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Possibilistic fuzzy c-means (PFCM) clustering is a kind of hybrid clustering method based on fuzzy c-means (FCM) and possibilistic c-means (PCM), which not only has the stability of FCM but also partly inherits the robustness of PCM. However, as an extension of FCM on the objective function, PFCM tends to find a suboptimal local minimum, which affects its performance. In this paper, we rederive PFCM using the majorization-minimization (MM) method, which is a new derivation approach not seen in other studies. In addition, we propose an effective optimization method to solve the above problem, called MMPFCM. Firstly, by eliminating the variable V ∈ R p × c , the original optimization problem is transformed into a simplified model with fewer variables but a proportional term. Therefore, we introduce a new intermediate variable s ∈ R c to convert the model with the proportional term into an easily solvable equivalent form. Subsequently, we design an iterative sub-problem using the MM method. The complexity analysis indicates that MMPFCM and PFCM share the same computational complexity. However, MMPFCM requires less memory per iteration. Extensive experiments, including objective function value comparison and clustering performance comparison, demonstrate that MMPFCM converges to a better local minimum compared to PFCM. [ABSTRACT FROM AUTHOR]

Majorization–minimization (MM) is a versatile optimization technique that operates on surrogate functions satisfying tangency and domination conditions. Our focus is on differentiable optimization using inexact MM with quadratic surrogates, which amounts to approximately solving a sequence of symmetric positive definite systems. We begin by investigating the convergence properties of this process, from subconvergence to R-linear convergence, with emphasis on tame objectives. Then we provide a numerically stable implementation based on truncated conjugate gradient. Applications to multidimensional scaling and regularized inversion are discussed and illustrated through numerical experiments on graph layout and X-ray tomography. In the end, quadratic MM not only offers solid guarantees of convergence and stability, but is robust to the choice of its control parameters. [ABSTRACT FROM AUTHOR]

Environmental signals, acquired, e.g., by remote sensing, often present large gaps of missing observations in space and time. In this work, we present an innovative approach to identify the main variability patterns, in space–time data, when data may be affected by complex missing data structures. We formalize the problem in the framework of functional data analysis, proposing an innovative method of functional principal component analysis (fPCA) for incomplete space–time data. The functional nature of the proposed method permits to borrow information from measurements observed at nearby spatio-temporal locations. The resulting functional principal components are smooth fields over the considered spatio-temporal domain, and can lead to interesting insights in the spatio-temporal dynamic of the phenomenon under study. Moreover, they can be used to provide a reconstruction of the missing entries, also under severe missing data patterns. The proposed model combines a weighted rank-one approximation of the data matrix with a roughness penalty. We show that the estimation problem can be solved using a majorize–minimization approach, and provide a numerically efficient algorithm for its solution. Thanks to a discretization based on finite elements in space and B-splines in time, the proposed method can handle multidimensional spatial domains with complex shapes, such as water bodies with complicated shorelines, or curved spatial regions with complex orography. As shown by simulation studies, the proposed space–time fPCA is superior to alternative techniques for Principal Component Analysis with missing data. We further highlight the potentiality of the proposed method for environmental problems, by applying space–time fPCA to the study of the lake water surface temperature (LWST) of Lake Victoria, in Central Africa, starting from satellite measurements with large gaps. LWST is considered one of the fundamental indicators of how climate change is affecting the environment, and is recognized as an essential climate variable. [ABSTRACT FROM AUTHOR]

We consider the minimization of a differentiable Lipschitz gradient but non necessarily convex, function F defined on R N . We propose an accelerated gradient descent approach which combines three strategies, namely (i) a variable metric derived from the majorization-minimization principle; (ii) a subspace strategy incorporating information from the past iterates; (iii) a block alternating update. Under the assumption that F satisfies the Kurdyka–Łojasiewicz property, we give conditions under which the sequence generated by the resulting block majorize-minimize subspace algorithm converges to a critical point of the objective function, and we exhibit convergence rates for its iterates. [ABSTRACT FROM AUTHOR]

Majorization–minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the objective function so that along the iterations the objective value decreases. We present a stochastic higher-order algorithmic framework for minimizing the average of a very large number of sufficiently smooth functions. Our stochastic framework is based on the notion of stochastic higher-order upper bound approximations of the finite-sum objective function and minibatching. We derive convergence results for nonconvex and convex optimization problems when the higher-order approximation of the objective function yields an error that is p times differentiable and has Lipschitz continuous p derivative. More precisely, for general nonconvex problems we present asymptotic stationary point guarantees and under Kurdyka–Lojasiewicz property we derive local convergence rates ranging from sublinear to linear. For convex problems with uniformly convex objective function, we derive local (super)linear convergence results for our algorithm. Compared to existing stochastic (first-order) methods, our algorithm adapts to the problem's curvature and allows using any batch size. Preliminary numerical tests support the effectiveness of our algorithmic framework. [ABSTRACT FROM AUTHOR]

Hilbert-Schmidt Independence Criterion (HSIC) has recently been introduced to the field of single-index models to estimate the directions. Compared with other well-established methods, the HSIC based method requires relatively weak conditions. However, its performance has not yet been studied in the prevalent high-dimensional scenarios, where the number of covariates can be much larger than the sample size. In this article, based on HSIC, we propose to estimate the possibly sparse directions in the high-dimensional single-index models through a parameter reformulation. Our approach estimates the subspace of the direction directly and performs variable selection simultaneously. Due to the non-convexity of the objective function and the complexity of the constraints, a majorize-minimize algorithm together with the linearized alternating direction method of multipliers is developed to solve the optimization problem. Since it does not involve the inverse of the covariance matrix, the algorithm can naturally handle large p small n scenarios. Through extensive simulation studies and a real data analysis, we show that our proposal is efficient and effective in the high-dimensional settings. The Matlab codes for this method are available online. [ABSTRACT FROM AUTHOR]

