Minorization-maximization Research Articles

A novel minorization–maximization framework for simultaneous feature selection and clustering of high-dimensional count data

A novel minorization–maximization framework for simultaneous feature selection and clustering of high-dimensional count data

Secrecy communications of intelligent reflecting surfaces aided NOMA networks

This paper investigates the physical layer security of an intelligent reflecting surface (IRS) aided non-orthogonal multiple access (NOMA) networks, where a remote user is regarded as an eavesdropper to intercept the information of nearby user. To evaluate the security performance of IRS-aided NOMA networks, a problem of maximizing achievable secrecy rate is formulated via jointly optimizing the beamforming and phase shifting. More specifically, we aim to tackle the non-convex problem by optimizing beamforming vector as well as phase shifting matrix with the assistance of block coordinate descent (BCD) and minorization maximization (MM) algorithms. Numerical results illustrate that: 1) The secrecy rates of IRS-aided NOMA with BCD and MM algorithms are superior to that of orthogonal multiple access schemes; 2) With increasing the number of reflecting elements, the secrecy rates of IRS-aided NOMA networks are achieved carefully; and 3) The IRS-aided NOMA networks are capable of relieving the transmission pressure of base station.

Rate Splitting Multiple Access for Multigroup Multicast Beamforming in Cache-Enabled C-RAN

This paper investigates rate splitting multiple access (RSMA) for multigroup multicast beamforming in a cache-enabled cloud radio access network (C <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^2$</tex-math></inline-formula> -RAN). To maximize the minimum weighted rate among all users and ensure the base station (BS) transmit power and backhaul capacity constraints, we jointly optimize the dynamic BS clustering, message splitting, and beamforming vectors. More specifically, users requesting the same content are collected to a multicast group and served by a cluster of BSs. Each BS has limited storage space and connects to the central processor (CP) via a backhaul link. However, the resulting optimization problem is discrete and nonconvex and has a non-smooth objective function. To alleviate these problems, we construct two surrogates to approximate the objective function locally. These surrogates are strictly lower bounds and concave. Also, we build an upper-bound convex surrogate function to handle the backhaul cost constraint and derive a minorization-maximization (MM)-based iterative algorithm. Besides, we adopt a quadratic transform method to recast the achievable rate and binary BS selection problems to a more tractable form to reduce time cost. We transform the resulting problem into a two-tier alternating optimization problem; the outer-tier problem is handled with closed-form expressions while the inner-tier one is solved by a convex framework. We thus develop a quadratic transform-based alternating (QTA) algorithm. Extensive simulation results confirm the superiority of our proposed transmit strategy and algorithms.

Optimal precoders and power splitting factors in multiuser multiple‐input multiple‐output cognitive decode‐and‐forward relay systems with wireless energy harvesting

SummaryThis paper considers an underlay cognitive radio (CR) wireless network with the assistance of a two‐hop decode‐and‐forward (DF) relay node. Different from the conventional CR relay networks, in this paper, the relay node using power‐splitting (PS) techniques harvests wireless energy transmitted from the secondary base station (SBS) and, then, uses its harvested energy to forward the received signals to multiple secondary receive users (SRUs). Due to the highly mutual dependence of the transmission strategies at nodes on the system performance, the optimal design of signal processing at transceivers to efficiently handle the interference and energy constraints is crucial. This paper studies the jointly optimal design of the precoders, PS factors to maximize the minimum user rate under the transmit power, harvested energy, and interference power constraints. Owing to the nonlinearly and mutually coupled design matrix variables in both objective function and constraints, the joint design of the precoders and PS factors for the concerned problem is mathematically challenging. To tackle these difficulties, we devise the appropriate surrogate functions to recast the nonconvex optimization problem into the convex one. By using the minorization–maximization framework, an efficient iterative algorithm with provable convergence is developed by solving the convex optimization problem in each iteration. Numerical results are provided to evaluate the achievable user rate performance of the considered system and investigate the effects of the interference power thresholds at the primary receive users and the number of antennas at the SBS and the relay on the minimum achievable user rate.

