Alternative Minimization Research Articles

A novel linear discriminant analysis based on alternate ratio sum minimization

Linear discriminant analysis (LDA) and its variants are popular supervised dimension reduction methods, which have been widely used to handle high-dimensional data. Since most of previous LDA methods are developed based on the trace ratio (TR) criterion, they usually obtain the low-dimensional data feature with weak discriminative ability, due to the projections with small variance. The ratio sum (RS) criterion was developed to alleviate this drawback. However, the conventional ratio sum is formulated to maximize the arithmetic mean of items which suffers from the domination of the largest objectives and might deteriorate the recognition accuracy in practical applications. In this paper, a novel ratio sum minimization based linear discriminant analysis (RSM-LDA) method is proposed in this paper. Specifically, a new ratio sum minimization (RSM) criterion is developed, which is based on the properties of the harmonic mean and effectively avoids the dominance problem to discover more discriminative features of the data. However, obtaining a closed solution for the RSM-LDA problem is challenging. For this purpose, three optimization methods are used to solve the optimization problem of RSM-LDA, and the inherent relationships between the methods are discussed. Experimental results demonstrate that the proposed RSM-LDA method has better performance in classification tasks on several datasets, when compared with some comparison methods based dimensionality reduction methods. In addition, combined with other experimental results, the effectiveness of RSM-LDA was verified.

Numerical implementation and comparison study on simulating thermo-elastic fracture using adaptive phase-field method combined with BFGS algorithm and AM algorithm

In this paper, the computational performance of alternate minimization (AM) and Broyden–Fletcher–Goldfarb–Shanno (BFGS) to solve the coupled partial differential equations arising within the framework of the phase field method is numerically studied. Both the numerical approaches are employed on an adaptive phase field method. In the case of BFGS, a double-loop recursive algorithm in combination with a line search is implemented. The local refinement is based on a pre-defined threshold on the damage variable and element size. The incompatible nodes due to adaptive refinement are handled by variable-node elements. The performance of the solution algorithm is numerically studied for a few problems with different loading conditions, viz., pure mechanical, pure thermal and combined thermo-mechanical. From the study, it is opined that the BFGS algorithm is 2∼5 times faster than the AM approach, which is typically used for adaptive phase field framework. In addition, the detailed numerical implementation is presented.

A Calibration Scheme for a 800-Ms/s 14 Bit Pipelined ADC in 28-nm CMOS

Abstract A calibration scheme is proposed to compensate linear and nonlinear errors including offset, cap mismatch, second- and higher-order harmonics and memory induced errors in pipelined analog-to-digital converters (ADCs). The alternating minimization (AM) algorithm is proposed to accurately estimate the coefficients of the errors. As an accurate input value is hardly acquired in practical measurements, instead, the proposed scheme estimates the input and the error coefficients jointly. Once the error coefficient was calculated, it will be recorded in a lookup table (LUT). The scheme has been demonstrated in a 800-Ms/s 14-bit pipelined ADC fabricated in a 28nm CMOS process, which features a signal-to-noise ratio (SNR) and spurious-free dynamic range (SFDR) improvement of 2.49 dB and 11.49 dB at 800-Ms/s.

Fuzzy clustering with capacity constraints: Algorithm, convergence analysis and numerical experiments

In this paper we study the fuzzy clustering problem with capacity constraints. Despite of the fact that the fuzzy clustering approach is widely encountered in the literature, the inclusion of capacity constraints is recent and has several practical applications. We propose a general formulation of the clustering problem, where each point has an associated weight and the sum of the weights of the points that compose each group is established a priori. We discuss existence of solutions of the involved problems, providing a mathematical foundation for the established formulas. Besides, we propose a practical algorithm for solving this problem and present its convergence analysis. This algorithm follows an alternate minimization scheme, wherein a given iteration addresses the problem first in terms of the probabilities of each point xj belonging to each cluster i, denoted as uij, finding subsequently the position of the centroids, ci,i=1,…,g,j=1,…,n. This procedure is K-means-like, with the distinction that, as a point does not exclusively belong to a group, the computation of uij requires optimization techniques. In our case, this involves solving a linear system derived from the Karush–Kuhn–Tucker (KKT) conditions. With the aim of validating our algorithm, we present numerical tests with synthetic and real-world data to demonstrate its performance for the given problems. Since the proposal successfully solved these numerical tests within a reasonable computational time, it can be considered a valuable resource for addressing real-world applications.

Fourier Domain Robust Denoising Decomposition and Adaptive Patch MRI Reconstruction.

