Manifold Optimization Research Articles

Benign-malignant classification of pulmonary nodule with deep feature optimization framework

Convolutional neural network (CNN) has been widely utilized for benign-malignant classification of pulmonary nodules in Computed Tomography images. For traditional CNN models, single-input strategy limits the ability of feature extraction, while multi-input CNN models usually achieve better performance by exploring comprehensive information with pulmonary nodules. However, the concatenation layer in multi-input CNN methods generates high-dimensional deep features, which can easily bring about the curse of dimensionality. To tackle these issues, a manifold-based deep learning model termed deep feature optimization framework (DFOF) is proposed to perk up the performance. In feature extraction stage, a two-stream network is adopted for extracting perinodular and intranodular features from CT images, which forms high-dimensional features. In feature optimization stage, a manifold optimization process is proposed to compact intraclass neighbors while separating interclass samples in low-dimensional embedding space. After that, the optimization features are classified by classifiers, such as nearest neighbor, support vector machine, and random forest. Experiments were conducted using two datasets with 5-cross-validation. The accuracy, area under curve, precision, recall, and F-score reach 92.13%, 95.54%, 94.16%, 87.16%, and 89.93% on the LIDC-IDRI dataset, 90.03%, 94.06%, 96.95%, 89.91%, and 93.38% on the external validation dataset. The results indicate that DFOF has a remarkably better benign-malignant classification performance than several state-of-the-art methods.

Manifold biomedical text sentence embedding

Pretrained distributed sentence embeddings have been proven to be useful in various biomedical text tasks. However, the current research on biomedical text sentence embeddings is mainly based on Euclidean space. The geometric structure of sentences and the relations with the representations of sentence context contribute to more accurate representations of sentence semantics and still need further investigation. To address this issue, in this study, we propose a manifold biomedical text sentence embedding model. To learn biomedical text sentence embedding in the manifold space, we develop an efficient optimization algorithm with neighbourhood preserving embedding based on manifold optimization. We conducted experiments on two tasks of biomedical text classification and clustering, and the experimental results outperformed the state-of-the-art baseline models.

Sparse reduced-rank regression for simultaneous rank and variable selection via manifold optimization

We consider the problem of constructing a reduced-rank regression model whose coefficient parameter is represented as a singular value decomposition with sparse singular vectors. The traditional estimation procedure for the coefficient parameter often fails when the true rank of the parameter is high. To overcome this issue, we develop an estimation algorithm with rank and variable selection via sparse regularization and manifold optimization, which enables us to obtain an accurate estimation of the coefficient parameter even if the true rank of the coefficient parameter is high. Using sparse regularization, we can also select an optimal value of the rank. We conduct Monte Carlo experiments and a real data analysis to illustrate the effectiveness of our proposed method.

Refining electronic medical records representation in manifold subspace

BackgroundElectronic medical records (EMR) contain detailed information about patient health. Developing an effective representation model is of great significance for the downstream applications of EMR. However, processing data directly is difficult because EMR data has such characteristics as incompleteness, unstructure and redundancy. Therefore, preprocess of the original data is the key step of EMR data mining. The classic distributed word representations ignore the geometric feature of the word vectors for the representation of EMR data, which often underestimate the similarities between similar words and overestimate the similarities between distant words. This results in word similarity obtained from embedding models being inconsistent with human judgment and much valuable medical information being lost.ResultsIn this study, we propose a biomedical word embedding framework based on manifold subspace. Our proposed model first obtains the word vector representations of the EMR data, and then re-embeds the word vector in the manifold subspace. We develop an efficient optimization algorithm with neighborhood preserving embedding based on manifold optimization. To verify the algorithm presented in this study, we perform experiments on intrinsic evaluation and external classification tasks, and the experimental results demonstrate its advantages over other baseline methods.ConclusionsManifold learning subspace embedding can enhance the representation of distributed word representations in electronic medical record texts. Reduce the difficulty for researchers to process unstructured electronic medical record text data, which has certain biomedical research value.