Design of High-Dimensional Grassmannian Frames via Block Minorization Maximization

In this letter, we present an iterative algorithm for constructing high-dimensional incoherent Grassmannian Frames (GFs) which are sets of unit-norm vectors that are minimax optimal: the maximum absolute value of their inner products is a minimum. We formulate the GF design as a nonconvex optimization problem and solve it via an efficient iterative algorithm. The bulk of each iteration of the proposed algorithm is a Linear Program (LP) for which there are a host of efficient solvers. The proposed algorithm is based on the theoretically sound Minorization Maximization technique which, unlike some of the state-of-the-art design approaches, monotonically minimizes the design criterion and can construct GFs with low coherence values.

Joint Active and Passive Beamforming Design for the IRS-Assisted MIMOME-OFDM Secure Communications

The effective combination of physical layer security communication and intelligent reflecting surface (IRS) technology has recently attracted extensive attention to improve the system security. Unlike existing works that mostly focus on single-carrier systems, we consider an IRS-assisted multi-carrier MIMO wireless physical layer security communication system, which consists of a legitimate transmitter, a legitimate receiver, an IRS node and an eavesdropper. With the aim of maximizing the sum secrecy rate, the multi-carrier transmit beamforming and IRS reflecting coefficient matrix are jointly optimized under the constraints on the transmit power budget and unit modulus of IRS reflecting coefficients. Since the formulated problem is non-convex, an alternate optimization (AO) algorithm is proposed to deal with it. Specifically, for the given IRS reflecting coefficient matrix, the minorization-maximization (MM) scheme is adopted to approximate the objective function of the subproblem and following that, the closed-form solution of the multi-carrier transmit beamforming is obtained through the Lagrange multiplier method. Then, for the given multi-carrier beamforming, the IRS reflecting coefficient matrix is also optimized through the MM scheme and a suboptimal closed-form solution that satisfies the KKT conditions is derived. Moreover, the discussion is extended to the discrete IRS phase shift case and a heuristic projection method (HPM) is then proposed. Finally, the simulation results validate the effectiveness of the proposed AO based algorithm.

Energy Efficiency Optimization for Multi-Cell Massive MIMO: Centralized and Distributed Power Allocation Algorithms

This paper investigates the energy efficiency (EE) optimization in downlink multi-cell massive multiple-input multiple-output (MIMO). In our research, the statistical channel state information (CSI) is exploited to reduce the signaling overhead. To maximize the minimum EE among the neighbouring cells, we design the transmit covariance matrices for each base station (BS). Specifically, optimization schemes for this max-min EE problem are developed, in the centralized and distributed ways, respectively. To obtain the transmit covariance matrices, we first find out the closed-form optimal transmit eigenmatrices for the BS in each cell, and convert the original transmit covariance matrices designing problem into a power allocation one. Then, to lower the computational complexity, we utilize an asymptotic approximation expression for the problem objective. Moreover, for the power allocation design, we adopt the minorization maximization method to address the non-convexity of the ergodic rate, and use Dinkelbach's transform to convert the max-min fractional problem into a series of convex optimization subproblems. To tackle the transformed subproblems, we propose a centralized iterative water-filling scheme. For reducing the backhaul burden, we further develop a distributed algorithm for the power allocation problem, which requires limited inter-cell information sharing. Finally, the performance of the proposed algorithms are demonstrated by extensive numerical results.

Model-based clustering for random hypergraphs

A probabilistic model for random hypergraphs is introduced to represent unary, binary and higher order interactions among objects in real-world problems. This model is an extension of the latent class analysis model that introduces two clustering structures for hyperedges and captures variation in the size of hyperedges. An expectation maximization algorithm with minorization maximization steps is developed to perform parameter estimation. Model selection using Bayesian Information Criterion is proposed. The model is applied to simulated data and two real-world data sets where interesting results are obtained.

