Subspace Techniques Research Articles

Improved Direction-of-Arrival Estimation of an Acoustic Source Using Support Vector Regression and Signal Correlation.

The direction-of-arrival (DoA) estimation of an acoustic source can be estimated with a uniform linear array using classical techniques such as generalized cross-correlation, beamforming, subspace techniques, etc. However, these methods require a search in the angular space and also have a higher angular error at the end-fire. In this paper, we propose the use of regression techniques to improve the results of DoA estimation at all angles including the end-fire. The proposed methodology employs curve-fitting on the received multi-channel microphone signals, which when applied in tandem with support vector regression (SVR) provides a better estimation of DoA as compared to the conventional techniques and other polynomial regression techniques. A multilevel regression technique is also proposed, which further improves the estimation accuracy at the end-fire. This multilevel regression technique employs the use of linear regression over the results obtained from SVR. The techniques employed here yielded an overall improvement over the classical generalized cross-correlation technique.

Online Construction of Variable Span Linear Filters Using a Fixed-Point Approach

The variable span linear filters (VSLFs) constitute a unified framework of conventional subspace and linear filtering techniques for noise reduction. The construction of VSLFs, however, relies on the generalized eigendecomposition (GEVD) methods, which are computationally expensive. This in turn stymies the employment of such filters in practical online processing problems. To address this issue, we first propose in this paper a fixed-point iteration technique to extract the generalized eigenvectors. It is based on maximizing the pre-whitened generalized Rayleigh quotient (GRQ). We then integrate this technique with online statistic estimation to construct VSLFs. Our proposed method is computationally efficient and can also harness parallel architectures. To show its effectiveness, we consider a speech enhancement application and compare the results with those of several existing methods.

Subspace identification of fault modes for a twin-rotor system

PurposeThe purpose of this paper is to identify the fault modes of a nonlinear twin-rotor system (TRS) using the subspace technique to facilitate fault identification, diagnosis and control applications.Design/methodology/approachFor identification of fault modes, three types of system malfunctions are introduced. First malfunction resembles actuator, second internal system dynamics and third represents sensor malfunction or offset. For each fault scenario, the resulting TRS model is applied with persistently exciting inputs and corresponding outputs are recorded. The collected input–output data are invoked in NS4SID subspace system identification algorithm to obtain the unknown fault model. The identified actuator fault modes of the TRS can be used for fault diagnostics, fault isolation or fault correction applications.FindingsThe identified models obtained through system identification are validated for correctness by comparing the response of the actual model under the fault condition and identified model. The results certify that the identified fault modes correctly resemble the respective fault conditions in the actual system.Originality/valueThe utilization of proposed work for current research emphasized the area of fault detection, diagnosis and correction applications that makes its value significantly. These modes when used for diagnosis purposes allow users to timely get intimated and rectify the performance degradation of the plant before it gets totally malfunctioned. Moreover, the slight performance degradation is also indicated when fault diagnosis is performed.

Localization for mixed far-field and near-field sources utilizing improved symmetric nested array

Nested arrays exhibit higher spatial resolution (SR) and enhanced degrees-of-freedom (DOFs) with fewer sensors, and they have been utilized for direction-of-arrival (DOA) estimation of both far-field (FF) and near-field (NF) sources. In this study, an improved symmetric nested array configuration with a given number of sensors was developed, which achieved increased consecutive and unique lags and thus resolved more targets than the actual number of inherent array sensors. In particular, the analytical expressions of the number of consecutive lags, the number of unique lags, and the virtual array aperture were derived for quantitative evaluation and comparison, as well as the corresponding array composition parameters of the optimal array geometry were obtained. In the mixed sources localization scheme, a special cumulant matrix was constructed to eliminate the range parameter in the NF steer vectors by exploiting the symmetric feature. Both subspace and sparse reconstruction techniques were exploited in order to directly obtain the DOAs of both FF and NF sources. With the estimated DOAs and the covariance matrix of the array output, the NF sources could be identified, and the corresponding range parameters could also be obtained by a one-dimension (1-D) spectrum search scheme. Numerous simulation results demonstrated that the proposed array showed a remarkable performance in terms of estimation accuracy, SR capacity, and numerous DOFs compared to state-of-the-art symmetric nested arrays.