The sparsity of the Fourier transform domain has been applied to magnetic resonance imaging (MRI) reconstruction in k -space. Although unsupervised adaptive patch optimization methods have shown promise compared to data-driven-based supervised methods, the following challenges exist in MRI reconstruction: 1) in previous k -space MRI reconstruction tasks, MRI with noise interference in the acquisition process is rarely considered. 2) Differences in transform domains should be resolved to achieve the high-quality reconstruction of low undersampled MRI data. 3) Robust patch dictionary learning problems are usually nonconvex and NP-hard, and alternate minimization methods are often computationally expensive. In this article, we propose a method for Fourier domain robust denoising decomposition and adaptive patch MRI reconstruction (DDAPR). DDAPR is a two-step optimization method for MRI reconstruction in the presence of noise and low undersampled data. It includes the low-rank and sparse denoising reconstruction model (LSDRM) and the robust dictionary learning reconstruction model (RDLRM). In the first step, we propose LSDRM for different domains. For the optimization solution, the proximal gradient method is used to optimize LSDRM by singular value decomposition and soft threshold algorithms. In the second step, we propose RDLRM, which is an effective adaptive patch method by introducing a low-rank and sparse penalty adaptive patch dictionary and using a sparse rank-one matrix to approximate the undersampled data. Then, the block coordinate descent (BCD) method is used to optimize the variables. The BCD optimization process involves valid closed-form solutions. Extensive numerical experiments show that the proposed method has a better performance than previous methods in image reconstruction based on compressed sensing or deep learning.

Multispectral and hyperspectral images fusion based on subspace representation and nonlocal low-rank regularization

ABSTRACT Multispectral image (MSI) and hyperspectral image (HSI) fusion is a popular method for HSI super-resolution reconstruction (HSI-SR). MSI-HSI fusion problem is ill-posed and demands several image priors or regularization terms to solve accurately, which is a challenging issue. In this paper, we propose an MSI-HSI fusion model via subspace representation and nonlocal low-rank regularization (SRNLRR). SRNLRR model incorporates the global spectral correlations and spatial nonlocal similarities of HSI to improve the fusion results, where the priors complement each other. First, we use the mode-n tensor-matrix product to project latent high spatial resolution HSI (HR-HSI) into spectral subspace, which can capture spectral low-rankness and reduce computational complexity. Then, based on low-rank representation (LRR) and nonlocal processing strategy, we design a spatial nonlocal LRR regularization (spa-NLRR) and a spectral global LRR regularization (spe-GLRR). These two regularizations analyze the spatial nonlocal similarities and spectral global correlations from intermediate-level vision. Finally, we use the residual regularization program to obtain more image information and input it into the fusion model. We use alternate minimization (AM) methods to optimize the SRNLRR model and employ the alternating direction method (ADM) on spatial/spectral LRR learning. Comparison experiments between the SRNLRR method and six advanced methods on three HSI datasets indicate the superiority of our method.

One‐bit DOA estimation in non‐uniform noise with alternating minimization method

AbstractThis letter presents a method to optimize the estimation of direction of arrival (DOA) using the uniform linear array (ULA) with one‐bit signals in the presence of non‐uniform noise. With the Toeplitz properties and the rank characteristics of the signal subspace matrix formed by the ULA, the alternating minimization (AM) method is employed to optimize the estimation problem. To address this challenge further, we utilize the singular value thresholding (SVT) method and the approximate projection method. The angle deviations caused by non‐uniform noise can be effectively corrected and a significant improvement in the estimation performance can be achieved. The feasibility and effectiveness of the proposed method are demonstrated through simulation results.

On the Convergence of Inexact Alternate Minimization in Problems with $$\ell _0$$ Penalties

On the Convergence of Inexact Alternate Minimization in Problems with $$\ell _0$$ Penalties

Simulation of dynamic pulsing fracking in poroelastic media by a hydro-damage-mechanical coupled cohesive phase field model