Joint Design of Hybrid Beamforming and Reflection Coefficients in RIS-Aided mmWave MIMO Systems

This paper considers a reconfigurable intelligent surface (RIS)-aided millimeter wave (mmWave) downlink communication system where hybrid analog-digital beamforming is employed at the base station (BS). We formulate a power minimization problem by jointly optimizing hybrid beamforming at the BS and the response matrix at the RIS, under the signal-to-interference-plus-noise ratio (SINR) constraints at all users. The problem is highly challenging to solve due to the non-convex SINR constraints as well as the unit-modulus phase shift constraints for both the RIS reflection coefficients and the analog beamformer. A two-layer penalty-based algorithm is proposed to decouple variables in SINR constraints, and manifold optimization is adopted to handle the non-convex unit-modulus constraints. We also propose a low-complexity sequential optimization method, which optimizes the RIS reflection coefficients, the analog beamformer, and the digital beamformer sequentially without iteration. Furthermore, the relationship between the power minimization problem and the max-min fairness (MMF) problem is discussed. Simulation results show that the proposed penalty-based algorithm outperforms the state-of-the-art semidefinite relaxation (SDR)-based algorithm. Results also demonstrate that the RIS plays an important role in the power reduction.

Improved Estimation of High-dimensional Additive Models Using Subspace Learning

Additive models have been widely used as a flexible nonparametric regression method that can overcome the curse of dimensionality. Using sparsity-inducing penalty for variable selection, several methods are developed for fitting additive models when the number of predictors is very large, sometimes even larger than the sample size. However, despite good asymptotic properties, the finite sample performance of these methods may deteriorate considerably when the number of relevant predictors becomes moderately large. This article proposes a new method that reduces the number of unknown functions to be nonparametrically estimated through learning a predictive subspace representation shared by the additive component functions. The subspace learning is integrated with sparsity-inducing penalization in a penalized least squares formulation and an efficient algorithm is developed for computation involving Stiefel matrix manifold optimization and proximal thresholding operators on matrices. Theoretical convergence properties of the algorithm are studied. The proposed method is shown to be competitive with existing methods in simulation studies and a real data example. Supplementary materials for this article are available online.

Aerial intelligent reflecting surface for secure wireless networks: Secrecy capacity and optimal trajectory strategy

This work investigates the potential of the aerial intelligent reflecting surface (AIRS) in secure communication, where an intelligent reflecting surface (IRS) carried by an unmanned aerial vehicle (UAV) is utilized to help the communication between the ground nodes. Specifically, we formulate the joint design of the AIRS's deployment and the phase shift to maximize the secrecy rate. To solve the non-convex objective, we develop an alternating optimization (AO) approach, where the phase shift optimization is solved by the Riemannian manifold optimization (RMO) method, while the deployment optimization is handled by the successive convex approximation (SCA) technique. Furthermore, to reduce the computational complexity of the RMO method, an element-wise block coordinate descent (EBCD) based method is employed. Simulation results verify the effect of AIRS in improving the communication security, as well as the importance of designing the deployment and phase shift properly.

Maximizing dirty-paper coding rate of RIS-assisted multi-user MIMO broadcast channels

We consider a downlink multi-user scenario and investigate the use of reconfigurable intelligent surfaces (RISs) to maximize the dirty-paper-coding (DPC) sum rate of the RIS-assisted broadcast channel. Different from prior works, which maximize the rate achievable by linear precoders, we assume a capacity-achieving DPC scheme is employed at the transmitter and optimize the transmit covariances and RIS reflection coefficients to directly maximize the sum capacity of the broadcast channel. We propose an optimization algorithm that iteratively alternates between optimizing the transmit covariances using convex optimization and the RIS reflection coefficients using Riemannian manifold optimization. Our results show that the proposed technique can be used to effectively improve the sum capacity in a variety of scenarios compared to benchmark schemes.

Double Intelligent Reflecting Surface-Assisted Multi-User MIMO Mmwave Systems With Hybrid Precoding

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.

