Sparse Problem Research Articles

Machine learning-enabled MIMO-FBMC communication channel parameter estimation in IIoT: A distributed CS approach

Compressed Sensing (CS) is a Machine Learning (ML) method, which can be regarded as a single-layer unsupervised learning method. It mainly emphasizes the sparsity of the model. In this paper, we study an ML-based CS Channel Estimation (CE) method for wireless communications, which plays an important role in Industrial Internet of Things (IIoT) applications. For the sparse correlation between channels in Multiple Input Multiple Output Filter Bank MultiCarrier with Offset Quadrature Amplitude Modulation (MIMO-FBMC/OQAM) systems, a Distributed Compressed Sensing (DCS)-based CE approach is studied. A distributed sparse adaptive weak selection threshold method is proposed for CE. Firstly, the correlation between MIMO channels is utilized to represent a joint sparse model, and CE is transformed into a joint sparse signal reconstruction problem. Then, the number of correlation atoms for inner product operation is optimized by weak selection threshold, and sparse signal reconstruction is realized by sparse adaptation. The experiment results show that the proposed DCS-based method not only estimates the multipath channel components accurately but also achieves higher CE performance than classical Orthogonal Matching Pursuit (OMP) method and other traditional DCS methods in the time-frequency dual selective channels.

Development and calibration data for the Illness Burden item bank: a new computer adaptive test for persons with type 2 diabetes mellitus.

The purpose of this study was to develop a new measure, the Re-Engineered Discharge for Diabetes Computer Adaptive Test (REDD-CAT) Illness Burden item bank, to evaluate the impact that a chronic condition has on independent living, the ability to work (including working at home), social activities, and relationships. Semi-structured interviews were used to inform the development of an item pool (47 items) that captured patients' beliefs about how a diagnosis of type 2 diabetes interferes with different aspects of their lives. The Illness Burden item bank was developed and tested in 225 people with type 2 diabetes mellitus. No items had sparse response option cells or problems with monotonicity; two items were deleted due to low item-rest correlations. Factor analyses supported the retention of 29 items. With those 29 remaining items, a constrained (common slope) graded response model fit assessment indicated that two items had misfit; they were excluded. No items displayed differential item functioning by age, sex, education, or socio-economic status. The final item bank is comprised of 27 items. Preliminary data supported the reliability (internal consistency and test-retest reliability) and validity (convergent, discriminant, and known-groups) of the new bank. The Illness Burden item bank can be administered as a computer adaptive test or a 6-item short form. This new measure captures patients' perceptions of the impact that having type 2 diabetes has on their daily lives; it can be used in conjunction with the REDD-CAT measurement system to evaluate important social determinants of health in persons with type 2 diabetes mellitus.

Sparse Optimal Control of Pattern Formations for an SIR Reaction-Diffusion Epidemic Model

Pattern formation arising from the reaction-diffusion epidemic model is a space-time depiction of the distribution and transmission of infectious diseases. Disease control can be achieved by controlling the associated pattern formations. For an SIR reaction-diffusion epidemic model, we review its Turing pattern formations with different transmission rates under the case of a constant recovery rate. To control pattern formations of the SIR epidemic model, we introduce a regulator as a control function of the recovery rate. For a perfect control strategy, it not only leads to a desired pattern formation, but also has a small support in space-time domains. In order to obtain such a control strategy, we propose a sparse optimal control problem governed by the SIR epidemic model. We study the existence of optimal solutions, derive the first order necessary optimality system, obtain the sparsity structure of the control function, and numerically solve the control problem. Numerical results demonstrate the feasibility and effectivity of our method.