This study develops a hydro-damage-mechanical fully coupled numerical method capable of modelling complex fluid-driven transient dynamic crack propagation in quasi-brittle poroelastic media. In this method, the fluid flow in both fractures and porous media is described by a fluid continuity equation with the modified Darcy-Poiseuille law based on the Biot's poroelastic theory. The fluid pressure and the inertial force of solids are coupled by governing equations of the mesh-insensitive phase-field regularized cohesive zone model that can simulate quasi-brittle multi-crack initiation, propagation, branching and merging without remeshing or crack tracking. The resultant displacement-pressure-damage coupled multiphysics system of equations is solved using an alternative minimization Newton-Raphson iterative algorithm with an implicit Newmark integration scheme within the finite element framework. The new method was first validated by a few 2D problems, including crack branching and deflecting in solids, fracking in a concrete cube, and consolidation and stress wave propagation in poroelastic media, subjected to various impulsive loadings. It was then applied to pressure pulsing fracking of a 40 m granite rock reservoir with extensive parametric studies of fluid viscosity and pulsing injection rate, mode and period. It was found that pulsing injection with higher fluid rates and lower fluid viscosities resulted in more developed crack patterns, and in particular, there existed an optimal pulsing injection period that could promote fracking under relatively low injection pressures. 3D horizontal well problems with multiple non-planar crack propagation and bifurcation were also successfully simulated to demonstrate the capacity and potential of the new method for engineering design and optimization of pressure pulsing fracking.

Structural knowledge-driven meta-learning for task offloading in vehicular networks with integrated communications, sensing and computing

Task offloading is a potential solution to satisfy the strict requirements of computation-intensive and latency-sensitive vehicular applications due to the limited onboard computing resources. However, the overwhelming upload traffic may lead to unacceptable uploading time. To tackle this issue, for tasks taking environmental data as input, the data perceived by roadside units (RSU) equipped with several sensors can be directly exploited for computation, resulting in a novel task offloading paradigm with integrated communications, sensing and computing (I-CSC). With this paradigm, vehicles can select to upload their sensed data to RSUs or transmit computing instructions to RSUs during the offloading. By optimizing the computation mode and network resources, in this paper, we investigate an I-CSC-based task offloading problem to reduce the cost caused by resource consumption while guaranteeing the latency of each task. Although this non-convex problem can be handled by the alternating minimization (AM) algorithm that alternatively minimizes the divided four sub-problems, it leads to high computational complexity and local optimal solution. To tackle this challenge, we propose a creative structural knowledge-driven meta-learning (SKDML) method, involving both the model-based AM algorithm and neural networks. Specifically, borrowing the iterative structure of the AM algorithm, also referred to as structural knowledge, the proposed SKDML adopts long short-term memory (LSTM) network-based meta-learning to learn an adaptive optimizer for updating variables in each sub-problem, instead of the handcrafted counterpart in the AM algorithm. Furthermore, to pull out the solution from the local optimum, our proposed SKDML updates parameters in LSTM with the global loss function. Simulation results demonstrate that our method outperforms both the AM algorithm and the meta-learning without structural knowledge in terms of both the online processing time and the network performance.

A phase‐field formulation based on an extended F‐criterion for rock fracture

AbstractIn this paper a phase‐field formulation based on an extended F‐criterion (the normalized strain energy release rate criterion) is proposed to simulate tensile‐compressive‐shear rock fractures. By applying the F‐criterion, the phase‐field crack‐driving energy decomposition is determined by a direction search which maximizes the local fracture dissipation. In compressive‐shear states, the computation is supplemented by an explicitly expressed confinement‐dependent mode‐II fracture energy release rate, and the cracking angle is determined by both the fracture energy and strain states. The hybrid formulation and alternate minimization algorithm are adopted for the numerical examples in this paper. Fractures for rock and rock‐like specimens subjected to compression demonstrate the ability of the present model in capturing tensile‐compressive‐shear rock fracture behaviors.

Metalearning-Based Alternating Minimization Algorithm for Nonconvex Optimization.

In this article, we propose a novel solution for nonconvex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of subproblems corresponding to each variable and then iteratively optimizes each subproblem using a fixed updating rule. However, due to the intrinsic nonconvexity of the original optimization problem, the optimization can be trapped into a spurious local minimum even when each subproblem can be optimally solved at each iteration. Meanwhile, learning-based approaches, such as deep unfolding algorithms, have gained popularity for nonconvex optimization; however, they are highly limited by the availability of labeled data and insufficient explainability. To tackle these issues, we propose a meta-learning based alternating minimization (MLAM) method that aims to minimize a part of the global losses over iterations instead of carrying minimization on each subproblem, and it tends to learn an adaptive strategy to replace the handcrafted counterpart resulting in advance on superior performance. The proposed MLAM maintains the original algorithmic principle, providing certain interpretability. We evaluate the proposed method on two representative problems, namely, bilinear inverse problem: matrix completion and nonlinear problem: Gaussian mixture models. The experimental results validate the proposed approach outperforms AM-based methods.

