SO noncircularity rate of the interferences increases. Illustrative numerical simulations are provided to support the theoretical results.

cs.IT↗

arXiv2021

Variational Embedding Multiscale Sample Entropy:complexity-based analysis for multichannel systems

To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer from a limitation of data length especially when it comes to practical scenarios. And this shortcoming is further highlighted by involving coarse graining procedure in multi-scale process. The unbalance between embedding dimension and data size will undoubtedly result in inaccurate and undefined estimation. To that cause, Variational Embedding Multiscale Sample Entropy is proposed in this paper, which assigns signals from various channels with distinct embedding dimensions. And this algorithm is tested by both stimulated and real signals. Furthermore, the performance of the new entropy is investigated and compared with Multivariate Multiscale Sample Entropy and Variational Embedding Multiscale Diversity Entropy. Two real-world database, wind data sets with varying regimes and physiological database recorded from young and elderly people, were utilized. As a result, the proposed algorithm gives an improved separation for both situations.

eess.SP↗

arXiv2021

Reducing Computational Complexity of Tensor Contractions via Tensor-Train Networks

There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that offer greater opportunities for algorithmic developments and computationally faster operations than the standard flat-view matrix approach. Tensors, or multi-way arrays, provide such an algebraic framework which is naturally suited to data of such large volume, diversity, and veracity. Indeed, the associated tensor decompositions have demonstrated their potential in breaking the Curse of Dimensionality associated with traditional matrix methods, where a necessary exponential increase in data volume leads to adverse or even intractable consequences on computational complexity. A key tool underpinning multi-linear manipulation of tensors and tensor networks is the standard Tensor Contraction Product (TCP). However, depending on the dimensionality of the underlying tensors, the TCP also comes at the price of high computational complexity in tensor manipulation. In this work, we resort to diagrammatic tensor network manipulation to calculate such products in an efficient and computationally tractable manner, by making use of Tensor Train decomposition (TTD). This has rendered the underlying concepts easy to perceive, thereby enhancing intuition of the associated underlying operations, while preserving mathematical rigour. In addition to bypassing the cumbersome mathematical multi-linear expressions, the proposed Tensor Train Contraction Product model is shown to accelerate significantly the underlying computational operations, as it is independent of tensor order and linear in the tensor dimension, as opposed to performing the full computations through the standard approach (exponential in tensor order).

math.NA↗

arXiv2021

Dynamic Portfolio Cuts: A Spectral Approach to Graph-Theoretic Diversification

Stock market returns are typically analyzed using standard regression, yet they reside on irregular domains which is a natural scenario for graph signal processing. To this end, we consider a market graph as an intuitive way to represent the relationships between financial assets. Traditional methods for estimating asset-return covariance operate under the assumption of statistical time-invariance, and are thus unable to appropriately infer the underlying true structure of the market graph. This work introduces a class of graph spectral estimators which cater for the nonstationarity inherent to asset price movements, and serve as a basis to represent the time-varying interactions between assets through a dynamic spectral market graph. Such an account of the time-varying nature of the asset-return covariance allows us to introduce the notion of dynamic spectral portfolio cuts, whereby the graph is partitioned into time-evolving clusters, allowing for online and robust asset allocation. The advantages of the proposed framework over traditional methods are demonstrated through numerical case studies using real-world price data.

q-fin.PM↗

arXiv2021

Recurrent Graph Tensor Networks: A Low-Complexity Framework for Modelling High-Dimensional Multi-Way Sequence

Recurrent Neural Networks (RNNs) are among the most successful machine learning models for sequence modelling, but tend to suffer from an exponential increase in the number of parameters when dealing with large multidimensional data. To this end, we develop a multi-linear graph filter framework for approximating the modelling of hidden states in RNNs, which is embedded in a tensor network architecture to improve modelling power and reduce parameter complexity, resulting in a novel Recurrent Graph Tensor Network (RGTN). The proposed framework is validated through several multi-way sequence modelling tasks and benchmarked against traditional RNNs. By virtue of the domain aware information processing of graph filters and the expressive power of tensor networks, we show that the proposed RGTN is capable of not only out-performing standard RNNs, but also mitigating the Curse of Dimensionality associated with traditional RNNs, demonstrating superior properties in terms of performance and complexity.

cs.LG↗

arXiv2021

Tensor-Train Recurrent Neural Networks for Interpretable Multi-Way Financial Forecasting

Recurrent Neural Networks (RNNs) represent the de facto standard machine learning tool for sequence modelling, owing to their expressive power and memory. However, when dealing with large dimensional data, the corresponding exponential increase in the number of parameters imposes a computational bottleneck. The necessity to equip RNNs with the ability to deal with the curse of dimensionality, such as through the parameter compression ability inherent to tensors, has led to the development of the Tensor-Train RNN (TT-RNN). Despite achieving promising results in many applications, the full potential of the TT-RNN is yet to be explored in the context of interpretable financial modelling, a notoriously challenging task characterized by multi-modal data with low signal-to-noise ratio. To address this issue, we investigate the potential of TT-RNN in the task of financial forecasting of currencies. We show, through the analysis of TT-factors, that the physical meaning underlying tensor decomposition, enables the TT-RNN model to aid the interpretability of results, thus mitigating the notorious "black-box" issue associated with neural networks. Furthermore, simulation results highlight the regularization power of TT decomposition, demonstrating the superior performance of TT-RNN over its uncompressed RNN counterpart and other tensor forecasting methods.

cs.LG↗