In unmanned aerial vehicle (UAV) networks, introducing multiple-input/multiple-output (MIMO) technology brings promising capacity gains by exploiting spatial multiplexing. However, for UAV communications in urban scenarios, dense buildings block air-to-ground links, which leads to non-consistent service for users. In this paper, a user-centric joint beamforming design for multi-UAV networks aiming at maximizing the sum-rate performance is proposed, where the distributed antennas are deployed in UAV clusters forming virtual MIMO links to seamlessly guarantee user service under the 3D blockage effect. Specifically, the UAV clusters are constructed dynamically in a user-centric way for cooperative transmissions, which are dominated by the line-of-sight (LoS) connections considering building blockage effects. In addition, the selected user-to-UAV links must be less affected by the building blockages which are measured through the established channel model from comprehensive dimensions including sizes, locations, and heights. Within the UAV clusters, the proposed joint beamforming is performed based on the majorization-minimization (MM) algorithm for the NP-hard problem under per-antenna power constraints, and the optimal UAV parameters including UAV placement and antenna configuration with a fixed total number of antennas are investigated under different blockage effect. Simulation results demonstrate that the proposed design can improve sum-rate performance by more than $1\times $ compared with single UAV deployment under densely-located building environments.

Limited power and computational resources make the employment of complex classical encryption schemes unrealistic in resource-limited networks, e.g., the Internet of Things (IoT). To this end, physical layer security (PLS) has shown great potential in securing such resource-limited networks. To further combat the power scarcity in IoT nodes, radio frequency (RF) based energy harvesting (EH) is an attractive energy source while relaying can enhance the energy efficiency and extend the range of data transmission. Additionally, due to deploying low-cost hardware, imperfections in the RF chain of IoT transceivers are common. Against this background, in this paper, we investigate an untrusted EH relay-aided secure communication with RF impairments. Specifically, the relay simultaneously receives the desired signal from the source and the jamming from the destination in the first phase. Hence the relay is unable to extract the confidential desired signal. The resultant composite signal is then amplified by the relay in the second phase by using the energy harvested from the composite signal followed by its transmission to the destination. Since the destination is the original source of the jamming, its effect can be readily subtracted from the composite signal to recover the original desired signal of the source. Moreover, in the face of hardware impairments (HWIs) in all nodes, maintaining optimal power management both at the source and destination may impose excessive computations on an IoT node. We solve this problem by deep learning (DL) based optimal power management maximizing the secrecy rate based on the instantaneous channel coefficients. We show that our learning-based scheme can reach the accuracy of the exhaustive search method despite its considerably lower computational complexity. Moreover, we developed an optimization framework for judiciously sharing HWIs across the nodes, so that we attain the maximum secrecy rate. To derive an efficient solution, we utilize a majorization-minimization (MM)algorithm, which is a particular instance in the family of successive convex approximation (SCA) methods. The simulation results show that the proposed HWI aware design considerably improves the secrecy rate.

Biomedical measurements are generally contaminated with substantial noise from various sources, including thermal noise, interference from other physiological signals, environment, or electrode movements. Complete restoration of biosignals from noisy measurements using linear filtering techniques is not feasible owing to the spectral overlapping problem. This paper proposes an arithmetic–geometric mean inequality-based robust denoising method. The proposed method incorporates a novel convexified cost function using the concept of majorization-minimization. A two-step algorithm is derived using the forward–backward splitting technique. An optimality condition is derived to set the hyperparameters of the new algorithm. The proposed convex optimization-based method effectively denoises cardiovascular signals, including both electrocardiogram and photoplethysmography. Furthermore, the efficacy of the proposed approach is verified over different datasets. The quantitative and qualitative results obtained using the proposed method demonstrate the superiority of the proposed method in biosignal denoising concerning state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

Automated methods for facial animation are a necessary tool in the modern industry since the standard blendshape head models consist of hundreds of controllers, and a manual approach is painfully slow. Different solutions have been proposed that produce output in real-time or generalize well for different face topologies. However, all these prior works consider a linear approximation of the blendshape function and hence do not provide a high-enough level of detail for modern realistic human face reconstruction. A second-order blendshape approximation leads to higher fidelity facial animation but generates a non-linear least squares optimization problem with high dimensionality. We derive a method for solving the inverse rig in blendshape animation using quadratic corrective terms, which increases accuracy. At the same time, due to the proposed construction of the objective function, it yields a sparser estimated weight vector compared to the state-of-the-art methods. The former feature means lower demand for subsequent manual corrections of the solution, while the latter indicates that the manual modifications are also easier to include. Our algorithm is iterative and employs a Majorization–Minimization paradigm to cope with the increased complexity produced by adding corrective terms. The surrogate function is easy to solve and allows for further parallelization on the component level within each iteration. This paper is complementary to an accompanying paper (Racković et al. arxiv preprint. https://arxiv.org/abs/2302.04843, 2023) where we provide detailed experimental results and discussion, including highly-realistic animation data, and show a clear superiority of the results compared to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Imbalanced class data are commonly observed in pattern analysis, machine learning, and various real-world applications. Conventional approaches often resort to resampling techniques in order to address the imbalance, which inevitably alter the original data distribution. This paper proposes a novel classification method that leverages optimal transport for handling imbalanced data. Specifically, we establish a transport plan between training and testing data without modifying the original data distribution, drawing upon the principles of optimal transport theory. Additionally, we introduce a non-convex interclass regularization term to establish connections between testing samples and training samples with the same class labels. This regularization term forms the basis of a regularized discrete optimal transport model, which is employed to address imbalanced classification scenarios. Subsequently, in line with the concept of maximum minimization, a maximum minimization algorithm is introduced for regularized discrete optimal transport. Subsequent experiments on 17 Keel datasets with varying levels of imbalance demonstrate the superior performance of the proposed approach compared to 11 other widely used techniques for class-imbalanced classification. Additionally, the application of the proposed approach to water quality evaluation confirms its effectiveness. [ABSTRACT FROM AUTHOR]