Online mixture-based clustering for high dimensional count data using Neerchal–Morel distribution

In this paper, we propose an online learning technique for unsupervised clustering based on a mixture of Neerchal–Morel distributions (NMD). Online learning is able to overcome the drawbacks of batch learning in such a way that the mixture’s parameters can be updated instantly for any new data instances. Then, we use a novel Minorization–Maximization framework to address the issue of high dimensional optimization and the mixture’s parameters estimation. Finally, by implementing a minimum message length model selection criterion, the weights of irrelevant mixture components are driven towards zero, which resolves the problem of knowing the number of clusters beforehand. To evaluate the performance of our proposed model, we have considered 3 challenging real-world applications that involve high-dimensional count vectors, namely, topic clustering, medical diagnosis and human action recognition. The results show that the mixture model based on the NMD performs better than other similar models.

Heteroscedastic Laplace mixture of experts regression models and applications

Mixture of Experts (MoE) regression models are widely studied in statistics and machine learning for modeling heterogeneity in data for regression, clustering and classification. Laplace distribution is one of the most important statistical tools to analyze thick and tail data. Laplace Mixture of Linear Experts (LMoLE) regression models are based on the Laplace distribution which is more robust. Similar to modelling variance parameter in a homogeneous population, we propose and study a new novel class of models: heteroscedastic Laplace mixture of experts regression models to analyze the heteroscedastic data coming from a heterogeneous population in this paper. The issues of maximum likelihood estimation are addressed. In particular, Minorization-Maximization (MM) algorithm for estimating the regression parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo simulations. Results from the analysis of two real data sets are presented.

Multiuser Full-Duplex Two-Way Communications via Intelligent Reflecting Surface

Low-cost passive intelligent reflecting surfaces (IRSs) have recently been envisioned as a revolutionary technology capable of reconfiguring the wireless propagation environment through carefully tuning reflection elements. This paper proposes deploying an IRS to cover the dead zone of cellular multiuser full-duplex (FD) two-way communication links while suppressing user-side self-interference (SI) and co-channel interference (CI). Based on information exchanged by the base station (BS) and all users, this approach can potentially double the spectral efficiency. To ensure network fairness, we jointly optimize the precoding matrix of the BS and the reflection coefficients of the IRS to maximize the weighted minimum rate (WMR) of all users, subject to maximum transmit power and unit-modulus constraints. We reformulate this non-convex problem and decouple it into two subproblems. Then the optimization variables in the equivalent problem are alternately optimized by adopting the block coordinate descent (BCD) algorithm. In order to further reduce the computational complexity, we propose the minorization-maximization (MM) algorithm for optimizing the precoding matrix and the reflection coefficient vector by defining minorizing functions in the surrogate problems. Finally, simulation results confirm the convergence and efficiency of our proposed algorithm, and validate the advantages of introducing IRS to improve coverage in blind areas.

Mixture‐based clustering for count data using approximated Fisher Scoring and Minorization–Maximization approaches

AbstractThe multinomial distribution has been widely used to model count data. To increase clustering efficiency, we use an approximation to the Fisher scoring algorithm, which is more robust regarding the choice of initial parameter values. Then, we use a novel approach to estimate the optimal number of components, based on minimum message length criterion. Moreover, we consider a generalization of the multinomial model obtained by introducing the Dirichlet as prior, yielding the Dirichlet Compound Multinomial (DCM). Even though DCM can address the burstiness phenomenon of count data, the presence of Gamma function in its density function usually leads to undesired complications. In this article, we use two alternative representations of DCM distribution to perform clustering based on finite mixture models, where the mixture parameters are estimated using the minorization–maximization framework. To evaluate and compare the performance of our proposed models, we have considered three challenging real‐world applications that involve high‐dimensional count vectors, namely, sentiment analysis, facial expression recognition, and human action recognition. The results show that the proposed algorithms increase the clustering efficiency of their respective models remarkably, and the best results are achieved by the second parametrization of DCM, which can accommodate over‐dispersed count data.