Design of a novel wireless information surveillance scheme assisted by reconfigurable intelligent surface

This paper investigates a novel wireless information surveillance scheme assisted by reconfigurable intelligent surface (RIS) beamforming and artificial noise jamming cooperation, aiming at monitoring the information sent by an access point (AP) to a suspicious illegal user (SIU). It is assumed that the AP adopt the fixed maximum ratio transmission (MRT) precoding scheme, which is not affected by the information monitoring party. The goal of this paper is to maximize the effective information monitoring rate by jointly optimizing the RIS phase shifts, the receive beamforming vector of the legitimate receiver (LR), and the transmit beamforming vector along with jamming power of the jamming antenna (JA). The resultant optimization problem is non-convex, and its optimization variables are highly coupled in the objective function and constraints. To tackle this difficulty, the optimization variables are optimized under the alternate optimization (AO) framework. Especially, the intractable RIS phase shifts are optimized by using Riemannian manifold optimization (RMO) algorithm under the penalty dual decomposition (PDD) framework and the semidefinite relaxation (SDR) technique, respectively. Numerical results verify the effectiveness of the proposed algorithms, and also demonstrate the superiority of the designed wireless information surveillance scheme over other benchmark schemes.

A Riemannian Geometric Approach to Blind Signal Recovery for Grant-Free Radio Network Access

We propose a new nonconvex framework for blind multiple signal demixing and recovery. The proposed Riemannian geometric approach extends the well known constant modulus algorithm to facilitate grant-free wireless access for simultaneous demixing and recovery of multiple signal demixing and recovery. We formulate the problem as non-convex problem optimization problem integrated with the signal orthogonality constraint in the form of Riemannian Orthogonal CMA (ROCMA). Unlike traditional stochastic gradient solutions that require large data samples, parameter tuning, and careful initialization, we leverage Riemannian geometry and transform the orthogonality requirement of recovered signals into a Riemannian manifold optimization. Our solution demonstrates full recovery of multiple access signals without large data sample size or special initialization with high probability of success.

A Riemannian Newton trust-region method for fitting Gaussian mixture models

Gaussian Mixture Models are a powerful tool in Data Science and Statistics that are mainly used for clustering and density approximation. The task of estimating the model parameters is in practice often solved by the expectation maximization (EM) algorithm which has its benefits in its simplicity and low per-iteration costs. However, the EM converges slowly if there is a large share of hidden information or overlapping clusters. Recent advances in Manifold Optimization for Gaussian Mixture Models have gained increasing interest. We introduce an explicit formula for the Riemannian Hessian for Gaussian Mixture Models. On top, we propose a new Riemannian Newton Trust-Region method which outperforms current approaches both in terms of runtime and number of iterations. We apply our method on clustering problems and density approximation tasks. Our method is very powerful for data with a large share of hidden information compared to existing methods.

Exploiting Reconfigurable Intelligent Surfaces in Edge Caching: Joint Hybrid Beamforming and Content Placement Optimization

Edge caching can effectively reduce backhaul burden at core network and increase quality-of-service at wireless edge nodes. However, the beneficial role of edge caching cannot be fully realized when the offloading link is in deep fade. Fortunately, the impairments induced by wireless propagation environments could be renovated by a reconfigurable intelligent surface (RIS). In this paper, a new RIS-aided edge caching system is proposed, where a network cost minimization problem is formulated to optimize content placement at cache units, active beamforming at base station and passive phase shifting at RIS. After decoupling the content placement subproblem with the hybrid beamforming design, we propose an alternating optimization algorithm to tackle the active beamforming and passive phase shifting. For active beamforming, we transfer the problem into a semidefinite programming (SDP) and prove that the optimal solution of SDP is always rank-one. For passive phase shifting, we introduce the block coordinate descent method to alternately optimize the auxiliary variables and the RIS phase shifts. Further, a conjugate gradient algorithm based on manifold optimization is proposed to deal with the non-convex unit-modulus constraints. Numerical results show that our RIS-aided edge caching design can effectively decrease the network cost by improving the quality of offloading links.

