arXiv subjects

Danilo P. Mandic

Publications and source records attributed to Danilo P. Mandic.

70 records · Page 4Linked to original sources

arXiv2018

Tensor Ensemble Learning for Multidimensional Data

In big data applications, classical ensemble learning is typically infeasible on the raw input data and dimensionality reduction techniques are necessary. To this end, novel framework that generalises classic flat-view ensemble learning to multidimensional tensor-valued data is introduced. This is achieved by virtue of tensor decompositions, whereby the proposed method, referred to as tensor ensemble learning (TEL), decomposes every input data sample into multiple factors which allows for a flexibility in the choice of multiple learning algorithms in order to improve test performance. The TEL framework is shown to naturally compress multidimensional data in order to take advantage of the inherent multi-way data structure and exploit the benefit of ensemble learning. The proposed framework is verified through the application of Higher Order Singular Value Decomposition (HOSVD) to the ETH-80 dataset and is shown to outperform the classical ensemble learning approach of bootstrap aggregating.

eess.SP↗

arXiv2018

A Data Analytics Perspective of the Clarke and Related Transforms in Power Grid Analysis

Affordable and reliable electric power is fundamental to modern society and economy, with the Smart Grid becoming an increasingly important factor in power generation and distribution. In order to fully exploit it advantages, the analysis of modern Smart Grid requires close collaboration and convergence between power engineers and signal processing and machine learning experts. Current analysis techniques are typically derived from a Circuit Theory perspective; such an approach is adequate for only fully balanced systems operating at nominal conditions and non-obvious for data scientists - this is prohibitive for the analysis of dynamically unbalanced smart grids, where Data Analytics is not only well suited but also necessary. A common language that bridges the gap between Circuit Theory and Data Analytics, and the respective community of experts, would be a natural step forward. To this end, we revisit the Clarke and related transforms from a subspace, latent component, and spatial frequency analysis frameworks, to establish fundamental relationships between the standard three-phase transforms and modern Data Analytics. We show that the Clarke transform admits a physical interpretation as a "spatial dimensionality" reduction technique which is equivalent to Principal Component Analysis (PCA) for balanced systems, but is sub-optimal for dynamically unbalanced systems, such as the Smart Grid, while the related Park transform performs further "temporal" dimensionality reduction. Such a perspective opens numerous new avenues for the use Signal Processing and Machine Learning in power grid research, and paves the way for innovative optimisation, transformation, and analysis techniques that are not accessible to arrive at from the standard Circuit Theory principles, as demonstrated in this work through the possibility of simultaneous frequency estimation and fault detection.

eess.SP↗

arXiv2018

An Augmented Nonlinear LMS for Digital Self-Interference Cancellation in Full-Duplex Direct-Conversion Transceivers

In future full-duplex communications, the cancellation of self-interference (SI) arising from hardware non-idealities will play an important role in the design of mobile-scale devices. To this end, we introduce an optimal digital SI cancellation solution for shared-antenna-based direct-conversion transceivers. To establish that the underlying widely linear signal model is not adequate for strong transmit signals, the impact of various circuit imperfections, including power amplifier (PA) distortion, frequency-dependent I/Q imbalance, quantization noise and thermal noise, on the performance of the conventional augmented least mean square (LMS) based SI canceller, is analyzed. In order to achieve a sufficient signal-to-interference-plus-noise ratio (SINR) when the nonlinear SI components are not negligible, we propose an augmented nonlinear LMS based SI canceller for a joint cancellation of both the linear and nonlinear SI components by virtue of a widely nonlinear model fit. A rigorous mean and mean square performance evaluation is conducted to justify the performance advantages of the proposed scheme over the conventional augmented LMS solution. Simulations on orthogonal frequency division multiplexing (OFDM)-based wireless local area network (WLAN) standard compliant waveforms support the analysis.

cs.IT↗

arXiv2018

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.