DOA and polarization estimation for compressed EMVS array with arbitrary sensor geometry

Electromagnetic vector sensors (EMVS) are widely used in array signal processing because of their advantages in polarization diversity, which enables the estimation of the received polarization angle (RPA) in addition to the direction of arrival (DOA). However, these benefits are accompanied by a huge burden on hardware cost and computational complexity. Specifically, compared to scalar arrays, EMVS array signal processing requires more complex hardware devices, for instance, a larger number of front-end chains and higher computational complexity for multidimensional parameter estimation algorithms. We propose a novel compression framework to reduce the hardware cost while achieving high performance. Unlike the existing ones in the literature, the proposed compression network is a sparse network consisting of analog phase shifters; In addition, the proposed compression framework only works on spatial information except for polarization information; Further, for such a compressed EMVS array, we propose a two-step multi-parameter estimation algorithm. In detail, we firstly propose a compressed ESPRIT-like method to estimate the 2D-DOA coarsely. Then, we adopt a small-scale 2D search in the vicinity of the coarse estimate to obtain a high-accuracy estimate of 2D-DOA. After that, we obtain a high-accuracy estimate of 2D-RPA in a closed-form. Furthermore, to avoid any possible performance deterioration of the proposed estimators due to the randomly selected compression weights (a.k.a. compression matrix) from Gaussian distribution (as in literature) and thus cause loss of information, we propose an optimization algorithm to find the optimal solution for the compression matrix under the maximum signal-to-noise ratio (SNR) principle. In this way, we convert the intractable sparse complex matrix optimization problem into a quadratically constrained quadratic programming (QCQP); Then, we employ the semidefinite relaxation technique (SDR) to find the optimal compression matrix. Numerical simulations illustrate that the proposed algorithms could obtain high-accuracy multi-parameter estimates with reduced front-end chains and low computational complexity.

An efficient semismooth Newton method for adaptive sparse signal recovery problems

We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional methods might work not so well. Recently, it was shown that using the difference between - and -norm as a regularization always has superior performance. In this paper, we consider an adaptive - model where the -norm with measures the data fidelity and the -term measures the sparsity. This proposed model has the ability to deal with different types of noises and extract the sparse property even under high coherent condition. We use a proximal majorization-minimization technique to handle the non-convex regularization term and then employ a semismooth Newton method to solve the corresponding convex relaxation subproblem. We prove that the sequence generated by the semismooth Newton method admits fast local convergence rate to the subproblem under some technical assumptions. Finally, we do some numerical experiments to demonstrate the superiority of the proposed model and the progressiveness of the proposed algorithm.

A two-step parallel iteration method for large sparse horizontal linear complementarity problems

In this work, a two-step modulus-based synchronous multisplitting iteration method is constructed for solving large sparse horizontal linear complementarity problems. Some convergence theorems of the proposed method are presented, which can generalize the convergence results of some existing methods. Numerical tests on parallel computers by OpenACC show that the proposed method is efficient.

Permanent-Magnet Optimization for Stellarators as Sparse Regression

A common scientific inverse problem is the placement of magnets that produce a desired magnetic field inside a prescribed volume. This is a key component of stellarator design, and recently permanent magnets have been proposed as a potentially useful tool for magnetic field shaping. Here, we take a closer look at possible objective functions for permanent magnet optimization, reformulate the problem as sparse regression, and propose an algorithm that can efficiently solve many convex and nonconvex variants. The algorithm generates sparse solutions that are independent of the initial guess, explicitly enforces maximum strengths for the permanent magnets, and accurately produces the desired magnetic field. The algorithm is flexible, and our implementation is open-source and computationally fast. We conclude with two new permanent magnet configurations for the NCSX and MUSE stellarators. Our methodology can be additionally applied for effectively solving permanent magnet optimizations in other scientific fields, as well as for solving quite general high-dimensional, constrained, sparse regression problems, even if a binary solution is required.

Dictionary Learning-Based Channel Estimation for RIS-Aided MISO Communications

In this letter, we study the channel estimation problem for the reconfigurable intelligent surface (RIS)-aided multi-input single-output (MISO) system. By exploiting the channel sparsity, compressive sensing (CS) based sparse channel estimators can be applied to the system to reduce the training overhead. However, these existing sparse channel estimators adopt predefined dictionaries when formulating the sparse matrix recovery problem, which will cause grid mismatch issues and estimation performance degradation. Hence, in this letter, we formulate the channel estimation problem as a joint dictionary parameter learning and sparse signal recovery problem, in which the dictionary parameter can be optimized to adapt to the channel measurements, thereby improving the robustness of sparse channel representation and estimation performance. Then, we propose an iterative re-weighted algorithm to solve this non-convex problem efficiently. Simulation results show that the proposed algorithm outperforms other benchmark schemes significantly.

