Adaptive Weight Vector Research Articles

Multigraph Random Walk for Joint Learning of Multiview Clustering and Semisupervised Classification

Recent researches on multiview learning have received widespread attention due to the increasing generalization of multiview data. As an effective probabilistic model, random walk has also shown encouraging performance in various fields. To further exploit the potential of utilizing random walk schemes to address multiview learning problems, this article proposes a simple yet efficient multigraph random walk scheme for both multiview clustering and semisupervised classification tasks. The proposed model integrates random walk with multiview learning, and recursively learns a globally stable probability distribution matrix from multiple views, on the basis of which the label indicator is obtained in the scene of clustering or semisupervised classification. Furthermore, an adaptive weight vector is learned to incorporate the diversity and complementarity of multiview data. Besides, the relationships between the proposed scheme and spectral clustering, neighborhood embedding and manifold embedding are analyzed theoretically. Finally, comprehensive comparative experiments are conducted with several state-of-the-art multiview clustering and semisupervised classification methods on eight real-world datasets. The experimental results demonstrate the superiority of the proposed method in terms of both clustering and classification performance.

Sidelobe Reduction in NC-OFDM-Based CRNs Using Differential Evolution-Assisted Generalized Sidelobe Canceller

Noncontiguous orthogonal frequency division multiplexing (NC-OFDM) is considered a suitable candidate for the cognitive radio network (CRN) to accomplish efficient data transmission. The NC-OFDM allows secondary users (SUs) to access the primary user (PU) spectrum while being detected idle. However, interference may occur in the adjacent frequency bands of the PU due to sidelobes of the SU transmission. The use of cancellation carriers (CCs) and generalized sidelobe canceller (GSC) is a widely adopted technique to tackle the sidelobes. To this end, this paper presents a differential evolution- (DE-) based GSC (DE-GSC) scheme to suppress unwanted sidelobes. At first, in the DE-GSC1 scheme, the adaptive weight vector is calculated using the DE algorithm while considering the complete samples of the sidelobes for optimization. The optimized weights are then added with the original weights to reduce the sidelobe issue. Next, in the DE-GSC2 scheme, selected elements for the adaptive weight vector near the main NC-OFDM signal are computed using the DE to reduce the search space. The performance of the proposed methods in terms of power spectral density (PSD) is compared with some of the recent techniques employing five different scenarios. Simulation results in the presence of single and multiple spectral hole scenarios validate that the proposed DE-GSC1 and DE-GSC2 methods result in enhanced suppression performance compared with the: original signal, simple CC, simple GSC, DE-based CC (DE-CC), and genetic algorithm- (GA-) based CC (GA-CC) schemes.

Generalized sidelobe canceler beamforming combined with Eigenspace-Wiener postfilter for medical ultrasound imaging.

BACKGROUND: The beamforming algorithm is key to the image quality of the medical ultrasound system. The generalized sidelobe canceler (GSC) beamforming can improve the image quality in lateral resolution, but the contrast is not improved correspondingly.OBJECTIVE: In our research, we try to optimize the generalized sidelobe canceler to obtain images that achieve an improvement in both lateral resolution and contrast.METHODS: We put forward a new beamforming algorithm which combines the generalized sidelobe canceler and Eigenspace-Wiener postfilter. According to eigenspace decomposition of the covariance matrix of the received data, the components of the Wiener postfilter can be calculated from the signal matrix and the noise matrix. Then, the adaptive weight vector of GSC is further constrained by the Eigenspace-Wiener postfilter, which make the output energy of the receiving array closer to the desired signal than the conventional GSC output.RESULTS: We compare the new beamforming algorithm with delay-and-sum (DS) beamforming, synthetic aperture (SA) beamforming, and GSC beamforming using the simulated and experimental data sets. The quantitative results show that our method reduces the FWHM by 85.5%, 80.5%, and 38.9% while improving the CR by 123.6%, 47.7%, 84.4% on basis of DS, SA, and GSC beamforming, respectively.CONCLUSIONS: The new beamforming algorithm can obviously improve the imaging quality of medical ultrasound imaging systems in both lateral resolution and contrast.

Robust Beamforming Based on Covariance Matrix Reconstruction in FDA-MIMO Radar to Suppress Deceptive Jamming.