Correntropy-based DOA estimation algorithm under impulsive noise environments

In this paper, the direction of arrival (DOA) estimation of signals in the presence of impulsive noise environment is studied. Complex isotropic symmetric alpha-stable (SαS) random variables are modeled as impulsive noise, then a novel second-order statistic method that correntropy-based covariance matrix (CBCM) is defined, based on the combination of the CBCM of the array sensor outputs with the signal subspace technique (e.g., multiple signal classification (MUSIC)), which can be achieved source localization under impulsive noise environments. The Monte-Carlo simulation results illustrate the improved performance of CBCM-MUSIC for DOA estimation under a wide range of impulsive noise conditions.

A Kernel Design Approach to Improve Kernel Subspace Identification

Subspace identification methods, such as canonical variate analysis (CVA), are noniterative tools suitable for the state-space modeling of multi-input, multi-output processes, e.g., industrial processes, using input-output data. To learn nonlinear system behavior, kernel subspace techniques are commonly used. However, the issue of kernel design must be given more attention because the type of kernel can influence the kind of nonlinearities that the model can capture. In this article, a new kernel design is proposed for CVA-based identification, which is a mixture of a global and local kernel to enhance generalization ability and includes a mechanism to vary the influence of each process variable into the model response. During validation, model hyper-parameters were tuned using random search. The overall method is called feature-relevant mixed kernel CVA (FR-MKCVA). Using an evaporator case study, the trained FR-MKCVA models show a better fit to observed data than those of single-kernel CVA, linear CVA, and neural net models under both interpolation and extrapolation scenarios. This work provides a basis for future exploration of deep and diverse kernel designs for system identification.

Parameter estimation for coherently distributed noncircular sources under impulsive noise environments

The signal source generates angular expansion in space due to scattering, reflection and other phenomena in a complex environment, which requires a distributed signal model for processing. This paper extends the method of joint angular estimation for coherently distributed (CD) sources consisting of noncircular signals to the impulsive noise scenario. In an actual wireless passive positioning environment, impulsive noise is very common. However, most algorithms only consider Gaussian noise environments and are not suitable for angle estimation in impulsive noise scenarios. This paper proposes the generalized complex correntropy (GCC) and shows that it can eliminate the effects of outliers in an impulsive noise environment. This is because the complex correntropy is an effective tool to analyze higher-order statistical moments in the impulsive noise environment. In order to improve the accuracy of the estimation, we construct a GCC matrix based on extended array output and apply the subspace techniques to extract the angle information of the CD noncircular sources. The simulation results show that the estimation performance of the proposed algorithms is better than the traditional algorithm applied to the noncircular CD sources.

A limited memory BFGS subspace algorithm for bound constrained nonsmooth problems

The subspace technique has been widely used to solve unconstrained/constrained optimization problems and there exist many results that have been obtained. In this paper, a subspace algorithm combining with limited memory BFGS update is proposed for large-scale nonsmooth optimization problems with box-constrained conditions. This algorithm can ensure that all iteration points are feasible and the sequence of objective functions is decreasing. Moreover, rapid changes in the active set are allowed. The global convergence is established under some suitable conditions. Numerical results show that this method is very effective for large-scale nonsmooth box-constrained optimization, where the largest dimension of the test problems is 11,000 variables.