Iterative Variational Bayesian Inference Based Channel Estimation for TWR mmWave Systems

Millimeter wave (mmWave) with two way relaying (TWR) is an emerging paradigm towards cellular fifth/sixth generation (5G/6G) technology that can support various data hungry applications with improve coverage, network throughput, and reliability. The foreseen potential of mmWave TWR system can be further alleviated by using large-scale multiple input multiple output (MIMO) architecture. However, high power consumption, hardware complexity and cost of fully digital large-scale MIMO architecture restricts its application. As a countermeasure, hybrid precoding structures with reduced RF chains are utilized. Therefore, the amalgamation of TWR MIMO mmWave system with hybrid precoding structure demands an accurate channel state information (CSI) to avail the maximum gain of two way MIMO communications. Furthermore, the inherent self-interference in TWR systems in collusion with sparse mmWave channels imposes severe challenges in acquiring accurate CSI. The challenge is further aggravated in case of frequency-selective mmWave channel. To solve this problem, we propose a novel iterative variational Bayesian inference (IVBI)-based channel estimation (CE) scheme in the time domain for TWR system with reduced RF chain. In the proposed method, we follow the alternative minimization method involving variational Bayesian inference (VBI) to estimate all the channels of mmWave TWR system. The performance of the proposed algorithm are evaluated over both flat fading and frequency-selective channel. Extensive simulation results for symmetric and non-symmetric MIMO structure validate the proposed algorithm. The Bayesian Cramer-Rao bound (BCRB) of the proposed estimator is also derived. This novel scheme converges fast and achieves significant improvement in terms of normalized mean square error (NMSE) and bit error rate (BER) as compared to state-of-art.

Joint Detection and State Estimate with GSAs in PMU-Based Smart Grids

The Phasor Measurement Unit (PMU) with a GPS signal receiver is a synchronized sensor widely used for power system state estimation. While the GPS receiver ensures time accuracy, it is vulnerable to network attacks. GPS spoofing attacks can alter the phase angle of PMU measurement signals and manipulate system states. This paper derives a power system state model based on PMUs under GPS spoofing attacks, according to the characteristics of changes in bus voltages and branch currents after GSA. Based on the characteristics of this model, a detection and correction algorithm for attacked data is proposed to detect GSA and correct attacked measurements. The corrected measurements can be used for power system state estimation. Simulation results on the IEEE 14-bus system show that the proposed algorithm improves the accuracy of state estimation under one or multiple GSAs, especially when multiple GSAs are present, compared to classical Weighted Least Squares Estimation (WLSE) and Alternating Minimization (AM) algorithms. Further research indicates that this algorithm is also applicable to large-scale networks.

Variational approach and experimental investigation of the phase-field model predicting brittle fracture

Cracks are described as sharp and diffusive surfaces in failure mechanical models. In this paper, a finite element model is developed by using a diffusive description of crack discontinuities. The main objective of this study is to prove the accuracy of the phase-field model in which the alternate minimization iteration and the spectral decomposition formulation are considered. We conduct a set of benchmark numerical tests on notched specimens using the phase-field model, which allows the prediction of the quasi-brittle failure. The fracture surface is approximated by a diffusive field, which interpolates between undamaged and fully damaged states. A mechanical loading was applied on quenched C90 steel and different obtained crack patterns are discussed. Microstructural analyses are performed to prove the accuracy of the proposed numerical approach. Through the determination of microstructural properties of untreated and quenched C90 steel, it is concluded that the presence of the micro-cracks may have a great influence on the crack path evolution.

Performance analysis of alternating minimization based low complexity detection for MIMO communication system

Several antennas are used for sending and receiving in large MIMO (Multiple-Input-Multiple-Output) devices and assist in enhanced performances of wireless communication systems. One important component of Large MIMO systems is that MIMO detectors are placed at receiver ends, whose functions are to regain symbols broadcasts from multiple antennas. In this paper, novelAMLCD (Alternating Minimizationbased Low Complexity Detections) method is proposed in which AMs (Alternating Minimizations) are applied in initial stages to detect signals. Soft value generation is used for the second stage to estimate the signals. Finally, the more optimal estimated signal value will be chosen by applying the MPSOs (Modified Particle Swarm Optimizations). The system's functions are evaluated using CPMs (Continuous Phase Modulations) and channel’s AWGNs (Additive White Gaussian Noises). According to the results obtained, the suggested AMLCD method with modulations of CPMs outperform known methods using QAMs (Quadrature Amplitude Modulations) under multiple antennas in terms of BERs (Bit Error Rates). The AMLCD method also reduces the time complexity and computational complexity compared to the existing methods.