Frequency diverse array (FDA)-multiple-input multiple-output (MIMO) radars can generate a range-angle two-dimensional transmit steering vector (SV), which is capable of suppressing mainbeam deceptive jamming in the transmit–receive frequency domain by utilizing additional degrees of freedom (DOFs) in the range dimension. However, when there are target SV mismatch, covariance matrix estimation error and target contamination, the jamming suppression performance degrades severely. In this paper, a robust adaptive beamforming algorithm for anti-jammer application based on covariance matrix reconstruction is proposed in FDA-MIMO radar. In this method, the residual noise is further determined by using the spatial power spectrum estimation approach, which results in improved estimation accuracy of the signal covariance matrix and the desired target SV. The jamming SV is obtained from vectors in the intersection of two subspaces (namely, the signal-jamming subspace derived from the sample covariance matrix (SCM) and the jamming subspace generated from the jamming covariance matrix) by an alternating projection algorithm. Furthermore, the jamming power is obtained by exploiting the orthogonality between the different SVs. With the obtained parameters of target and jamming, the optimal adaptive beamformer weight vector is calculated. Simulation results demonstrate that the proposed algorithm can cope with the mainbeam deceptive jamming suppression under various model mismatches and has excellent performance over a wide range of signal-to-noise ratios (SNRs).

Two-stage adaptive weight vector design method for decomposition based many-objective evolutionary algorithm

Two-stage adaptive weight vector design method for decomposition based many-objective evolutionary algorithm

Two-stage adaptive weight vector design method for decomposition based many-objective evolutionary algorithm

Two-stage adaptive weight vector design method for decomposition based many-objective evolutionary algorithm

Robust Fuzzy Clustering Algorithm Based on Adaptive Neighbors

In pattern recognition, fuzzy logic is widely used in unsupervised classification or clustering methods. Fuzzy c-means (FCM) clustering algorithm is a typical dynamic clustering algorithm of the fuzzy c-means algorithm based on the error square sum criterion. It introduces fuzzy membership and optimizes the objective function to obtain each sample point for all classes. The membership degree of the center is used to automatically classify the data sample. However, the FCM algorithm is susceptible to the noise points and outliers, and the unbalanced data structure reduces the generalization performance of the algorithm. In this paper, we propose a fuzzy c-means clustering algorithm with adaptive neighbors weight learning. Through adaptive neighborhood robust weight learning, an adaptive weight vector with robustness and sparsity is obtained. During the optimization, we only activate the k samples with the shortest distance to the cluster center and eliminate extreme noise samples to improve the global robustness and sparsity of the algorithm. Finally, empirical analysis verifies the superiority and effectiveness of the proposed clustering method.

Fast and robust adaptive beamforming algorithms for large-scale arrays with small samples

The adaptive beamformer of large-scale sensor array mainly suffers from two limits. One limit is an insufficient number of training snapshots, which usually results in an ill-posed sample covariance matrix in many real applications. The other limit is the high computation complexity of the beamformer that severely restricts its online processing. To overcome these two limits, two fast and robust adaptive beamforming algorithms are proposed in this paper, which refers to the linear kernel approaches and formulates the weight vector as a linear combination of the training samples and the signal steering vector. The proposed algorithms only need to calculate a low-dimensional combination vector instead of the high-dimensional adaptive weight vector, which remarkably reduces the computation complexity. Moreover, regularization techniques are utilized to suppress the excessive variation of the combination vector caused by an underdetermined estimation of the Gram matrix. Experimental results show that the proposed algorithms achieve better performance and lower computation complexity than algorithms in the literature. Especially, like the kernel approaches, the proposed algorithms achieve good performance under the small sample case.

Adaptive Weight Vector Solving Based on the Summation of Partial Eigenbeams in STAP

For the side-looking airborne or spaceborne early warning radar, Space-time adaptive processing (STAP) is a well-established technique. The adaptive weight vector can be written in the form of summation that equivalents to the inversion of covariance matrix. In order to reduce the computational complexity of the adaptive weight vector, this paper proposes a modified calculation method based on the weighted sum of partial eigenbeams according to the array model of the radar system. Both the loss of signal-to-interference and noise ratio (LSINR) and adapted patterns are used as performance metrics. Computer simulations verified the effectiveness of the method and its adaptability in traditional full-dimension, fixed-structure reduced dimension STAP.