An Enhanced Competitive Swarm Optimizer With Strongly Convex Sparse Operator for Large-Scale Multiobjective Optimization

Sparse multiobjective optimization problems (MOPs) have become increasingly important in many applications in recent years, e.g., the search for lightweight deep neural networks and high-dimensional feature selection. However, little attention has been paid to sparse large-scale MOPs, whose Pareto-optimal sets are sparse, i.e., with many decision variables equal to zero. To address this issue, this article proposes an enhanced competitive swarm optimization algorithm assisted by a strongly convex sparse operator (SCSparse). A tricompetition mechanism is introduced into competitive swarm optimization, aiming to strike a better balance between exploration and exploitation. In addition, the SCSparse is embedded in the position updating of the particles to generate sparse solutions. Our simulation results show that the proposed algorithm outperforms the state-of-the-art methods on both sparse test problems and application examples.

Enhance Document Contextual Using Attention-LSTM to Eliminate Sparse Data Matrix for E-Commerce Recommender System

E-commerce has been the most important service in the last two decades. E-commerce services influence the growth of the economic impact worldwide. A recommender system is an essential mechanism for calculating product information for e-commerce users. The successfulness of recommender system adoption influences the target revenue of an e-commerce company. Collaborative filtering (CF) is the most popular algorithm for creating a recommender system. CF applied a matrix factorization mechanism to calculate the relationship between user and product using rating variable as intersection value between user and product. However, the number of ratings is very sparse, where the number of ratings is less than 4%. Product Document is the product side information representation. The document aims to advance the effectiveness of matrix factorization performance. This research considers to the enhancement of document context using LSTM with an attention mechanism to capture a contextual understanding of product review and incorporate matrix factorization based on probabilistic matrix factorization (PMF) to produce rating prediction. This study employs a real dataset using MovieLens dataset ML.1M and Amazon information video (AIV) to observe our ATT-PMF model. Movielens dataset represents of number sparse rating that only contains below 4% (ML.1M). Our experiment report shows that ATT-PMF outperforms more than 2% on average than previous work. Moreover, our model is also suitable to implement on huge datasets. For further research, enhancement of product document context will be a good factor in eliminating sparse data problems in big data problems.

A Multi-UCAV Cooperative Decision-Making Method Based on an MAPPO Algorithm for Beyond-Visual-Range Air Combat

To solve the problems of autonomous decision making and the cooperative operation of multiple unmanned combat aerial vehicles (UCAVs) in beyond-visual-range air combat, this paper proposes an air combat decision-making method that is based on a multi-agent proximal policy optimization (MAPPO) algorithm. Firstly, the model of the unmanned combat aircraft is established on the simulation platform, and the corresponding maneuver library is designed. In order to simulate the real beyond-visual-range air combat, the missile attack area model is established, and the probability of damage occurring is given according to both the enemy and us. Secondly, to overcome the sparse return problem of traditional reinforcement learning, according to the angle, speed, altitude, distance of the unmanned combat aircraft, and the damage of the missile attack area, this paper designs a comprehensive reward function. Finally, the idea of centralized training and distributed implementation is adopted to improve the decision-making ability of the unmanned combat aircraft and improve the training efficiency of the algorithm. The simulation results show that this algorithm can carry out a multi-aircraft air combat confrontation drill, form new tactical decisions in the drill process, and provide new ideas for multi-UCAV air combat.

Convex optimization under combinatorial sparsity constraints

We present a heuristic approach for convex optimization problems containing different types of sparsity constraints. Whenever the support is required to belong to a matroid, we propose an exchange heuristic adapting the support in every iteration. The entering non-zero is determined by considering the dual multipliers of the bounds on variables being fixed to zero. While this algorithm is purely heuristic, we show experimentally that it often finds near-optimal solutions for cardinality-constrained knapsack problems and for sparse regression problems.