The Adjustment of Covariates in Cox’s Model under Case-Cohort Design

Case-cohort design is a biased sampling method. Due to its cost-effective and theoretical significance, this design has extensive application value in many large cohort studies. The case-cohort data includes a subcohort sampled randomly from the entire cohort and all the failed subjects outside the subcohort. In this paper, the adjustment for the distorted covariates is considered to case-cohort data in Cox’s model. According to the existing adjustable methods of distorted covariates for linear and nonlinear models, we propose estimating the distorting functions by nonparametrically regressing the distorted covariates on the distorting factors; then, the estimators for the parameters are obtained using the estimated covariates. The proof of consistency and being asymptotically normal is completed. For calculating the maximum likelihood estimates of the regression coefficients subject in Cox’s model, a minorization-maximization (MM) algorithm is developed. Simulation studies are performed to compare the estimations with the covariates undistorted, distorted, and adjusted to illustrate the proposed methods.

Beamforming Optimization for IRS-Aided Communications With Transceiver Hardware Impairments

In this paper, we focus on intelligent reflecting surface (IRS) assisted multi-antenna communications with transceiver hardware impairments encountered in practice. In particular, we aim to maximize the received signal-to-noise ratio (SNR) taking into account the impact of hardware impairments, where the source transmit beamforming and the IRS reflect beamforming are jointly designed under the proposed optimization framework. To circumvent the non-convexity of the formulated design problem, we first derive a closed-form optimal solution to the source transmit beamforming. Then, for the optimization of IRS reflect beamforming, we obtain an upper bound to the optimal objective value via solving a single convex problem. A low-complexity minorization-maximization (MM) algorithm was developed to approach the upper bound. Simulation results demonstrate that the proposed beamforming design is more robust to the hardware impairments than that of the conventional SNR maximized scheme. Moreover, compared to the scenario without deploying an IRS, the performance gain brought by incorporating the hardware impairments is more evident for the IRS-aided communications.

Demand Estimation Under the Multinomial Logit Model from Sales Transaction Data

Problem definition: A major task in retail operations is to optimize the assortments exhibited to consumers. To this end, retailers need to understand customers’ preferences for different products. Academic/practical relevance: This is particularly challenging when only sales and product-availability data are recorded, and not all products are displayed in all periods. Similarly, in revenue management contexts, firms (airlines, hotels, etc.) need to understand customers’ preferences for different options in order to optimize the menu of products to offer. Methodology: In this paper, we study the estimation of preferences under a multinomial logit model of demand when customers arrive over time in accordance with a nonhomogeneous Poisson process. This model has recently caught important attention in both academic and industrial practices. We formulate the problem as a maximum-likelihood estimation problem, which turns out to be nonconvex. Results: Our contribution is twofold: From a theoretical perspective, we characterize conditions under which the maximum-likelihood estimates are unique and the model is identifiable. From a practical perspective, we propose a minorization-maximization (MM) algorithm to ease the optimization of the likelihood function. Through an extensive numerical study, we show that our algorithm leads to better estimates in a noticeably short computational time compared with state-of-the-art benchmarks. Managerial implications: The theoretical results provide a solid foundation for the use of the model in terms of the quality of the derived estimates. At the same time, the fast MM algorithm allows the implementation of the model and the estimation procedure at large scale, compatible with real industrial applications.

Fast QLB algorithm and hypothesis tests in logistic model for ophthalmologic bilateral correlated data

ABSTRACT In ophthalmologic or otolaryngologic studies, bilateral correlated data often arise when observations involving paired organs (e.g., eyes, ears) are measured from each subject. Based on Donner's model , in this paper, we focus on investigating the relationship between the disease probability and covariates (such as ages, weights, gender, and so on) via the logistic regression for the analysis of bilateral correlated data. We first propose a new minorization–maximization (MM) algorithm and a fast quadratic lower bound (QLB) algorithm to calculate the maximum likelihood estimates of the vector of regression coefficients, and then develop three large-sample tests (i.e., the likelihood ratio test, Wald test, and score test) to test if covariates have a significant impact on the disease probability. Simulation studies are conducted to evaluate the performance of the proposed fast QLB algorithm and three testing methods. A real ophthalmologic data set in Iran is used to illustrate the proposed methods.