A Low-complexity Minimum-variance Beamformer Based on Orthogonal Decomposition of the Compounded Subspace.

Minimum-variance (MV) beamforming, as a typical adaptive beamforming method, has been widely studied in medical ultrasound imaging. This method achieves higher spatial resolution than traditional delay-and-sum (DAS) beamforming by minimizing the total output power while maintaining the desired signals. However, it suffers from high computational complexity due to the heavy calculation load when determining the inverse of the high-dimensional matrix. Low-complexity MV algorithms have been studied recently. In this study, we propose a novel MV beamformer based on orthogonal decomposition of the compounded subspace (CS) of the covariance matrix in synthetic aperture (SA) imaging, which aims to reduce the dimensions of the covariance matrix and therefore reduce the computational complexity. Multiwave spatial smoothing is applied to the echo signals for the accurate estimation of the covariance matrix, and adaptive weight vectors are calculated from the low-dimensional subspace of the original covariance matrix. We conducted simulation, experimental and in vivo studies to verify the performance of the proposed method. The results indicate that the proposed method performs well in maintaining the advantage of high spatial resolution and effectively reduces the computational complexity compared with the standard MV beamformer. In addition, the proposed method shows good robustness against sound velocity errors.

Robust Adaptive Beamforming Based on Covariance Matrix Reconstruction With Annular Uncertainty Set and Vector Space Projection

The performance of adaptive beamforming will degrade dramatically in practical application due to system errors including signal direction error, array geometry error, gain, and phase errors. Besides, the performance will further deteriorate when the desired signal is contained in the sample data. Therefore, a robust adaptive beamforming method based on the covariance matrix reconstruction with annular uncertainty set (AUS) and vector space projection (VSP) is proposed in this letter. By integrating the corresponding Capon spectrum over the surface of AUS, the interference-plus-noise covariance matrix (INCM) and the desired signal covariance matrix are reconstructed, respectively. Because the steering vector (SV) of desired signal lies in the intersection of the signal subspaces of the sample covariance matrix and the reconstructed desired signal covariance matrix, it can be estimated by the VSP method. Finally, the adaptive weight vector is calculated based on the reconstructed INCM and the estimated SV. Simulation and experiment results show that the proposed method can effectively suppress the interference and achieve excellent performance under system errors.

Single-Point Array Response Control: An Efficient Beampattern Synthesis Approach Based on the Maximum Magnitude Response Principle

This article considers the beampattern synthesis problem, and a single-point array response control (SPARC) algorithm is presented to adjust the array response at an arbitrary direction. Based on the theoretical analysis, it is found that the adaptive array theory-based optimal weight vector is a linear combination of the signal steering vector and the interference steering vector multiplied by a complex factor, and that the complex factor determines the array response at the interference direction. Inspired by this observation, the SPARC algorithm is presented to achieve quiescent pattern control. In contrast to other array response control-based pattern synthesis techniques, the SPARC algorithm obtains a deterministic expression of the complex factor after maximizing the magnitude response at the main-beam direction, and the closed-form expression of the designed weight vector is devised. Because of different pattern constraints in focused and shaped beampatterns, two low-complexity pattern synthesis schemes are presented employing the SPARC algorithm in an iterative manner. Moreover, the parameter selection principle of the SPARC and its comparison with other pattern synthesis methods are discussed. Simulation results show the effectiveness of the SPARC algorithm and the efficiency of the beampattern synthesis schemes.

Robust Wideband Adaptive Beamforming Based on Focusing Transformation and Steering Vector Compensation

The wideband adaptive beamforming method would deteriorate severely when the desired signal is contained in the training snapshots, especially the mismatched signal steering vector existed simultaneously. Therefore, a robust wideband adaptive beamforming method is proposed based on focusing transformation and steering vector compensation. In proposed method, the received wideband signals are first decomposed into narrow sub-bands. Then, based on the direction of arrivals of signals, the interference plus noise covariance matrix of each sub-band is reconstructed to remove the desired signal and transformed into the reference frequency by the focusing transformation. Subsequently, the mismatched signal steering vector is compensated based on the error vector decomposition and the optimization of output power of adaptive beamformer. Finally, the adaptive weight vector of robust wideband beamforming is calculated based on the minimum variance distortionless response criterion. The effectiveness of proposed method is verified by numerical simulations.