Partially-Connected Hybrid Beamforming for Spectral Efficiency Maximization via a Weighted MMSE Equivalence

Hybrid beamforming (HBF) is an attractive technology for practical massive multiple-input and multiple-output (MIMO) millimeter wave (mmWave) systems. Compared with the fully-connected HBF architecture, the partially-connected one can further reduce the hardware cost and power consumption. However, the special block diagonal structure of its analog beamforming matrix brings additional design challenges. In this paper, we develop effective HBF algorithms for spectral efficiency maximization (SEM) in wideband mmWave massive MIMO systems with the partially-connected architecture. One main contribution is that we prove the equivalence of the SEM problem and a weighted mean square error minimization (WMMSE) problem, which leads to a convenient algorithmic approach to directly tackle the SEM problem. Specifically, we decompose the equivalent WMMSE problem into the hybrid precoding and hybrid combining subproblems, for which both the optimal digital precoder and combiner have closed-form solutions. For the more challenging analog precoder and combiner, we propose an element iteration based algorithm and a manifold optimization based algorithm. Finally, the hybrid precoder and combiner are alternatively updated. The overall HBF algorithms are proved to monotonously increase the spectral efficiency and converge. Furthermore, we also propose modified algorithms with reduced computational complexity and finite-resolution phase shifters. Simulation results demonstrate that the proposed HBF algorithms achieve significant performance gains over conventional algorithms.

Reconfigurable Intelligent Surfaces Aided mmWave NOMA: Joint Power Allocation, Phase Shifts, and Hybrid Beamforming Optimization

In this paper, a reconfigurable intelligent surface (RIS)-aided millimeter wave (mmWave) non-orthogonal multiple access (NOMA) system is analyzed. In particular, we consider an RIS-aided mmWave-NOMA downlink system with a hybrid beamforming structure. To maximize the achievable sum-rate under a minimum rate constraint for the users and a maximum transmit power constraint, a joint RIS phase shifts, hybrid beamforming, and power allocation problem is formulated. To solve this non-convex optimization problem, we develop an alternating optimization (AO) algorithm. Specifically, first, the non-convex problem is transformed into three subproblems, i.e., power allocation, joint phase shifts and analog beamforming optimization, and digital beamforming design. Then, we solve the power allocation problem by keeping fixed the phase shifts of the RIS and the hybrid beamforming. Finally, given the power allocation matrix, an alternating manifold optimization (AMO)-based method and a successive convex approximation (SCA)-based method are utilized to design the phase shifts, analog beamforming, and transmit beamforming, respectively. Numerical results reveal that the proposed AO algorithm outperforms existing schemes in terms of sum-rate. Moreover, compared to a conventional mmWave-NOMA system without RIS, the proposed RIS-aided mmWave-NOMA system is capable of improving the achievable sum-rate.

Achievable Rate Region Maximization in Intelligent Reflecting Surfaces-Assisted Interference Channel

In the achievable rate region maximization for intelligent reflecting surfaces (IRSs)-assisted interference channel (IFC), where more than one pair of transceivers communicates and interferes with each other simultaneously. Specifically, we optimize the transmit power and passive beamforming vectors at all the IRSs to obtain the Pareto boundary of the achievable rate region in IFC, subject to the unit-modulus constraints for the passive beamforming vectors at the IRSs and transmit power budgets at the transmitters. To solve the formulated non-convex optimization problem efficiently, we resort to optimize each variable alternatively until convergence. The optimization of transmit power is based on a locally optimal fixed-point iteration method. Instead of using the conventional high-complexity and sub-optimal Gaussian randomization-aided semi-definite relaxation (SDR) technique for the passive beamforming design, we first propose a novel locally optimal homotopy optimization based majorization-minimization method. To further reduce the computational complexity, a locally optimal log-sum-exp approximation based manifold optimization method is also proposed. Simulation results validate that our proposed methods can significantly decrease the computational complexity and outperform the conventional SDR-based algorithm.