Soft Computing Ensemble Models Based on Logistic Regression for Groundwater Potential Mapping

Groundwater potential maps are one of the most important tools for the management of groundwater storage resources. In this study, we proposed four ensemble soft computing models based on logistic regression (LR) combined with the dagging (DLR), bagging (BLR), random subspace (RSSLR), and cascade generalization (CGLR) ensemble techniques for groundwater potential mapping in Dak Lak Province, Vietnam. A suite of well yield data and twelve geo-environmental factors (aspect, elevation, slope, curvature, Sediment Transport Index, Topographic Wetness Index, flow direction, rainfall, river density, soil, land use, and geology) were used for generating the training and validation datasets required for the building and validation of the models. Based on the area under the receiver operating characteristic curve (AUC) and several other validation methods (negative predictive value, positive predictive value, root mean square error, accuracy, sensitivity, specificity, and Kappa), it was revealed that all four ensemble learning techniques were successful in enhancing the validation performance of the base LR model. The ensemble DLR model (AUC = 0.77) was the most successful model in identifying the groundwater potential zones in the study area, followed by the RSSLR (AUC = 0.744), BLR (AUC = 0.735), CGLR (AUC = 0.715), and single LR model (AUC = 0.71), respectively. The models developed in this study and the resulting potential maps can assist decision-makers in the development of effective adaptive groundwater management plans.

3-D Full-Time TEM Modeling Using Shift-and-Invert Krylov Subspace Method

The 3-D time-domain electromagnetic (TEM) modeling is computationally expensive. Shift-and-invert (SAI) Krylov subspace technique has proved efficient for the modeling of OFF-time TEM data. However, the ON-time data, which also involves useful Earth conductivity information, have not been well treated. In this article, we extend the SAI Krylov subspace method to deal with the ON-time data and obtain a complete algorithm for modeling of the full-time data. To deal with the ON-time problem, while retaining the whole framework of an SAI-style method, we have developed a new time integration method, based on the exponential trapezoidal rule, to help discrete the integral terms into matrix exponential function. Next, the solution of this matrix exponential function is obtained by constructing a new type of SAI Krylov subspaces. Numerical results for typical transmitting waveforms, such as half-sine, versatile-time-domain-electromagnetic (VTEM), and MULTIPULSE, demonstrate that the novel algorithm is accuracy for full-time TEM modeling.

Fast Iterative Schemes for the Solution of Eddy-Current Problems Featuring Multiple Conductors by Integral Formulations

Integral formulations lead to full matrices that, despite the use of efficient low-rank approximation techniques, are impossible to be solved when the number of unknowns is large enough. To overcome this limitation, we propose a novel direct-iterative hybrid technique to solve eddy currents by taking advantage of the domain splitting into disjoint conductors: each subproblem is solved via direct solvers on each subdomain, whereas the Krylov subspace techniques are applied to compute the mutual effects between the substructures iteratively. In this way, the entries related to the mutual contributions between the subdomains are not stored. In particular, this article focuses on testing the convergence of the iterative method.

State-Space Network Topology Identification From Partial Observations

In this article, we explore the state-space formulation of a network process to recover from partial observations the network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system identification literature and extend them to the network topology identification problem. This approach provides a unified view of network control and signal processing on graphs. In addition, we provide theoretical guarantees for the recovery of the topological structure of a deterministic continuous-time linear dynamical system from input-output observations even when the input and state interaction networks are different. Our mathematical analysis is accompanied by an algorithm for identifying from data,a network topology consistent with the system dynamics and conforms to the prior information about the underlying structure. The proposed algorithm relies on alternating projections and is provably convergent. Numerical results corroborate the theoretical findings and the applicability of the proposed algorithm.

A Subspace Modified Broyden–Fletcher–Goldfarb–Shanno Method for $$\mathcal {B}$$-eigenvalues of Symmetric Tensors

In this paper, finding the $$\mathcal {B}$$-eigenvalues of a symmetric tensor is equivalent to solving a least-square optimization problem. Based on the subspace technique, a trust region algorithm is presented. In trust region subproblem, the modified Broyden–Fletcher–Goldfarb–Shanno formula is adopted to generate the approximated matrices. In order to reduce the computation cost in each iteration, the quadratic subproblem is constructed in a subspace with lower dimension. Theoretic analysis of the given algorithm and convergence properties of the optimal solutions are established. Numerical results show that this method is efficient.