Representation-based Classification (RC) algorithms have been extensively applied in the domain of face recognition. This paper introduces a novel approach by incorporating arbitrary norms into both the objective and constraint functions of conventional RC algorithms, resulting in the development of the Generalized RC (GRC) algorithm. The primary goal of this enhancement is to fully leverage the unique advantages offered by various norms. Within the majorization-minimization framework, an iterative procedure was designed to solve the optimization problem of GRC. This approach ensures that a closed-form solution is obtained in each iteration and a locally optimal solution can be found upon convergence. Experimental results on four benchmark face databases demonstrated that GRC generally outperforms competing RC algorithms in face recognition. Data and source code of this study are publicly available on the GitHub repository at https://github.com/yuzhounh/GRC. [ABSTRACT FROM AUTHOR]

Possibilistic fuzzy c-means (PFCM) clustering is a kind of hybrid clustering method based on fuzzy c-means (FCM) and possibilistic c-means (PCM), which not only has the stability of FCM but also partly inherits the robustness of PCM. However, as an extension of FCM on the objective function, PFCM tends to find a suboptimal local minimum, which affects its performance. In this paper, we rederive PFCM using the majorization-minimization (MM) method, which is a new derivation approach not seen in other studies. In addition, we propose an effective optimization method to solve the above problem, called MMPFCM. Firstly, by eliminating the variable V∈Rp×c, the original optimization problem is transformed into a simplified model with fewer variables but a proportional term. Therefore, we introduce a new intermediate variable s∈Rc to convert the model with the proportional term into an easily solvable equivalent form. Subsequently, we design an iterative sub-problem using the MM method. The complexity analysis indicates that MMPFCM and PFCM share the same computational complexity. However, MMPFCM requires less memory per iteration. Extensive experiments, including objective function value comparison and clustering performance comparison, demonstrate that MMPFCM converges to a better local minimum compared to PFCM.

AbstractSurface anomaly detection by using 3D point cloud data has recently received significant attention. To completely measure the common free-form surfaces without loss of details, advanced 3D scanning technologies, such as 3D laser scanners, can be applied and will produce an unstructured point cloud. However, this irregular data structure poses challenges to anomaly detection, in that the existing methods based on regular data, e.g., 2D image, cannot be directly applied. This article proposes a sparse learning framework with a graph representation of the unstructured point cloud for anomaly detection (PointSGRADE). Specifically, the free-form surface is assumed to be smooth. Then, the associated point cloud can be represented as a graph. Subsequently, considering the sparse anomalies, we propose a sparse learning framework and formulate the anomaly detection problem as a penalized optimization problem, which is further solved by a computationally efficient majorization-minimization framework. Case studies demonstrate the accuracy and robustness of the proposed method. This article proposes a novel methodology for sparse anomaly detection on smooth free-form surfaces represented by unstructured point cloud, which is critical for quality inspection in manufacturing and other application areas. [ABSTRACT FROM AUTHOR]

The reconstruction of biomedical signals from noisy measurements has been an indispensable research topic. A majority of biosignals exhibit typical piecewise characteristics. The recovery of these piecewise biomedical signals embedded in noise through conventional nonlinear filtering schemes fails due to the lack of proper balance between strict sparsity and smoothness-inducing property of regularizers at large noise levels. This work proposes a nonlinear convex optimization-based filtering approach, which incorporates a Moreau envelope-based regularizer using the majorized version of the total variation function. The source signals are restored by exploiting their piecewise characteristics through a majorized cost function. The majorized functions provide some relaxation in solving non-convex functions. The relaxation of the stringent sparsifying penalty provides the balance between the smoothness property and the piecewise features of biosignals. The optimality criterion for the proposed method is analyzed in this work. Furthermore, we evaluate the new method using a standard IoT platform. The recovery performance of this method is found to be superior to various state-of-the-art techniques for piecewise synthetic and real-world physiological signals corrupted by additive noise. [ABSTRACT FROM AUTHOR]

Single nucleotide polymorphism (SNP) set analysis aggregates both common and rare variants and tests for association between phenotype(s) of interest and a set. However, multiple SNP-sets, such as genes, pathways, or sliding windows are usually investigated across the whole genome in which all groups are tested separately, followed by multiple testing adjustments. We propose a novel method to prioritize SNP-sets in a joint multivariate variance component model. Each SNP-set corresponds to a variance component (or kernel), and model selection is achieved by incorporating either convex or nonconvex penalties. The uniqueness of this variance component selection framework, which we call VCSEL, is that it naturally encompasses multivariate traits (VCSEL-M) and SNP-set-treatment or -environment interactions (VCSEL-I). We devise an optimization algorithm scalable to many variance components, based on the majorization-minimization (MM) principle. Simulation studies demonstrate the superiority of our methods in model selection performance, as measured by the area under the precision-recall (PR) curve, compared to the commonly used marginal testing and group penalization methods. Finally, we apply our methods to a real pharmacogenomics study and a real whole exome sequencing study. Some top ranked genes by VCSEL are detected as insignificant by the marginal test methods which emphasizes formal inference of individual genes with a strict significance threshold. This provides alternative insights for biologists to prioritize follow-up studies and develop polygenic risk score models.