Robust low‐range‐sidelobe target synthesis for airborne FDMA–MIMO STAP radar

With the multi-function need for airborne space-time adaptive processing (STAP) radar, range synthesis is usually necessary for the follow-up function of target recognition. Utilising the excellent performance on orthogonality and bandwidth synthesis of the frequency division multiple access (FDMA) waveform and the longer accumulation time of multiple-input multiple-output (MIMO) radar, a robust low-sidelobe target synthesis method for airborne FDMA–MIMO STAP radar is developed. The spectra characteristics of target and clutter are first analysed. Then, the keystone transform is employed to mitigate velocity migration. To avoid gain fluctuation induced by multiple independent adaptive weight vectors, the robust STAP beamformer is developed. Finally, to decouple the range–angle coupling relationship resulted from the FDMA waveform, angle compensation is added in the robust STAP beamformer. Numerical examples are given to demonstrate the effectiveness of the presented method.

Multi-objective decomposition optimization algorithm based on adaptive weight vector and matching strategy

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) uses pre-set weight vector and random matching mechanism between sub-problems and individuals, which makes the algorithm simple and efficient. However, when solving the problem of discontinuous Pareto Front, this will lead to not only the decline of the diversity of population, but also the degradation of the performance of solution set. To solve these problems, a multi-objective decomposition optimization algorithm based on adaptive weight vector and matching strategy (MOEA/D-AVM) is proposed in the article. Firstly, the algorithm finds the invalid sub-problems in the discontinuous region, and then updates these sub-problems according to the current evolutionary stage. It can reduce the possibility that the invalid sub-problems mislead evolutionary process. Secondly, the matching mechanism is established according to the value of penalty-based boundary intersection (PBI) and the Euclidean distance between the sub-problems and individuals. This mechanism can enhance the relationship between individuals and sub-problems. Finally, individuals who perform well in the neighborhood replacement operation are saved in the external archive. It can improve the diversity of the optimal solution set obtained by the algorithm. The proposed algorithm is compared with other related algorithms in the standard test problem. The result shows that the solution set obtained by MOEA/D-AVM not only can better cover the Pareto Front, but also has a competitive performance in solving the problem of discontinuous Pareto Front.

Space‐time matched filter design for interference suppression in coherent frequency diverse array

By transmitting a single frequency-shifted waveform, coherent frequency diverse array (FDA) can provide a simple way to realize full spatial coverages with stable gains. Owing to the range-angle dependency in coherent FDA, the authors implement a two-dimensional angle-time matched filter to perform equivalent transmit beamforming and matched filtering simultaneously. However, such filter structures merely control main-lobes of equivalent transmit beams towards target directions. It fails to form nulls at interference directions. Moreover, traditional adaptive beamforming by designing adaptive weight vectors are no longer applicable. Additionally, they find that the range resolution scales linearly with the element number. To tackle these issues, a space-time matched filter (STMF) in combination with the hybrid coding technique is proposed. Aiming at mitigating interferences, the STMF is designed with a formulation of quadratically constrained quadratic programing. By relaxation of quadratic constraints, the hard non-convex problem can be turned into the second-order cone programing to obtain optimal filter parameters. Furthermore, the hybrid coding technique is devised to jointly improve the range resolution. Numerical experiments of both two-dimensional range-angle outputs and one-dimensional range profiles via filtering are provided, which demonstrate that the STMF with hybrid coding can effectively suppress sidelobe interferences with a range resolution enhancement.

Superior Implementation of Accelerated QR Decomposition for Ultrasound Imaging

In this work, a novel Minimum Variance Distortion less Response (MVDR) beamformer architecture in which the adaptive weight vector is computed based on modified Column wise Givens Rotation (CGR) is presented. As compared to the conventional MVDR beamformer, Quadrature Rotation Decomposition (QRD)-MVDR is suitable for hardware realizations. To improve the real-time performance requirements of the MVDR Beamformer, a parallel pipe-lined CGR based QRD architecture is employed in the adaptive weight computation stage of the MVDR Beamformer. A computationally efficient MVDR beamforming algorithm, which requires to compute only the R matrix in QRD, rather than matrix inverse is used to develop the architecture. The developed architecture generates the adaptive weight vector in 3.9ns, and hence a beam can be formed in 0.25msec time. The designed architecture is implemented using Verilog Register Transfer Level (RTL) coding, and the functional equivalence checking was carried with the Verasonics Vantage-64 Ultrasound Research Platform (URP). The architecture is also ported on Xilinx Kintex-7 FPGA based Emulation set up and validated in real-time, targeting medical ultrasound imaging applications. The developed architecture is compared with the existing architecture implementations. It concludes that the architecture is superior in terms of computational time and can be adapted for ultrafast adaptive beamforming applications.