Adapting step size algorithms for solving split equilibrium problems with applications to signal recovery

Recent developments in split equilibrium problems (SEPs) have found practical applications in convex optimization problems, information theory, and signal processing. In this paper, we present three novel algorithms with no prior knowledge of the operator norm of a bounded linear operator to approximated solutions for SEPs. Strong convergence results are well presented under appropriate conditions. In addition, we illustrate our main results by providing various numerical examples. Their computational performances are compared with those previously studied in the literature, and the results are presented by showing numerical implementation of the sparse sensor signal recovery problem.

Angle-incremental range estimation for FDA-MIMO radar via hybrid sparse learning

In this paper, a target parameter estimation problem is addressed for the recently emerging frequency diverse array multiple-input multiple-output (FDA-MIMO) radar system, utilizing sparse learning. The scene is modeled as a two dimensional (2D) angle-incremental range grid. To solve the resulting sparse problem, the recently proposed user-parameter free algorithms including block sparse learning via iterative minimization (BSLIM), iterative adaptive approach (IAA), sparse iterative covariance-based estimation (SPICE), likelihood-based estimation of sparse parameters (LIKES), and orthogonal matching pursuit (OMP) are applied which achieve excellent parameter estimation performance. However, these algorithms do not exhibit a uniform performance under different scenarios such as the number of available snapshots and the number of present targets. In this paper, we propose a hybrid estimation approach which utilizes the model order selection (MOS), and automatically selects the best algorithm for the scenario under test. The performance analyses show that the proposed hybrid algorithm presents higher accuracy in terms of root mean square error (RMSE), as compared with the discussed sparse algorithms, and converges to the Cramér-Rao lower bound (CRLB).

Neurodynamic approaches for sparse recovery problem with linear inequality constraints

This paper develops two neurodynamic approaches for solving the L1-minimization problem with the linear inequality constraints. First, a centralized neurodynamic approach is proposed based on projection operator and nonnegative quadrant. The stability and global convergence of the centralized neurodynamic approach are analyzed by the Lyapunov method in detail. Considering that the distributed optimization problem has the advantages of information protection and scalability, the L1-minimization problem with linear inequality constraints is transformed into a distributed sparse optimization problem under mild conditions. Then, using the centralized neurodynamic approach and multi-agent consensus theory, a distributed neurodynamic approach is proposed for the distributed optimization problem. Furthermore, relevant theories show that each agent globally converges to an optimal solution of the distributed optimization problem. Finally, the presented centralized neurodynamic approach is applied to sparse recovery problem with L∞-norm noise constraints and the effectiveness of distributed approach is shown by several experiments on sparse signal recovery.

A multiview graph collaborative filtering by incorporating homogeneous and heterogeneous signals

In the industrial e-commerce recommender systems, the sparsity of user–item interaction limits the improvement of the performance of collaborative filtering recommendation. Some studies have leveraged attribute co-occurrence or similar neighbors to enhance the semantic representation quality of users and items. Previous methods consider collaborative signals of homogeneous type nodes, such as <user,user>→user and <item,item>→item. By exploiting homogeneous and heterogeneous signals of attribute and neighbor views, we design a multiview graph collaborative filtering (MVGCF) network for recommendation. The MVGCF model utilizes both co-occurrence features of various attribute values and collaborative preference of various neighbors to learn the embedding representation of nodes. Experimental results show that the MVGCF is superior to the state-of-the-art models in AUC and logloss metrics by 1.41% and 3.12% for MovieLens 1M dataset, and by 2.35% and 2.31% for BookCrossing dataset. Aiming at the sparse problem with a small amount of interaction records, our findings is that attribute co-occurrence and neighbor collaboration can improve the accuracy and provide a good explanation for e-commerce recommender systems.