Methods for electro- or magnetoencephalography (EEG/MEG) based brain source imaging (BSI) using sparse Bayesian learning (SBL) have been demonstrated to achieve excellent performance in situations with low numbers of distinct active sources, such as event-related designs. This paper extends the theory and practice of SBL in three important ways. First, we reformulate three existing SBL algorithms under the majorization-minimization (MM) framework. This unification perspective not only provides a useful theoretical framework for comparing different algorithms in terms of their convergence behavior, but also provides a principled recipe for constructing novel algorithms with specific properties by designing appropriate bounds of the Bayesian marginal likelihood function. Second, building on the MM principle, we propose a novel method called LowSNR-BSI that achieves favorable source reconstruction performance in low signal-to-noise-ratio (SNR) settings. Third, precise knowledge of the noise level is a crucial requirement for accurate source reconstruction. Here we present a novel principled technique to accurately learn the noise variance from the data either jointly within the source reconstruction procedure or using one of two proposed cross-validation strategies. Empirically, we could show that the monotonous convergence behavior predicted from MM theory is confirmed in numerical experiments. Using simulations, we further demonstrate the advantage of LowSNR-BSI over conventional SBL in low-SNR regimes, and the advantage of learned noise levels over estimates derived from baseline data. To demonstrate the usefulness of our novel approach, we show neurophysiologically plausible source reconstructions on averaged auditory evoked potential data.

The excellent remote sensing ability of synthetic aperture radar (SAR) will be misled seriously when it encounters deceptive jamming which possesses high fidelity and fraudulence. In this paper, the dynamic synthetic aperture (DSA) scheme is used to extract the difference between the true and false targets. A simultaneous deceptive jamming suppression and target reconstruction method is proposed for a single channel SAR system to guarantee remote sensing ability. The system model is formulated as a sparse signal recovery problem with an unknown parametric dictionary to be estimated. An iterative re-weighted method is employed to jointly handle the dictionary parameter learning and target reconstruction problem in an majorization-minimization framework, where a surrogate function majorizing the Gaussian entropy in the objective function is introduced to circumvent its non-convexity. After dictionary parameter learning, the grid mismatching problem in a fixed grid based method is avoided. Therefore, the proposed method can reap a super resolution result. Besides, a simple yet effective DSA section scheme is developed for the SAR data excerpting, in which only two DSAs are required. Experimental results about location error and reconstruction power error reveal that the proposed method is able to achieve a good performance in deceptive jamming suppression.

Imbalanced class data are commonly observed in pattern analysis, machine learning, and various real-world applications. Conventional approaches often resort to resampling techniques in order to address the imbalance, which inevitably alter the original data distribution. This paper proposes a novel classification method that leverages optimal transport for handling imbalanced data. Specifically, we establish a transport plan between training and testing data without modifying the original data distribution, drawing upon the principles of optimal transport theory. Additionally, we introduce a non-convex interclass regularization term to establish connections between testing samples and training samples with the same class labels. This regularization term forms the basis of a regularized discrete optimal transport model, which is employed to address imbalanced classification scenarios. Subsequently, in line with the concept of maximum minimization, a maximum minimization algorithm is introduced for regularized discrete optimal transport. Subsequent experiments on 17 Keel datasets with varying levels of imbalance demonstrate the superior performance of the proposed approach compared to 11 other widely used techniques for class-imbalanced classification. Additionally, the application of the proposed approach to water quality evaluation confirms its effectiveness.

This article introduces a new penalized majorization–minimization subspace algorithm (P-MMS) for solving smooth, constrained optimization problems. In short, our approach consists of embedding a subspace algorithm in an inexact exterior penalty procedure. The subspace strategy, combined with a majoration–minimization step-size search, takes great advantage of the smoothness of the penalized cost function, while the penalty method allows to handle a wide range of constraints. The main drawback of exterior penalty approaches, namely ill-conditioning for large values of the penalty parameter, is overcome by using a trust-region-like technique. The convergence of the resulting algorithm is analyzed. Numerical experiments carried out on two large-scale image recovery applications demonstrate that, compared with state-of-the-art algorithms, the proposed method performs well in terms of computational time. [ABSTRACT FROM AUTHOR]

A wide class of problems involves the minimization of a coercive and differentiable function F on R N whose gradient cannot be evaluated in an exact manner. In such context, many existing convergence results from standard gradient-based optimization literature cannot be directly applied and robustness to errors in the gradient is not necessarily guaranteed. This work is dedicated to investigating the convergence of Majorization-Minimization (MM) schemes when stochastic errors affect the gradient terms. We introduce a general stochastic optimization framework, called StochAstic suBspace majoRIzation-miNimization Algorithm SABRINA that encompasses MM quadratic schemes possibly enhanced with a subspace acceleration strategy. New asymptotical results are built for the stochastic process generated by SABRINA. Two sets of numerical experiments in the field of machine learning and image processing are presented to support our theoretical results and illustrate the good performance of SABRINA with respect to state-of-the-art gradient-based stochastic optimization methods. [ABSTRACT FROM AUTHOR]

This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes the distance from the covariance estimate to a symmetric sparsity set. This formulation avoids unwanted shrinkage induced by more common norm penalties, and enables optimization of the resulting nonconvex objective by solving a sequence of smooth, unconstrained subproblems. These subproblems are generated and solved via the proximal distance version of the majorization-minimization principle. The resulting algorithm executes rapidly, gracefully handles settings where the number of parameters exceeds the number of cases, yields a positive-definite solution, and enjoys desirable convergence properties. Empirically, we demonstrate that our approach outperforms competing methods across several metrics, for a suite of simulated experiments. Its merits are illustrated on international migration data and a case study on flow cytometry. Our findings suggest that the marginal and conditional dependency networks for the cell signalling data are more similar than previously concluded. [ABSTRACT FROM AUTHOR]

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated as low-rank semi-definite programming (SDP) problems. Traditional formulations use the square loss, which is notorious for being sensitive to outliers. We propose to replace this with more robust noise models, including the $\ell _1$ ℓ 1 -loss and other nonconvex losses. However, the resultant optimization problem becomes difficult as the objective is no longer convex or smooth. To alleviate this problem, we design an efficient algorithm based on majorization-minimization. The crux is on constructing a good optimization surrogate, and we show that this surrogate can be efficiently obtained by the alternating direction method of multipliers (ADMM). By properly monitoring ADMM's convergence, the proposed algorithm is empirically efficient and also theoretically guaranteed to converge to a critical point. Extensive experiments are performed on four machine learning applications using both synthetic and real-world data sets. Results show that the proposed algorithm is not only fast but also has better performance than the state-of-the-arts. [ABSTRACT FROM AUTHOR]