A Multi-objective Improved Squirrel Search Algorithm based on Decomposition with External Population and Adaptive Weight Vectors Adjustment

In order to further improve the performance of the Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) in solving multi-objective optimization problems, this paper constructs a multi-objective optimization algorithm by taking MOEA/D as the multi-objective framework and the Squirrel Search Algorithm (SSA) as the core evolutionary strategy. Besides, both of them are modified and the Multi-objective Improved Squirrel Search Algorithm based on Decomposition with External Population and Adaptive Weight Vectors Adjustment (MOEA/D-EWA-ISSA) is proposed. MOEA/D-EWA-ISSA establishes an external population for every individual to retain the evolutionary information and maintain the population diversity, external individuals participate in evolution and produce better offspring, the convergence and distribution of Pareto Front (PF) are improved. As for SSA, the jumping search method and the progressive search method are introduced to it, different evolutionary strategies are provided to solve subproblems, which further improves the ability of core evolutionary strategy to solve subproblems and the convergence of the obtained PF. Furthermore, MOEA/D-EWA-ISSA adjusts every weight vector adaptively according to the population’s actual evolutionary direction and the representative neighbor weight vectors, the distribution of the obtained PF is improved as well. The experimental results on multi-objective test functions show that the convergence and distribution of PF have obvious improvement when the improved SSA, the improved MOEA/D and the whole MOEA/D-EWA-ISSA are used to solve multi-objective optimization problems.

Low-rank graph optimization for multi-view dimensionality reduction.

Graph-based dimensionality reduction methods have attracted substantial attention due to their successful applications in many tasks, including classification and clustering. However, most classical graph-based dimensionality reduction approaches are only applied to data from one view. Hence, combining information from different data views has attracted considerable attention in the literature. Although various multi-view graph-based dimensionality reduction algorithms have been proposed, the graph construction strategies utilized in them do not adequately take noise and different importance of multiple views into account, which may degrade their performance. In this paper, we propose a novel algorithm, namely, Low-Rank Graph Optimization for Multi-View Dimensionality Reduction (LRGO-MVDR), that overcomes these limitations. First, we construct a low-rank shared matrix and a sparse error matrix from the graph that corresponds to each view for capturing potential noise. Second, an adaptive nonnegative weight vector is learned to explore complementarity among views. Moreover, an effective optimization procedure based on the Alternating Direction Method of Multipliers scheme is utilized. Extensive experiments are carried out to evaluate the effectiveness of the proposed algorithm. The experimental results demonstrate that the proposed LRGO-MVDR algorithm outperforms related methods.

Covariance‐free non‐homogeneity STAP detector in compound Gaussian clutter based on robust statistics

Space-time adaptive processing (STAP) detects targets by computing adaptive weight vectors for each cell under test using its covariance matrix, as estimated from surrounding secondary cells. In this study, the non-homogeneity detector (NHD) excludes the anomalous secondary cells that adversely affect the detection performance. The existing robust NHDs require estimating the covariance matrix of each secondary cell, which hinders their implementation in modern radars with large-dimensional range cells. In this study, the authors propose a new low-complexity NHD that is suitable for highly correlated clutter environments with both Gaussian and non-Gaussian heavy-tailed distributions. The proposed detector, which is based on the projection depth function from the field of robust statistics, features a non-parametric and covariance-free test statistic. As a result, its computational complexity is much lower than that of current NHDs, such as the widely used normalised adaptive matched filter (NAMF) detector, especially for large-dimensional range cells. In Monte Carlo simulations with different clutter distributions and radar system configurations, the proposed detector shows comparable performance to that of NAMF. The low complexity and robust performance of the new detector make it particularly attractive for real-time applications.