Mobile User Trajectory Tracking for IRS Enabled Wireless Networks

In this paper, we consider an intelligent reflecting surface (IRS) enabled mobile network, where a fixed access point (AP) communicates with a mobile user (MU) via the aid of an IRS. We assume that the MU moves from one elementary square to another following a Markov random walk within a grid, and propose a maximum a posteriori (MAP) criterion to track the movement of the MU by leveraging the line-of-sight component of the IRS-MU link. Since it is infeasible to derive an explicit expression for the average probability of estimation error (APEE) for the proposed MAP criterion, we derive a closed-form upper bound for the APEE, which is used as the cost function to optimize the phase shifts of the IRS units. Considering the unit modulus constraints incurred by the IRS units, a manifold optimization (MO) method is firstly employed to gain a favorable solution to the formulated optimization problem, followed by a low-complexity codebook based solution to circumvent the high computational cost of the MO method. Our numerical results demonstrate the superior performance of the proposed IRS phase shift designs over the benchmark method.

Broad Coverage Precoder Design for Synchronization in Satellite Massive MIMO Systems

In this paper, we investigate the massive multi-input multi-output (MIMO) transmission for the satellite communication systems equipped with a uniform rectangular array (URA) and aim to design the precoder with broad coverage radiation power pattern to improve the performance of time and frequency synchronizations. The modified Cramér-Rao vector bounds (MCRVB) are chosen as the benchmark of symbol timing offset and frequency offset estimation problem, which can be viewed as the time and frequency synchronization performance metric for the broad coverage precoder design. By considering the minimax MCRVB criterion and the per-antenna equal power constraint, the precoder design approach is formulated as the non-convex constrained minimax problem over the discrete radiation power pattern. This optimization problem is solved by the smoothing techniques combined with the manifold optimization method. To reduce the calculation complexity, the nonmonotone conjugate gradient method is applied. Simulation results show that the average and the minimum received powers in the coverage area of the proposed scheme are higher than those of the scheme based on fairness criterion. Compared with the existing omnidirectional and broad coverage schemes, the proposed scheme has the best synchronization performance among all the contrast solutions.

Prediction of Mumps Incidence Trend in China Based on Difference Grey Model and Artificial Neural Network Learning.

Background:We aimed to compare the prediction efficiency of back propagation (BP) network and grey model (GM) (1.1) for mumps infectious diseases and compare the application effect of the two models.Methods:By calculating the average incidence rate of mumps in January 2014 –2016, we conducted the modeling of the BP time series, GM (1,1) grey model and the combination models of them, and predicted the incidence rate in June 2016 in comparison with the actual one. We compared the quarterly incidence rate to test the two prediction models, and compared the advantages and disadvantages of these models.Results:R value of BP model was 68.45%, for GM (1,1) was 58.49%, and for combined forecasting model was 86.95%. We used the principal component analysis clustering method to control the samples, and found that the samples were close to the population mean. We found that the GM (1.1) model was more suitable for the prediction of mumps infection mode. We carried out dimension reduction analysis on the model data, and the accuracy of the data after dimension reduction is within the range of Da. For the discrete degree of the data in the combined model, matlab pipeline was used to verify the reliability of the data and results. By calculation after manifold optimization small error probability was P=0.875 and semi mean relative error 2.43%.Conclusion:BP, GM (1,1) is a better method for modeling the epidemic trend of mumps in China, but the efficiency of prediction is not as high as the combination of them.

Reconfigurable Intelligent Surface Enhanced NOMA Assisted Backscatter Communication System

To enhance the backscatter-links with double fading effect in non-orthogonal multiple access assisted backscatter communication (NOMABC), a new reconfigurable intelligent surface (RIS) enhanced NOMABC (RIS-NOMABC) system is proposed. A joint optimization problem over power reflection coefficients at the backscatter devices (BDs) and phase shifts at the RIS is formulated. To solve this non-convex problem, a low complexity algorithm is proposed by invoking the alternative optimization, successive convex approximation and manifold optimization algorithms. Numerical results corroborate that the proposed RIS-NOMABC system outperforms the conventional NOMABC system without RIS, and demonstrate the feasibility and effectiveness of the proposed algorithm.