Penalized regression methods are used in many biomedical applications for variable selection and simultaneous coefficient estimation. However, missing data complicates the implementation of these methods, particularly when missingness is handled using multiple imputation. Applying a variable selection algorithm on each imputed dataset will likely lead to different sets of selected predictors. This article considers a general class of penalized objective functions which, by construction, force selection of the same variables across imputed datasets. By pooling objective functions across imputations, optimization is then performed jointly over all imputed datasets rather than separately for each dataset. We consider two objective function formulations that exist in the literature, which we will refer to as "stacked" and "grouped" objective functions. Building on existing work, we (i) derive and implement efficient cyclic coordinate descent and majorization-minimization optimization algorithms for continuous and binary outcome data, (ii) incorporate adaptive shrinkage penalties, (iii) compare these methods through simulation, and (iv) develop an R package miselect. Simulations demonstrate that the "stacked" approaches are more computationally efficient and have better estimation and selection properties. We apply these methods to data from the University of Michigan ALS Patients Biorepository aiming to identify the association between environmental pollutants and ALS risk. for this article are available online. [ABSTRACT FROM AUTHOR]

Belief propagation (BP) is a popular message passing algorithm for distributed cooperative localization. However, due to the nonlinearity of measurement functions, BP implementation has no closed-form expression and requires message approximations. While nonparametric BP can be used, it suffers from a high computational complexity, thus being impractical in energy-constrained networks. In this paper, a parametric Bayesian method with Gaussian BP implementation is proposed for distributed cooperative localization. With linearization of the Euclidean norm in ranging measurements, the joint posterior distribution of agents’ locations is successively approximated with a sequence of high-dimensional Gaussian distributions. At each iteration of the successive Gaussian approximation, vector-valued Gaussian BP is further adopted to compute the marginal distributions of agents’ locations in a distributed way. It is proved by the principle of majorization-minimization that the proposed successive Gaussian approximation is guaranteed to converge, and the sequence of the estimated agents’ locations converges to a stationary point of the objective function of the maximum a posteriori estimation. Furthermore, although cooperative localization involves loopy network topologies, in which convergence property of Gaussian BP is generally unknown, it is proved in this paper that vector-valued Gaussian BP converges, making the proposed parametric BP-based method being the first one achieving convergence guarantee. Compared to the nonparametric BP counterpart, the proposed method has a much lower computational complexity and communication overhead. Simulation results demonstrate that the proposed method achieves a superior performance in localization accuracy compared to existing cooperative localization methods. [ABSTRACT FROM AUTHOR]

Probabilistic control design is founded on the principle that a rational agent attempts to match modelled with an arbitrary desired closed-loop system trajectory density. The framework was originally proposed as a tractable alternative to traditional optimal control design, parametrizing desired behaviour through fictitious transition and policy densities and using the information projection as a proximity measure. In this work we introduce an alternative parametrization of desired closed-loop behaviour and explore alternative proximity measures between densities. It is then illustrated how the associated probabilistic control problems solve into uncertain or probabilistic policies. Our main result is to show that the probabilistic control objectives majorize conventional, stochastic and risk sensitive, optimal control objectives. This observation allows us to identify two probabilistic fixed point iterations that converge to the deterministic optimal control policies establishing an explicit connection between either formulations. Further we demonstrate that the risk sensitive optimal control formulation is also technically equivalent to a Maximum Likelihood estimation problem on a probabilistic graph model where the notion of costs is directly encoded into the model. The associated treatment of the estimation problem is then shown to coincide with the moment projected probabilistic control formulation. That way optimal decision making can be reformulated as an iterative inference problem. Based on these insights we discuss directions for algorithmic development. [ABSTRACT FROM AUTHOR]

In this letter, we deal with the problem of high-resolution time delay estimation (TDE) in multipath environments exploiting the matched filter (MF) outputs data. To this end, we develop a systematic post-processing framework, consisting of two sparsity-based algorithms and a refining procedure aimed at reducing the computational load. The TDE problem is formulated as a sparse signal recovery problem and efficiently solved resorting to a majorization-minimization paradigm and a cyclic procedure. At the design stage, we assume a complex-valued Gaussian distribution model for the MF samples and incorporate a module-product prior that promotes the sparsity more significantly than the conventional complex Laplacian distribution. The preliminary performance assessment, conducted on simulated data, shows that, at least for the considered parameter values, the proposed delay estimators approach the Cramér-Rao bound for different signal-to-noise ratios and bandwidths. [ABSTRACT FROM AUTHOR]

When applying the sequential quadratic programming (SQP) algorithm to topology optimization, using the quasi-Newton methods or calculating the Hessian matrix directly will result in a considerable amount of calculation, making it computationally infeasible when the number of optimization variables is large. To solve the above problems, this paper creatively proposes a method for calculating the approximate Hessian matrix for structural topology optimization with minimum compliance problems. Then, the second-order Taylor expansion transforms the original problem into a series of separable and easy-to-solve convex quadratic programming (QP) subproblems. Finally, the quadratic programming optimality criteria (QPOC) method and the QP solver of MATLAB are used to solve the subproblems. Compared with other sequential quadratic programming methods, the advantage of the proposed method is that the Hessian matrix is diagonally positive definite and its calculation is simple. Numerical experiments on an MBB beam and cantilever beam verify the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables interpretability of the factors. We factorize the Bernoulli parameter and consider an additional Beta prior on one of the factors to further improve the model’s expressive power. While similar models have been proposed in the literature, they only exploit the Beta prior as a proxy to ensure a valid Bernoulli parameter in a Bayesian setting; in practice it reduces to a uniform or uninformative prior. Besides, estimation in these models has focused on costly Bayesian inference. In this paper, we propose a simple yet very efficient majorization-minimization algorithm for maximum a posteriori estimation. Our approach leverages the Beta prior whose parameters can be tuned to improve performance in matrix completion tasks. Experiments conducted on three public binary datasets show that our approach offers an excellent trade-off between prediction performance, computational complexity, and interpretability. [ABSTRACT FROM AUTHOR]