math.NA↗

arXiv2017

The sum of tensor networks

Tensor networks (TNs) have been gaining interest as multiway data analysis tools owing to their ability to tackle the curse of dimensionality and to represent tensors as smaller-scale interconnections of their intrinsic features. However, despite the obvious advantages, the current treatment of TNs as stand-alone entities does not take full benefit of their underlying structure and the associated feature localization. To this end, embarking upon the analogy with a feature fusion, we propose a rigorous framework for the combination of TNs, focusing on their summation as the natural way for their combination. This allows for feature combination for any number of tensors, as long as their TN representation topologies are isomorphic. The benefits of the proposed framework are demonstrated on the classification of several groups of partially related images, where it outperforms standard machine learning algorithms.

eess.SP↗

arXiv2017

Tensor Valued Common and Individual Feature Extraction: Multi-dimensional Perspective

A novel method for common and individual feature analysis from exceedingly large-scale data is proposed, in order to ensure the tractability of both the computation and storage and thus mitigate the curse of dimensionality, a major bottleneck in modern data science. This is achieved by making use of the inherent redundancy in so-called multi-block data structures, which represent multiple observations of the same phenomenon taken at different times, angles or recording conditions. Upon providing an intrinsic link between the properties of the outer vector product and extracted features in tensor decompositions (TDs), the proposed common and individual information extraction from multi-block data is performed through imposing physical meaning to otherwise unconstrained factorisation approaches. This is shown to dramatically reduce the dimensionality of search spaces for subsequent classification procedures and to yield greatly enhanced accuracy. Simulations on a multi-class classification task of large-scale extraction of individual features from a collection of partially related real-world images demonstrate the advantages of the "blessing of dimensionality" associated with TDs.

eess.SP↗

arXiv2017

In-ear EEG biometrics for feasible and readily collectable real-world person authentication

The use of EEG as a biometrics modality has been investigated for about a decade, however its feasibility in real-world applications is not yet conclusively established, mainly due to the issues with collectability and reproducibility. To this end, we propose a readily deployable EEG biometrics system based on a `one-fits-all' viscoelastic generic in-ear EEG sensor (collectability), which does not require skilled assistance or cumbersome preparation. Unlike most existing studies, we consider data recorded over multiple recording days and for multiple subjects (reproducibility) while, for rigour, the training and test segments are not taken from the same recording days. A robust approach is considered based on the resting state with eyes closed paradigm, the use of both parametric (autoregressive model) and non-parametric (spectral) features, and supported by simple and fast cosine distance, linear discriminant analysis and support vector machine classifiers. Both the verification and identification forensics scenarios are considered and the achieved results are on par with the studies based on impractical on-scalp recordings. Comprehensive analysis over a number of subjects, setups, and analysis features demonstrates the feasibility of the proposed ear-EEG biometrics, and its potential in resolving the critical collectability, robustness, and reproducibility issues associated with current EEG biometrics.

cs.CR↗

arXiv2017

Automatic sleep monitoring using ear-EEG

The monitoring of sleep patterns without patient's inconvenience or involvement of a medical specialist is a clinical question of significant importance. To this end, we propose an automatic sleep stage monitoring system based on an affordable, unobtrusive, discreet, and long-term wearable in-ear sensor for recording the Electroencephalogram (ear-EEG). The selected features for sleep pattern classification from a single ear-EEG channel include the spectral edge frequency (SEF) and multi- scale fuzzy entropy (MSFE), a structural complexity feature. In this preliminary study, the manually scored hypnograms from simultaneous scalp-EEG and ear-EEG recordings of four subjects are used as labels for two analysis scenarios: 1) classification of ear-EEG hypnogram labels from ear-EEG recordings and 2) prediction of scalp-EEG hypnogram labels from ear-EEG recordings. We consider both 2-class and 4-class sleep scoring, with the achieved accuracies ranging from 78.5 % to 95.2 % for ear-EEG labels predicted from ear-EEG, and 76.8 % to 91.8 % for scalp-EEG labels predicted from ear-EEG. The corresponding kappa coefficients, which range from 0.64 to 0.83 for Scenario 1 and from 0.65 to 0.80 for Scenario 2, indicate a Substantial to Almost Perfect agreement, thus proving the feasibility of in-ear sensing for sleep monitoring in the community.