Fast secrecy rate optimization for MIMO wiretap channels in the presence of a multiple-antenna eavesdropper

We consider the secrecy rate maximization for multiple-input-multiple-output (MIMO) wiretap channels in the presence of a multiple-antenna eavesdropper. We propose an efficient algorithm based on minorization-maximization (MM) technique. The proposed algorithm constructs a simple surrogate function and has a closed-form solution at each iteration. In addition, we prove that the proposed algorithm has guaranteed convergence of the sequence of objective values. Moreover, an acceleration scheme, called squared iterative method (SQUAREM), is used to enhance the convergence rate of the proposed algorithm. Then, we extend the proposed algorithm to handle the transmission power minimization problem. Results show that the proposed algorithm have the same secrecy rate performance as the state-of-art algorithm but is much more computationally efficient.

Enhancing Secure MIMO Transmission via Intelligent Reflecting Surface

In this article, we consider an intelligent reflecting surface (IRS) assisted Guassian multiple-input multiple-output (MIMO) wiretap channel (WTC), and focus on enhancing its secrecy rate. Due to MIMO setting, all the existing solutions for enhancing the secrecy rate over multiple-input single-output WTC completely fall to this work. Furthermore, all the existing studies are simply based on an ideal assumption that full channel state information (CSI) of eavesdropper (Ev) is available. Therefore, we propose numerical solutions to enhance the secrecy rate of this channel under both full and no Ev's CSI cases. For the full CSI case, we propose a barrier method and one-by-one (OBO) optimization combined alternating optimization (AO) algorithm to jointly optimize the transmit covariance R at transmitter (Tx) and phase shift coefficient Q at IRS. For the case of no Ev's CSI, we develop an artificial noise (AN) aided joint transmission scheme to enhance the secrecy rate. In this scheme, a bisection search (BS) and OBO optimization combined AO algorithm is proposed to jointly optimize R and Q. Such scheme is also applied to enhance the secrecy rate under a special scenario in which the direct link between Tx and receiver (Rx)/Ev is blocked due to obstacles. In particular, we propose a BS and minorization-maximization (MM) combined AO algorithm with slightly faster convergence to optimize R and Q for this scenario. Simulation results have validated the monotonic convergence of the proposed algorithms, and it is shown that the proposed algorithms for the IRS-assisted design achieve significantly larger secrecy rate than the other benchmark schemes under full CSI. When Ev's CSI is unknown, the secrecy performance of this channel also can be enhanced by the proposed AN aided scheme, and there is a trade-off between increasing the quality of service at Rx and enhancing the secrecy rate.

Array resource allocation for radar and communication integration network

A radar and communication integration (RCI) system has great flexibility in allocating antenna resources to guarantee both radar and communication performance. This paper considers the array allocation problems for multiple target localization and multiple platforms communication in an RCI network. The objective of array allocation is to maximize the communication capacity for each channel and to minimize the localization error for each target. In this paper, we firstly build a localization and communication model for array allocation in an RCI network. Minorization maximization (MM) is then applied to create surrogate functions for multiple objective optimization problems. The projected gradient descent (PGD) method is further employed to solve two array allocation problems with and without a certain communication capacity constraint. Computer simulations are conducted to evaluate the performance of the proposed algorithms. The results show that the proposed algorithms have improved localization and communication performance after efficiently allocating the array resource in the RCI network.

Fast Adaptive Minorization-Maximization Procedure for Beamforming Design of Downlink NOMA Systems

We develop a novel technique to accelerate minorization-maximization (MM) procedure for the non-orthogonal multiple access (NOMA) weighted sum rate maximization problem. Specifically, we exploit the Lipschitz continuity of the gradient of the objective function to adaptively update the MM algorithm. With fewer additional analysis variables and low complexity second-order cone program (SOCP) to solve in each iteration of the MM algorithm, the proposed approach converges quickly at a small computational cost. By numerical simulation results, our algorithm is shown to greatly outperform known solutions in terms of achieved sum rates and computational complexity.