One of the main challenges in block-sparse signal recovery, as encountered in, e.g., multi-antenna mmWave channel models, is block-patterned estimation without knowledge of block sizes and boundaries. We propose a novel Sparse Bayesian Learning (SBL) method for block-sparse signal recovery under unknown block patterns. Contrary to conventional approaches that impose block-promoting regularization on the signal components, we apply two classes of hyperparameter regularizers for the SBL cost function, inspired by total variation (TV) denoising. The first class relies on a conventional TV difference unit and allows performing the SBL inference iteratively through a set of convex optimization problems, enabling a flexible choice of numerical solvers. The second class incorporates a region-aware TV penalty to penalize the signal and zero blocks in a dissimilar manner, enhancing the performance. We derive an alternating optimization algorithm based on expectation-maximization to perform the SBL inference through computationally efficient parallel updates for both the regularizer classes. The numerical results show that the proposed TV-regularized SBL algorithm is robust to the nature of the block structure and is capable of recovering signals with both block-patterned and isolated components, proving effective for various signal recovery systems. [ABSTRACT FROM AUTHOR]

Source localization plays a key role in many applications including radar, wireless and underwater communications. Among various localization methods, the most popular ones are Time-Of-Arrival (TOA), Time-Difference-Of-Arrival (TDOA), Angle-Of-Arrival (AOA) and Received Signal Strength (RSS) based. Since the Cramér-Rao lower bounds (CRLB) of these methods depend on the sensor geometry explicitly, sensor placement becomes a crucial issue in source localization applications. In this paper, we consider finding the optimal sensor placements for the TOA, TDOA, AOA and RSS based localization scenarios. We first unify the three localization models by a generalized problem formulation based on the CRLB-related metric. Then a unified optimization framework for optimal sensor placement (UTMOST) is developed through the combination of the alternating direction method of multipliers (ADMM) and majorization-minimization (MM) techniques. Unlike the majority of the state-of-the-art works, the proposed UTMOST neither approximates the design criterion nor considers only uncorrelated noise in the measurements. It can readily adapt to to different design criteria (i.e. A, D and E-optimality) with slight modifications within the framework and yield the optimal sensor placements correspondingly. Extensive numerical experiments are performed to exhibit the efficacy and flexibility of the proposed framework. [ABSTRACT FROM AUTHOR]

In this letter, the problem of non-coherent direction of arrival (DOA) estimation is investigated exploiting the sign of the measurements in order to resolve the inherent ambiguity of the problem. Although the phase values are inaccurate, the sign of real and imaginary parts of the measurements will most likely remain correct under limited phase errors. Furthermore, a new approach for solving the problem is proposed employing a modified version of the Majorization-Minimization (MM) technique, without any prior information about the number of incident signals. Some theoretical analyses of our proposed algorithm are also provided in the paper. Finally, the simulation results are presented, demonstrating the efficiency of the proposed algorithm in comparison to some state-of-the-art methods in the literature. [ABSTRACT FROM AUTHOR]

In this letter we address the problem of multistatic target localization using time-delay measurements corrupted by noise with unknown non-uniform variances. More concretely, we consider the problem of joint maximum likelihood (ML) estimation of the target position and the noise variances, for which we propose a majorization-minimization based algorithm. The proposed approach is compared with state-of-the-art algorithms, and the simulation results show the excellent accuracy of our algorithm. [ABSTRACT FROM AUTHOR]

Constant-modulus sequence set with low peak side-lobe level is a necessity for enhancing the performance of modern active sensing systems like Multiple Input Multiple Output (MIMO) RADARs. In this paper, we consider the problem of designing a constant-modulus sequence set by minimizing the peak side-lobe level, which can be cast as a non-convex minimax problem, and propose a Majorization-Minimization technique based iterative monotonic algorithm named as the PSL minimizer. The iterative steps of our algorithm are computationally not very demanding and they can be efficiently implemented via Fast Fourier Transform (FFT) operations. We also establish the convergence of our proposed algorithm and discuss the computational and space complexities of the algorithm. Finally, through numerical simulations, we illustrate the performance of our method with the state-of-the-art methods. To highlight the potential of our approach, we evaluate the performance of the sequence set designed via our approach in the context of probing sequence set design for MIMO RADAR angle-range imaging application and show results exhibiting good performance of our method when compared with other commonly used sequence set design approaches.

We consider multi-antenna wireless systems aided by reconfigurable intelligent surfaces (RIS). RIS presents a new physical layer technology for improving coverage and energy efficiency by intelligently controlling the propagation environment. In practice however, achieving the anticipated gains of RIS requires accurate channel estimation. Recent attempts to solve this problem have considered the least-squares (LS) approach, which is simple but also sub-optimal. The optimal channel estimator, based on the minimum mean-squared-error (MMSE) criterion, is challenging to obtain and is non-linear due to the non-Gaussianity of the effective channel seen at the receiver. Here we present approaches to approximate the optimal MMSE channel estimator. As a first approach, we analytically develop the best linear estimator, the LMMSE, together with a corresponding majorization-minimization-based algorithm designed to optimize the RIS phase shift matrix during the training phase. This estimator is shown to yield improved accuracy over the LS approach by exploiting second-order statistical properties of the wireless channel and the noise. To further improve performance and better approximate the globally-optimal MMSE channel estimator, we propose data-driven non-linear solutions based on deep learning. Specifically, by posing the MMSE channel estimation problem as an image denoising problem, we propose two convolutional neural network (CNN)-based methods to perform the denoising and approximate the optimal MMSE channel estimation solution. Our numerical results show that these CNN-based estimators give superior performance compared with linear estimation approaches. They also have low computational complexity requirements, thereby motivating their potential use in future RIS-aided wireless communication systems.