DOA estimation of non‐circular signals based on iterative soft thresholding algorithm

Based on compressed sensing technology, a DOA estimation algorithm for reconstructing the original signal is proposed. First, the over-complete dictionary of signal vectors is established based on the sparsity of signals in spatial domain. The DOA estimation problem is transformed into sparse signals reconstruction problem, and signals in spatial domain are reconstructed using iterative soft thresholding (IST) algorithm. At the same time, combined with the second-order statistical characteristic of non-circular signal, the array is virtual extended, and the spectrum estimation is performed by MUSIC algorithm. In addition, in order to further distinguish coherent signals, spatial smoothing technology is added to the algorithm. The simulation results show that the proposed algorithm can effectively resolve incoherent signals and coherent signals under small snapshots and low SNR.

Battery-Aware Cooperative Merging Strategy of Connected Electric Vehicles Based on Reinforcement Learning With Hindsight Experience Replay

Cooperative control of connected and automated electric vehicles (CAEVs) offers a great potential for a safe, high-efficient, sustainable transportation system. Among them, coordinated on-ramp merging based on an on-ramp merging vehicle and a mainline facilitating is a hot spot to lighten the impact of shockwave on highway junctions. Reinforcement learning (RL) is a promising solution to address this problem for its strong adaptiveness and self-learning ability. The existing methods are dedicatedly designed to circumvent the sparse reward problem of long-term merging safety but restrict the optimization space and neglect individual costs, especially irreversible loss, such as battery aging. In this article, a hindsight experience replay RL coordinated freeway on-ramp merging frame is proposed to face the sparse reward problem in ramp merging problem and, meanwhile, co-optimize traffic efficiency, energy-saving, and battery health performance. Compared with the existing optimization-based strategy, it fundamentally avoids abundant expert knowledge and elaborate design for reward shaping and model construction while ensuring the nature of merging tasks without excessive simplification. Numerical experiments are conducted to verify the optimality, adaptability, and self-learning ability of the proposed strategy. With comparison experiment, the proposed strategy surpasses state-of-the-art RL methods more than 13% in overall index throughput with 12% energy consumption while easing individual battery aging during the merging process.

A Dimension Reduction Technique for Large-Scale Structured Sparse Optimization Problems with Application to Convex Clustering

In this paper, we propose a novel adaptive sieving (AS) technique and an enhanced AS (EAS) technique, which are solver independent and could accelerate optimization algorithms for solving large scale convex optimization problems with intrinsic structured sparsity. We establish the finite convergence property of the AS technique and the EAS technique with inexact solutions of the reduced subproblems. As an important application, we apply the AS technique and the EAS technique on the convex clustering model, which could accelerate the state-of-the-art algorithm SSNAL by more than 7 times and the algorithm ADMM by more than 14 times.

Sparse Radon transform in the mixed frequency-time domain with ℓ1-2 minimization

Due to the finite acquisition aperture and sampling of seismic data, the Radon transform (RT) suffers from a smearing problem which reduces the resolution of the estimated model. In addition, inverting the RT is typically an ill-posed problem. To address these challenges, a sparse RT mixing the [Formula: see text] and [Formula: see text] norms of the RT coefficients in the mixed frequency-time domain is developed, and it is denoted as SRTL1-2. In most conventional sparse RTs, the sparse constraint term often is the [Formula: see text] norm of the Radon model. We prove that the sparsity effect of the [Formula: see text] minimization is better than that of the [Formula: see text] norm alone by comparing and analyzing their 2D distribution patterns and threshold functions. The difference of the convex functions algorithm and the alternating direction method of multipliers algorithm are modified by combining the forward and inverse Fourier transforms to solve the corresponding sparse inverse problem in the mixed frequency-time domain. Our method is compared with three RT methods, including a least-squares RT (LSRT), a frequency-domain sparse RT (FSRT), and a time-invariant RT in the mixed frequency-time domain based on an iterative 2D model shrinkage method (SRTIS). Furthermore, we modify the basis function in SRTL1-2 by including an orthogonal polynomial transform to fit the amplitude-variation-with-offset (AVO) signatures found in seismic data, and we denote this as high-order SRTL1-2. Compared to the SRTL1-2, the high-order SRTL1-2 performs better when processing seismic data with AVO signatures. Synthetic and real data examples indicate that our method has better performance than the LSRT, FSRT, and SRTIS in terms of attenuation of multiples, noise mitigation, and computational efficiency.