physics.med-ph↗

arXiv2016

Frequency estimation in three-phase power systems with harmonic contamination: A multistage quaternion Kalman filtering approach

Motivated by the need for accurate frequency information, a novel algorithm for estimating the fundamental frequency and its rate of change in three-phase power systems is developed. This is achieved through two stages of Kalman filtering. In the first stage a quaternion extended Kalman filter, which provides a unified framework for joint modeling of voltage measurements from all the phases, is used to estimate the instantaneous phase increment of the three-phase voltages. The phase increment estimates are then used as observations of the extended Kalman filter in the second stage that accounts for the dynamic behavior of the system frequency and simultaneously estimates the fundamental frequency and its rate of change. The framework is then extended to account for the presence of harmonics. Finally, the concept is validated through simulation on both synthetic and real-world data.

stat.ML↗

arXiv2014

Distributed Widely Linear Frequency Estimation in Unbalanced Three Phase Power Systems

A novel method for distributed estimation of the frequency of power systems is introduced based on the cooperation between multiple measurement nodes. The proposed distributed widely linear complex Kalman filter (D-ACKF) and the distributed widely linear extended complex Kalman filter (D-AECKF) employ a widely linear state space and augmented complex statistics to deal with unbalanced system conditions and the generality complex signals, both second order circular (proper) and second order noncircular (improper). It is shown that the current, strictly linear, estimators are inadequate for unbalanced systems, a typical case in smart grids, as they do not account for either the noncircularity of Clarke's αβ-voltage in unbalanced conditions or the correlated nature of nodal disturbances. We illuminate the relationship between the degree of circularity of Clarke's voltage and system imbalance, and prove that the proposed widely linear estimators are optimal for such conditions, while also accounting for the correlated and noncircular nature of real-world nodal disturbances. {Synthetic and real world} case studies over a range of power system conditions illustrate the theoretical and practical advantages of the proposed methodology.

eess.SY↗

arXiv2014

The Theory of Quaternion Matrix Derivatives

A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to handle both analytic and nonanalytic functions. This corrects a flaw in the existing methods, that is, the incorrect use of the traditional product rule. In the framework introduced, the derivatives of quaternion matrix functions can be calculated directly without the differential of this function. Key results are summarized in tables. Several examples show how the quaternion matrix derivatives can be used as an important tool for solving problems related to signal processing.

math.GM↗

arXiv2014

Quaternion Derivatives: The GHR Calculus

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-analytic functions of quaternion variables, however, both the HR and other functional calculus in quaternion analysis have encountered an essential technical obstacle, that is, the traditional product rule is invalid due to the non- commutativity of the quaternion algebra. To address this issue, a generalized form of the HR derivative is proposed based on a general orthogonal system. The so introduced generalization, called the generalized HR (GHR) calculus, encompasses not just the left- and right-hand versions of quaternion derivative, but also enables solutions to some long standing problems, such as the novel product rule, the chain rule, the mean-valued theorem and Taylor's theorem. At the core of the proposed approach is the quaternion rotation, which can naturally be applied to other functional calculi in non-commutative settings. Examples on using the GHR calculus in adaptive signal processing support the analysis.