Although the non-coherent direction of arrival (DOA) estimation problem can be solved by sparse phase retrieval algorithms, known reference signals are required to deal with the inherent ambiguity issue of this approach. To avoid the use of reference signals, an effective array structure employing two uniform linear arrays is proposed (although other array structures are possible, such as the circular array), based on which a phase retrieval problem employing group sparsity is formulated. It is then replaced by its convex surrogate alternative by applying the majorization-minimization technique and the proximal gradient method is employed to solve the surrogate problem. The proposed algorithm is referred to as fasT grOup sparsitY Based phAse Retreival (ToyBar). Unlike the existing phase-retrieval based DOA estimation algorithm GESPAR, it does not need to know the number of incident signals in advance. Simulation results indicate that the proposed algorithm has a fast convergence speed and a better estimation performance is achieved.

This work investigates the effect of double intelligent reflecting surface (IRS) in improving the spectrum efficient of multi-user multiple-input multiple-output (MIMO) network operating in the millimeter wave (mmWave) band. Specifically, we aim to solve a weighted sum rate maximization problem by jointly optimizing the digital precoding at the transmitter and the analog phase shifters at the IRS, subject to the minimum achievable rate constraint. To facilitate the design of an efficient solution, we first reformulate the original problem into a tractable one by exploiting the majorization-minimization (MM) method. Then, a block coordinate descent (BCD) method is proposed to obtain a suboptimal solution, where the precoding matrices and the phase shifters are alternately optimized. Specifically, the digital precoding matrix design problem is solved by the quadratically constrained quadratic programming (QCQP), while the analog phase shift optimization is solved by the Riemannian manifold optimization (RMO). The convergence and computational complexity are analyzed. Finally, simulation results are provided to verify the performance of the proposed design, as well as the effectiveness of double-IRS in improving the spectral efficiency. [ABSTRACT FROM AUTHOR]

This paper investigates a novel intelligent reflecting surface (IRS)-based symbiotic radio (SR) system architecture consisting of a transmitter, an IRS, and an information receiver (IR). The primary transmitter communicates with the IR and at the same time assists the IRS in forwarding information to the IR. Based on the IRS’s symbol period, we distinguish two scenarios, namely, commensal SR (CSR) and parasitic SR (PSR), where two different techniques for decoding the IRS signals at the IR are employed. We formulate bit error rate (BER) minimization problems for both scenarios by jointly optimizing the active beamformer at the base station and the phase shifts at the IRS, subject to a minimum primary rate requirement. Specifically, for the CSR scenario, a penalty-based algorithm is proposed to obtain a high-quality solution, where semi-closed-form solutions for the active beamformer and the IRS phase shifts are derived based on Lagrange duality and Majorization-Minimization methods, respectively. For the PSR scenario, we apply a bisection search-based method, successive convex approximation, and difference of convex programming to develop a computationally efficient algorithm, which converges to a locally optimal solution. Simulation results demonstrate the effectiveness of the proposed algorithms and show that the proposed SR techniques are able to achieve a lower BER than benchmark schemes. [ABSTRACT FROM AUTHOR]

The use of a large-scale antenna array (LSAA) has become an important characteristic of multi-antenna communication systems to achieve beamforming gains such as in designing millimeter-wave (mmWave) systems to combat severe propagation losses. In such applications, each antenna element has to be driven by a radio frequency (RF) chain for the implementation of fully-digital beamformers, significantly increasing the hardware cost, complexity, and power consumption. Therefore, constant-modulus analog beamforming (CMAB) becomes a viable solution. In this paper, we consider the scaled analog beamforming (SAB) or constant-modulus analog beamforming (CMAB) architecture and design the system parameters by solving two variants of beampattern matching problem. In the first case, both the magnitude and phase of the beampattern are matched to the given desired beampattern whereas in the second case, only the magnitude of the beampattern is matched. Both the beampattern matching problems are cast as a variant of the constant-modulus least-squares (CLS) problem. We provide efficient algorithms based on the alternating majorization-minimization (AMM) framework that combines the alternating minimization and the MM frameworks and the conventional-cyclic coordinate descent (C-CCD) algorithms to solve the problem in each case. We also propose algorithms based on a new modified-CCD (M-CCD) based approach. For all the developed algorithms we prove convergence to a Karush-Kuhn-Tucker (KKT) point (or a stationary point). Numerical results demonstrate that the proposed algorithms converge faster than the state-of-the-art solutions. Among all the algorithms, the M-CCD-based algorithms have faster convergence when evaluated in terms of the number of iterations and the AMM-based algorithms offer lower complexity. [ABSTRACT FROM AUTHOR]

In this paper, we propose an iterative algorithm named PGPAL for the phase-retrieval problem under the scenario when the measurements follow Poisson plus Gaussian (PG) distribution, which is a more realistic model in applications like astronomy, microscopy, medical imaging, and remote sensing. The proposed algorithm is based on majorization-minimization (MM) framework, in which a simple surrogate function that tightly upperbounds the challenging underlying maximum-likelihood (ML) objective is constructed and minimized iteratively. The proposed algorithm monotonically decreases the ML objective and the algorithm is guaranteed to converge to a stationary point of the ML objective. Numerical simulations are performed for the one-dimensional phase-retrieval case, and the performance of the proposed method is compared with the recently proposed Poisson phase-retrieval algorithm, which assumes the measurement model to be only Poisson distributed. The performance of the proposed MM-based algorithm in terms of the normalized root mean square error (NRMSE) is found to be much better in comparison to the method for Poisson phase-retrieval. [ABSTRACT FROM AUTHOR]