Inverse Halftoning Based on Weighted Nuclear Norm Minimization

The inverse halftoning technology refers to restoring a continuous-toned image from a halftoned image with only bi-level pixels. However, recovering the continuous images from their halftoned ones is normally ill-posed, which makes the inverse halftoning algorithm very challenging. In this paper, we propose an optimization model with two alternate projections (TAP) for image inverse halftoning under the weighted nuclear norm minimization (WNNM) framework. The main contributions are twofold. First, the WNNM nonlocal regularization term is established, which offers a powerful mechanism of nonlocal self-similarity to ensure a more reliable estimation. Second, the alternate minimization projections are formulated for solving the image inverse halftoning, which reconstructs the continuous-toned image without destroying the image details and structures. The experimental results showed that the proposed method outperformed the state of the arts in terms of both objective measurements and subjective visual performance. The codes and constructed models are available at: https://github.com/juneryoung2022/IH-WNNM.

Hippocampus Parcellation via Discriminative Embedded Clustering of fMRI Functional Connectivity.

Dividing a pre-defined brain region into several heterogenous subregions is crucial for understanding its functional segregation and integration. Due to the high dimensionality of brain functional features, clustering is often postponed until dimensionality reduction in traditional parcellation frameworks occurs. However, under such stepwise parcellation, it is very easy to fall into the dilemma of local optimum since dimensionality reduction could not take into account the requirement of clustering. In this study, we developed a new parcellation framework based on the discriminative embedded clustering (DEC), combining subspace learning and clustering in a common procedure with alternative minimization adopted to approach global optimum. We tested the proposed framework in functional connectivity-based parcellation of the hippocampus. The hippocampus was parcellated into three spatial coherent subregions along the anteroventral-posterodorsal axis; the three subregions exhibited distinct functional connectivity changes in taxi drivers relative to non-driver controls. Moreover, compared with traditional stepwise methods, the proposed DEC-based framework demonstrated higher parcellation consistency across different scans within individuals. The study proposed a new brain parcellation framework with joint dimensionality reduction and clustering; the findings might shed new light on the functional plasticity of hippocampal subregions related to long-term navigation experience.

Hybrid Analog and Digital Beamforming for RIS-Assisted mmWave Communications

Reconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) communications has been envisioned as a prominent technology for future wireless networks, since it is capable of simultaneously providing abundant spectrum resources and favorable propagation environments. The small wavelength at mmWave bands also enables the widespread use of large antenna arrays, of which the hybrid beamforming structure has emerged as a cost-effective solution. In this paper, we aim to minimize the sum-mean-square-error (sum-MSE) in the RIS-assisted mmWave multiuser multiple input multiple output (MU-MIMO) system by jointly optimizing the hybrid analog-digital precoders and the RIS reflection matrix. We demonstrate that the role of RIS in assisting mmWave communications can be completely replaced by a large-scale Kronecker-structured hybrid array. Moreover, an accelerated Riemannian gradient algorithm using majorization minimization technique is proposed to tackle the unit-modulus constrained analog precoder/RIS design. Under the assumption of perfect channel state information (CSI), we firstly consider the single-user MIMO (SU-MIMO) setup and propose an effective alternating minimization (AM) procedure to characterize the system performance limit. Moreover, a two-stage scheme is developed for low-complexity implementation. This AM procedure is then extended to the general MU-MIMO scenario. In addition, we develop a novel enhanced regularized zero-forcing (ERZF) scheme for simultaneously combating strong noise in the low-SNR regime and mitigating multi-user interference (MUI) in the high-SNR regime. The optimality of our proposed algorithms is validated for some simplified practical scenarios. Numerical results illustrate that the proposed algorithms outperform existing benchmark schemes in terms of the actual complexity and performance.

Self-Calibration Method of Sensors Array Errors Based on Rotation Measurement

Array calibration is the premise of successful array signal processing. The active calibration needs to know the direction of arrival (DOA) of calibration source signals accurately; otherwise, the performance will deteriorate. Although the conventional self-calibration does not need accurate DOA of calibration sources, it may suffer from falling into the local extremum since there are too many parameters to be estimated. Thus, we propose a novel self-calibration method based on the rotation measurement. The rotation measurement is that the array receives signals from a fixed source with different array rotation angles. The proposed method jointly estimates array errors and DOAs of the sources by an alternative minimization (AM) algorithm. Through the derivation of a suitable initial value in the AM algorithm, we could improve the robustness and reduce the computational complexity. The proposed method can achieve as high calibration accuracy as the active method even if there is an error in the source DOA information and can apply to arbitrary planar arrays. Both simulation and field experiment results demonstrate the effectiveness of the proposed method.