Scheduled relaxation Jacobi method as preconditioner of Krylov subspace techniques for large-scale Poisson problems

This article presents an assessment of the scheduled relaxation Jacobi (SRJ) method for the solution of large-scale Poisson problems arising in the numerical simulation of large eddy turbulent flow in large complex geometry. The SRJ schemes are used both as standalone solvers and as preconditioners to Krylov subspace solvers. The Navier-Stokes equation is solved using structured Cartesian grids (both uniform as well as nonuniform grids). Geometrical complexities are handled using the immersed boundary method (IBM) method. The performance of SRJ schemes as a standalone solver is first validated with the help of a rectangular channel flow problem whose exact solution is known. Numerical experiments are performed to evaluate the performance of SRJ schemes as preconditioners to two robust and efficient Krylov subspace solvers (PCG and BiCGSTAB), and compared with different preconditioners such as Jacobi (diagonal preconditioner), SOR(k) and multigrid preconditioners. SRJ schemes as standalone solver perform quite similarly as predicted before in literature. However, as preconditioner particularly some SRJ schemes work best among the rest for three-dimensional problems.

The Comparison of Reconstruction Algorithms for Diffuse Optical Tomography

Diffuse optical tomography (DOT) utilizes wavelength range of 750-950 nm to map the spatial distribution of the tissue chromophores of breast tissue for cancer diagnosis or follow up prognosis. DOT allows tomographic reconstructions of tissue optical properties. Several reconstruction methods have been developed to minimize artifacts and obtain more realistic tomographic images. In order to compare four different reconstruction algorithms, data acquired from tissue phantoms using a DOT system. Algebraic reconstruction technique (ART), simultaneous iteration reconstruction technique (SIRT), truncated singular value decomposition (TSVD) and truncated conjugate gradient (TCG) techniques have been compared in terms of location of inclusion in the tissue phantoms. It has been shown that images reconstructed by the subspace techniques, TSVD and TCG locating the inclusion position better than the algebraic methods ART and SIRT. Beside, images reconstructed by TSVD and TCG have less artifact when compared to images of ART and SIRT.

An Adaptive Robust Semi-supervised Clustering Framework Using Weighted Consensus of Random k-Means Ensemble

Semi-supervised cluster ensemble usually introduces a small amount of supervision in the first stage of cluster ensemble, i.e., ensemble generation, by performing many runs of semi-supervised clustering algorithms. However, it is neither efficient in terms of computational complexity, nor flexible in a dynamic learning environment where limited supervision changes over time. In this article we propose a new framework which generates base partitions in an unsupervised manner and attributes different weights to each cluster of the base partitions. The weighting scheme considers both the internal validation measures of clustering and the degrees of satisfaction of pairwise constraints. A weighted co-association matrix based consensus approach is then applied to achieve a final partition. To handle high-dimensional data, we generate base partitions using k-means with both random sampling and random subspace techniques. The new framework retains a high accuracy, and is efficient since it avoids performing semi-supervised clustering in ensemble generation and the complexity of the weighting scheme is independent of the number of instances in a dynamic environment. It is more adaptive than the traditional approach because it does not require rerunning semi-supervised clustering algorithms when the limited supervision changes. Empirical results on 12 datasets demonstrate that it is also more robust to noisy constraints.

Fourth-order direction finding in antenna arrays with partial channel gain/phase calibration

In this paper, we consider the problem of direction finding in partly calibrated uniform linear array (ULA) system with channel gain/phase mismatch, by taking advantage of the high-order statistics (HOS) of the array observations. In particular, we devise a (2M−1)×(2M−1) fourth-order cumulant (FOC) matrix for an M-element ULA and exploit it to estimate the directions-of-arrival (DOAs) with subspace techniques. The proposed FOC direction finding method is computationally attractive without spatial spectrum search and robust against spatially correlated noise. It is also able to achieve better DOA estimation performance than the existing method, as illustrated by numerical simulations.