In this letter, we investigate a multi-relay assisted over-the-air computation network for multi-modal sensing with direct links, where each node is equipped with multiple antennas and all the relays are operated in an amplify-and-forward mode. Specifically, the whole transmission is divided into two phases and all the sensors transmit symbols during both two phases. In particular, we are interested in minimizing the computation distortion measured by the mean-squared error (MSE) via jointly optimizing beamforming matrices at all nodes, subject to individual power constraints at the sensors and relays. The major difficulty lies in the strong coupling of beamforming matrices in the objective function and the non-convex transmit power constraints at the relays. To tackle this problem, a low-complexity locally optimal method based on alternating optimization is proposed, where closed-form expressions are obtained in each iteration. Furthermore, simulation results show that our proposed beamforming design can substantially enhance the computation MSE performance, as compared to other benchmark schemes. [ABSTRACT FROM AUTHOR]

We consider the design of constant-modulus waveforms for wideband multiple-input multiple-output radar. The aim is to match a desired transmit beampattern. To tackle the non-convex design problem, we develop an iterative algorithm, which is based on cyclic optimization and majorization–minimization. We prove that the sequence of the objective values of the proposed algorithm has guaranteed convergence. Moreover, we can obtain closed-form solutions for the associated optimization problems at every iteration. Furthermore, the proposed method can be implemented without matrix inversion and hence is computationally efficient. Simulation results demonstrate that the performance of the proposed algorithm is better than existing methods. [ABSTRACT FROM AUTHOR]

This paper considers a multiple-input multiple-output (MIMO) secure simultaneous wireless information and power transfer (SWIPT) system aided by the intelligent reflecting surface (IRS), where the transmitter (T), the information receiver (IR) and energy receiver (ER) are all equipped with multiple antennas. Assuming that the ER may be potential eavesdropper (Eve), we aim to maximize the secrecy rate via jointly designing the precoding matrix, the artificial noise (AN) covariance, and the phase shift matrix, subject to the harvested energy and unit modulus reflect coefficient (RC) constraints. The formulated secrecy rate maximization (SRM) problem is non-convex with multiple coupled variables. To tackle it, an inexact block coordinate descent (IBCD) method is proposed, where the unit modulus constraint is handled by the penalty majorization-minimization (MM) and the complex circle manifold (CCM) methods. Finally, simulation results validate the effectiveness of IRS in enhancing the security.

The optimization of the secrecy rate of the distributed intelligent reflecting surfaces (IRSs)-assisted millimeter wave (mmWave) communication system is studied in this paper. In this system, the users are served by multiple IRSs, and by adjusting the switch state of each IRS and optimizing the phase shift of the IRS to maximize the secrecy rate of the system. The problem is described as a joint IRS control, transmit beamforming design problem. Our objective is to maximize the secrecy rate of the distributed IRSs-aided system under the transmit power constraint of the access point (AP). Since the problem is non-convex, one alternating optimization algorithm is proposed for solving this problem. We use the successive convex approximation (SCA) algorithm to solve it, and the solution that is obtained by the SCA algorithm guarantees to converge to a stable point that satisfies the Karush-Kuhn-Tucker (KKT) conditions. Moreover, by using the dual method, we obtain the IRS switch. For the IRS phase shifts optimization problem, a low-complexity majorization-minimization (MM) algorithm is used to solve this problem. Numerical results show that the proposed scheme can achieve higher secrecy rate compared with the single IRS-aided scheme.

This paper proposes a basis training algorithm for discriminative non-negative matrix factorization (NMF) with applications to single-channel audio source separation. With an NMF-based approach to supervised audio source separation, NMF is first applied to train the basis spectra of each source using training examples and then applied to the spectrogram of a mixture signal using the pretrained basis spectra at test time. The source signals can then be separated out using a Wiener filter. Here, a typical way to train the basis spectra is to minimize the dissimilarity measure between the observed spectrogram and the NMF model. However, obtaining the basis spectra in this way does not ensure that the separated signal will be optimal at test time due to the inconsistency between the objective functions for training and separation (Wiener filtering). To address this mismatch, a framework called discriminative NMF (DNMF) has recently been proposed. While this framework is noteworthy in that it uses a common objective function for training and separation, the objective function becomes more analytically complex than that of regular NMF. In the original DNMF work, a multiplicative update algorithm was proposed for the basis training; however, the convergence of the algorithm is not guaranteed and can be very slow. To overcome this weakness, this paper proposes a convergence-guaranteed algorithm for DNMF based on a majorization-minimization principle. Experimental results show that the proposed algorithm outperform the conventional DNMF algorithm as well as the regular NMF algorithm in terms of both the signal-to-distortion and signal-to-interference ratios.

Methods for electro- or magnetoencephalography (EEG/MEG) based brain source imaging (BSI) using sparse Bayesian learning (SBL) have been demonstrated to achieve excellent performance in situations with low numbers of distinct active sources, such as event-related designs. This paper extends the theory and practice of SBL in three important ways. First, we reformulate three existing SBL algorithms under the majorization-minimization (MM) framework. This unification perspective not only provides a useful theoretical framework for comparing different algorithms in terms of their convergence behavior, but also provides a principled recipe for constructing novel algorithms with specific properties by designing appropriate bounds of the Bayesian marginal likelihood function. Second, building on the MM principle, we propose a novel method called LowSNR-BSI that achieves favorable source reconstruction performance in low signal-to-noise-ratio (SNR) settings. Third, precise knowledge of the noise level is a crucial requirement for accurate source reconstruction. Here we present a novel principled technique to accurately learn the noise variance from the data either jointly within the source reconstruction procedure or using one of two proposed cross-validation strategies. Empirically, we could show that the monotonous convergence behavior predicted from MM theory is confirmed in numerical experiments. Using simulations, we further demonstrate the advantage of LowSNR-BSI over conventional SBL in low-SNR regimes, and the advantage of learned noise levels over estimates derived from baseline data. To demonstrate the usefulness of our novel approach, we show neurophysiologically plausible source reconstructions on averaged auditory evoked potential data.