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In this letter, we revisit the recently proposed cell outlier-resistant method cellMCD (minimum covariance determinant) and derive a version of it called cellMCD+ that has better performance. We illustrate the performance gain of cellMCD+ via numerical simulations in the case of estimating low-rank structured covariance matrices.

This paper investigates the transmit beamforming design for multiple-input multiple-output systems to support both multi-target localization and multi-user communications. To enhance the target localization performance, we derive the asymptotic Cramér-Rao bound (CRB) for target angle estimation by assuming that the receive array is linear and uniform. Then we formulate a beamforming design problem based on minimizing an upper bound on the asymptotic CRB (which is shown to be equivalent to maximizing the harmonic mean of the weighted beampattern responses at the target directions). Moreover, we impose a constraint on the SINR of each received communication signal to guarantee reliable communication performance. Two iterative algorithms are derived to tackle the non-convex design problem: one is based on the alternating direction method of multipliers, and the other uses the majorization-minimization technique to solve an equivalent minimax problem. Numerical results show that, through elaborate dual-function beamforming matrix design, the proposed algorithms can simultaneously achieve superior angle estimation performance as well as high-quality multi-user communications.

In this letter we present a framework for estimating sparse covariance matrices, wherein we solve the l(0)-norm penalized maximum likelihood estimation problem using the extended Bayesian information criterion (EBIC), a high dimensional model selection rule. The framework combines choosing the sparsity pattern and estimating the covariance matrix in a single step, eliminating the need for any hyper-parameter tuning. Using the framework we propose a cyclic majorization-minimization based technique and apply it to synthetic data to evaluate its performance in terms of normalized root mean square error (NRMSE) and Kullback Leibler (KL) divergence.

Multistatic localization techniques employ noisy range measurements collected via multiple transmitters and receivers to localize a target. However, in many realistic scenarios the data are corrupted by outliers which may be due to the failure of or malicious attack on one or more sensors. The presence of outliers leads to performance degradation in terms of target localization accuracy. In this letter, we address the problem of multistatic target localization when the measurements contain outliers. We employ a multi-hypothesis testing method based on the false discovery rate (FDR) to detect the outliers. More specifically, we consider a penalized maximum likelihood problem for joint estimation of the number and positions of the outliers as well as the target position, and the noise variance. To solve this problem, an iterative algorithm employing the majorization-minimization technique that minimizes the objective in a monotonic manner is developed. Through numerical simulations, we compare the proposed algorithm with other robust state-of-the-art algorithms and show that the proposed algorithm has superior performance.

Graph learning is an important problem in the field of graph signal processing. However, the data available in real-world applications are often contaminated with outliers, which makes the application of traditional methods challenging. In this paper, we address this problem by developing an algorithm that effectively learns the graph Laplacian matrix from node signals corrupted by outliers. Specifically, we maximize the penalized log-likelihood of the uncorrupted data, where the penalty is chosen via the false discovery rate (FDR) principle, with respect to both the number of outliers and their locations, as well as the precision matrix of the data under the graph Laplacian constraints. To illustrate the robustness to outliers, we compare our method with two state-of-the-art graph learning methods, one that considers outliers in the data and one that does not, using different performance metrics. Our findings demonstrate that the proposed method efficiently detects the number and positions of outliers and accurately learns the graph in their presence.

Designing optimal measurement operators for quantum state discrimination (QSD) is an important problem in quantum communications and cryptography applications. Prior works have demonstrated that optimal quantum measurement operators can be obtained by solving a convex semidefinite program (SDP). However, solving the SDP can represent a high computational burden for many real-time quantum communication systems. To address this issue, a majorisation-minimisation (MM)-based algorithm, called Quantum Majorisation-Minimisation (QMM) is proposed for solving the QSD problem. In QMM, the authors reparametrise the original objective, then tightly upper-bound it at any given iterate, and obtain the next iterate as a closed-form solution to the upper-bound minimisation problem. Our numerical simulations demonstrate that the proposed QMM algorithm significantly outperforms the state-of-the-art SDP algorithm in terms of speed, while maintaining comparable performance for solving QSD problems in quantum communication applications. A computationally efficient majorisation-minimisation (MM)-based algorithm is proposed for solving the optimal quantum state discrimination (QSD) problem in quantum communications applications.