Coprime beamforming: fast estimation of more sources than sensors

In radar, the minimisation of redundancies within the sensing array can lead to significant hardware computational savings. Arrays with a coprime-pair configuration enjoy increased degrees of freedom and can detect more sources than sensors. To achieve this, a virtual array (VA) consisting of the full complement of lags is usually constructed and subspace-based algorithms are then employed to obtain the direction-of-arrival (DOA) or frequency estimates. However, the application of the subspace techniques to the VA incurs a significant computational cost and requires spatial smoothing. The authors propose and analyse the application of the fast iterative interpolated beamformer (FIIB) to the coprime DOA estimation problem. The FIIB enjoys a computational complexity of the same order as the fast Fourier transform and does not require spatial smoothing. They consider two implementations that construct the VA differently with the first selecting a single estimate for each lag and the other employing averaged values of the lag estimates. They present a comprehensive study of the estimation performance as a function of signal-to-noise ratio, number of snapshots and source separation. The results clearly show that the FIIB delivers high-fidelity frequency estimates that consistently outperform the high-resolution subspace-based methods.

Direction Finding for Bistatic MIMO Radar with Unknown Spatially Colored Noise

In this paper, we investigate the problem of joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation for bistatic multiple-input multiple-output radar with unknown spatially colored noise. By exploiting the sparse structure of the noise covariance matrix, a new de-noising scheme is designed. The signal covariance matrix is recast as a low-rank matrix with missing entries, which can be approximately tackled via solving an optimization problem. Thereafter, DODs and DOAs are obtained with the traditional subspace techniques. The proposed method does not bring any virtual aperture loss; thus, it achieves more accurate estimation performance than several state-of-the-art de-noising methods. Finally, the stochastic Cramer–Rao bound for joint direction finding is derived. Numerical computer simulations verify the effectiveness of the proposed algorithm.

Inferring Latent Disease-lncRNA Associations by Faster Matrix Completion on a Heterogeneous Network.

Current studies have shown that long non-coding RNAs (lncRNAs) play a crucial role in a variety of fundamental biological processes related to complex human diseases. The prediction of latent disease-lncRNA associations can help to understand the pathogenesis of complex human diseases at the level of lncRNA, which also contributes to the detection of disease biomarkers, and the diagnosis, treatment, prognosis and prevention of disease. Nevertheless, it is still a challenging and urgent task to accurately identify latent disease-lncRNA association. Discovering latent links on the basis of biological experiments is time-consuming and wasteful, necessitating the development of computational prediction models. In this study, a computational prediction model has been remodeled as a matrix completion framework of the recommendation system by completing the unknown items in the rating matrix. A novel method named faster randomized matrix completion for latent disease-lncRNA association prediction (FRMCLDA) has been proposed by virtue of improved randomized partial SVD (rSVD-BKI) on a heterogeneous bilayer network. First, the correlated data source and experimentally validated information of diseases and lncRNAs are integrated to construct a heterogeneous bilayer network. Next, the integrated heterogeneous bilayer network can be formalized as a comprehensive adjacency matrix which includes lncRNA similarity matrix, disease similarity matrix, and disease-lncRNA association matrix where the uncertain disease-lncRNA associations are referred to as blank items. Then, a matrix approximate to the original adjacency matrix has been designed with predicted scores to retrieve the blank items. The construction of the approximate matrix could be equivalently resolved by the nuclear norm minimization. Finally, a faster singular value thresholding algorithm with a randomized partial SVD combing a new sub-space reuse technique has been utilized to complete the adjacency matrix. The results of leave-one-out cross-validation (LOOCV) experiments and 5-fold cross-validation (5-fold CV) experiments on three different benchmark databases have confirmed the availability and adaptability of FRMCLDA in inferring latent relationships of disease-lncRNA pairs, and in inferring lncRNAs correlated with novel diseases without any prior interaction information. Additionally, case studies have shown that FRMCLDA is able to effectively predict latent lncRNAs correlated with three widespread malignancies: prostate cancer, colon cancer, and gastric cancer.