math.GM↗

arXiv2014

Quaternion Gradient and Hessian

The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions often require the calculation of the gradient and Hessian, however, real functions of quaternion variables are essentially non-analytic. To address this issue, we propose new definitions of quaternion gradient and Hessian, based on the novel generalized HR (GHR) calculus, thus making possible efficient derivation of optimization algorithms directly in the quaternion field, rather than transforming the problem to the real domain, as is current practice. In addition, unlike the existing quaternion gradients, the GHR calculus allows for the product and chain rule, and for a one-to-one correspondence of the proposed quaternion gradient and Hessian with their real counterparts. Properties of the quaternion gradient and Hessian relevant to numerical applications are elaborated, and the results illuminate the usefulness of the GHR calculus in greatly simplifying the derivation of the quaternion least mean squares, and in quaternion least square and Newton algorithm. The proposed gradient and Hessian are also shown to enable the same generic forms as the corresponding real- and complex-valued algorithms, further illustrating the advantages in algorithm design and evaluation.

math.NA↗

arXiv2013

Distributed Widely Linear Complex Kalman Filtering

We introduce cooperative sequential state space estimation in the domain of augmented complex statistics, whereby nodes in a network collaborate locally to estimate noncircular complex signals. For rigour, a distributed augmented (widely linear) complex Kalman filter (D-ACKF) suited to the generality of complex signals is introduced, allowing for unified treatment of both proper (rotation invariant) and improper (rotation dependent) signal distributions. Its duality with the bivariate real-valued distributed Kalman filter, along with several issues of implementation are also illuminated. The analysis and simulations show that unlike existing distributed Kalman filter solutions, the D-ACKF caters for both the improper data and the correlations between nodal observation noises, thus providing enhanced performance in real-world scenarios.

eess.SY↗

arXiv2013

A Unifying Approach to Quaternion Adaptive Filtering: Addressing the Gradient and Convergence

A novel framework for a unifying treatment of quaternion valued adaptive filtering algorithms is introduced. This is achieved based on a rigorous account of quaternion differentiability, the proposed I-gradient, and the use of augmented quaternion statistics to account for real world data with noncircular probability distributions. We first provide an elegant solution for the calculation of the gradient of real functions of quaternion variables (typical cost function), an issue that has so far prevented systematic development of quaternion adaptive filters. This makes it possible to unify the class of existing and proposed quaternion least mean square (QLMS) algorithms, and to illuminate their structural similarity. Next, in order to cater for both circular and noncircular data, the class of widely linear QLMS (WL-QLMS) algorithms is introduced and the subsequent convergence analysis unifies the treatment of strictly linear and widely linear filters, for both proper and improper sources. It is also shown that the proposed class of HR gradients allows us to resolve the uncertainty owing to the noncommutativity of quaternion products, while the involution gradient (I-gradient) provides generic extensions of the corresponding real- and complex-valued adaptive algorithms, at a reduced computational cost. Simulations in both the strictly linear and widely linear setting support the approach.

math.GM↗

arXiv2012

Higher-Order Partial Least Squares (HOPLS): A Generalized Multi-Linear Regression Method

A new generalized multilinear regression model, termed the Higher-Order Partial Least Squares (HOPLS), is introduced with the aim to predict a tensor (multiway array) $\tensor{Y}$ from a tensor $\tensor{X}$ through projecting the data onto the latent space and performing regression on the corresponding latent variables. HOPLS differs substantially from other regression models in that it explains the data by a sum of orthogonal Tucker tensors, while the number of orthogonal loadings serves as a parameter to control model complexity and prevent overfitting. The low dimensional latent space is optimized sequentially via a deflation operation, yielding the best joint subspace approximation for both $\tensor{X}$ and $\tensor{Y}$. Instead of decomposing $\tensor{X}$ and $\tensor{Y}$ individually, higher order singular value decomposition on a newly defined generalized cross-covariance tensor is employed to optimize the orthogonal loadings. A systematic comparison on both synthetic data and real-world decoding of 3D movement trajectories from electrocorticogram (ECoG) signals demonstrate the advantages of HOPLS over the existing methods in terms of better predictive ability, suitability to handle small sample sizes, and robustness to noise.

cs.AI↗