This monograph presents a theoretical background and a broad introduction to the M in-Max Framework for M ajori- zation-Minimization (MM4MM), an algorithmic methodology for solving minimization problems by formulating them as min-max problems and then employing majorizationminimization. The monograph lays out the mathematical basis of the approach used to reformulate a minimization problem as a min-max problem. With the prerequisites covered, including multiple illustrations of the formulations for convex and non-convex functions, this work serves as a guide for developing MM4MM-based algorithms for solving non-convex optimization problems in various areas of signal processing. As special cases, we discuss using the majorization-minimization technique to solve min-max problems encountered in signal processing applications and min- max problems formulated using the Lagrangian. Lastly, we present detailed examples of using MM4MM in ten signal processing applications such as phase retrieval, source localization, independent vector analysis, beamforming and optimal sensor placement in wireless sensor networks. The devised MM4MM algorithms are free of hyper-parameters and enjoy the advantages inherited from the use of the majorization-minimization technique such as monotonicity.

In this paper, we propose a numerical method for the optimal placement of the receivers in a multistatic target localization system (with a single transmitter and multiple receivers) in order to improve the achievable target estimation accuracy of time-sum-of-arrival (TSOA) localization techniques, for 2D and 3D scenarios. The proposed algorithm is based on the principle of block majorization minimization (block MM) which is a combination of block coordinate descent and majorization-minimization (MM) methods. More precisely, we formulate the design objective for the placement of sensors performing TSOA measurements using A− and D− optimality criteria, and propose an iterative algorithm to find the optimal solution by first splitting the design variable into M blocks (where M is the number of receivers) and then applying the principle of MM on each block. The proposed method can additionally handle the cases where the transmitter also acts as a receiver. The framework can also be applied to the case of non-uniform noise variances at the receivers. Several numerical simulation results are included to show the benefits offered by the developed design algorithm.

The Pearson-Matthews correlation coefficient (usually abbreviated MCC) is considered to be one of the most useful metrics for the performance of a binary classification. For multinary classification tasks (with more than two classes) the existing extension of MCC, commonly called the R K metric, has also been successfully used in many applications. The present paper begins with an introductory discussion on certain aspects of MCC. Then we go on to discuss the topic of multinary classification that is the main focus of this paper and which, despite its practical and theoretical importance, appears to be less developed than the topic of binary classification. Our discussion of the R K is followed by the introduction of two other metrics for multinary classification derived from the multivariate Pearson correlation (MPC) coefficients. We show that both R K and the MPC metrics suffer from the problem of not decisively indicating poor classification results when they should, and introduce three new enhanced metrics that do not suffer from this problem. We also present an additional new metric for multinary classification which can be viewed as a direct extension of MCC.

In a recent paper we have proposed an approach for estimating the covariance matrix from a multivariate data set {y(t)} that may contain outliers. If y(t) is flagged as outlying by this approach, then the entire vector y(t) is considered to contain no useful information and it is discarded. However, in some applications the data contains cell outliers, that is to say, not all elements of y(t) are outlying but only some of them. One then wants to eliminate only the cell outliers from the data, rather than the entire vector y(t) . In this paper, we propose a penalized maximum likelihood approach to outlier detection and covariance matrix estimation from data with cell outliers. Specifically we estimate the positions of the outliers in the data set, for a given estimate of the covariance matrix, by maximizing the penalized likelihood of the data with the penalty being derived from a property of the likelihood ratio and the false discovery rate (FDR) principle. We alternate this step with a majorization-minimization (MM) technique that estimates the covariance matrix for given outlier positions. The MM is more flexible than the expectation maximization (EM) algorithm commonly used for estimating the covariance matrix from data with missing cells, as the former can be utilized in cases in which the latter is not usable. The closest competitor of our approach is the cellMCD (minimum covariance determinant) method, compared with which the proposed approach has a number of advantages described in the introduction and the numerical study section.