Manifold Optimization Research Articles

Robustly learning the Hamiltonian dynamics of a superconducting quantum processor

Precise means of characterizing analog quantum simulators are key to developing quantum simulators capable of beyond-classical computations. Here, we precisely estimate the free Hamiltonian parameters of a superconducting-qubit analog quantum simulator from measured time-series data on up to 14 qubits. To achieve this, we develop a scalable Hamiltonian learning algorithm that is robust against state-preparation and measurement (SPAM) errors and yields tomographic information about those SPAM errors. The key subroutines are a novel super-resolution technique for frequency extraction from matrix time-series, tensorESPRIT, and constrained manifold optimization. Our learning results verify the Hamiltonian dynamics on a Sycamore processor up to sub-MHz accuracy, and allow us to construct a spatial implementation error map for a grid of 27 qubits. Our results constitute an accurate implementation of a dynamical quantum simulation that is precisely characterized using a new diagnostic toolkit for understanding, calibrating, and improving analog quantum processors.

Shaped pattern synthesis for hybrid analog–digital arrays via manifold optimization-enabled block coordinate descent

Hybrid analog–digital (HAD) architecture is a promising means to realize large-scale arrays owing to the judicious trade-off between system performance and hardware complexity. This paper investigates the beampattern shaping of HAD arrays through minimizing the beampattern matching error between desired and actual patterns. Due to the nonconvex constraints on analog and digital weights and the nonconvex nonsmooth objective function, the resultant codesign is NP-hard. To address this issue, we create an efficient algorithm by leveraging block coordinate descent (BCD) and Riemannian manifold optimization. We first equivalently represent the objective function as a smooth bi-quadratic function by introducing a uni-modulus auxiliary variable. Subsequently, we alternatingly optimize the scaling factor, digital weights, analog weights and auxiliary variable under the BCD framework, where the simultaneous update of analog weights and auxiliary variable is recast as uni-modular constrained quadratic programming which is efficiently solved by Riemannian Newton method, and the digital weights have a global optimal solution via Lagrangian multiplier method. We also derive an explicit convergence condition of this algorithm. Numerical results demonstrate that the proposed algorithm has superior performance and faster convergence speed than alternative algorithms, and produces nearly the same mainlobe gain as fully digital arrays with significantly fewer radio-frequency chains.

DAPLSR: Data Augmentation Partial Least Squares Regression Model via Manifold Optimization

Traditional Partial Least Squares Regression (PLSR) models frequently underperform when handling data characterized by uneven categories. To address the issue, this paper proposes a Data Augmentation Partial Least Squares Regression (DAPLSR) model via manifold optimization. The DAPLSR model introduces the Synthetic Minority Over-sampling Technique (SMOTE) to increase the number of samples and utilizes the Value Difference Metric (VDM) to select the nearest neighbor samples that closely resemble the original samples for generating synthetic samples. In solving the model, in order to obtain a more accurate numerical solution for PLSR, this paper proposes a manifold optimization method that uses the geometric properties of the constraint space to improve model degradation and optimization. Comprehensive experiments show that the proposed DAPLSR model achieves superior classification performance and outstanding evaluation metrics on various datasets, significantly outperforming existing methods.

VE-LIOM: A Versatile and Efficient LiDAR-Inertial Odometry and Mapping System

LiDAR has emerged as one of the most pivotal sensors in the field of navigation, owing to its expansive measurement range, high resolution, and adeptness in capturing intricate scene details. This significance is particularly pronounced in challenging navigation scenarios where GNSS signals encounter interference, such as within urban canyons and indoor environments. However, the copious volume of point cloud data poses a challenge, rendering traditional iterative closest point (ICP) methods inadequate in meeting real-time odometry requirements. Consequently, many algorithms have turned to feature extraction approaches. Nonetheless, with the advent of diverse scanning mode LiDARs, there arises a necessity to devise unique methods tailored to these sensors to facilitate algorithm migration. To address this challenge, we propose a weighted point-to-plane matching strategy that focuses on local details without relying on feature extraction. This improved approach mitigates the impact of imperfect plane fitting on localization accuracy. Moreover, we present a classification optimization method based on the normal vectors of planes to further refine algorithmic efficiency. Finally, we devise a tightly coupled LiDAR-inertial odometry system founded upon optimization schemes. Notably, we pioneer the derivation of an online gravity estimation method from the perspective of S2 manifold optimization, effectively minimizing the influence of gravity estimation errors introduced during the initialization phase on localization accuracy. The efficacy of the proposed method was validated through experimentation employing various LiDAR sensors. The outcomes of indoor and outdoor experiments substantiate its capability to furnish real-time and precise localization and mapping results.

Semi-supervised metric learning incorporating weighted triplet constraint and Riemannian manifold optimization for classification

Semi-supervised metric learning incorporating weighted triplet constraint and Riemannian manifold optimization for classification

From constraints fusion to manifold optimization: A new directional transport manifold metaheuristic algorithm

The ascent of geometry-based models and methodologies, exemplified by geometric deep learning and manifold numerical optimization algorithms, has inaugurated a novel domain across various applications that grapple with geometric data complexities, such as electroencephalogram signals represented by symmetric positive definite matrix manifold, hierarchical data represented by hyperbolic manifold. The imperative fuels this inevitable paradigm shift to encapsulate the intricacies and richness inherent in data, areas where traditional methods prove inadequate. While metaheuristic algorithms are renowned for their versatile adaptability across applications, offering practical solutions within reasonable timeframes. However, the conventional metaheuristic algorithms fail on manifold applications with meaningless solutions. From an extrinsic optimization perspective, we treat manifold optimization problems as general optimization problems with multiple fused constraints that limit the optimization path to the manifold. This study pioneered the proposal and implementation of a metaheuristic manifold optimization, introducing a novel directional transport operator to rectify previously identified issues. Through experimentation across five sets of 25 problems, comparing against five algorithms, including both gradient-free and gradient-dominant counterparts, our proposed algorithm emerges as the optimal performer within the gradient-free category, demonstrating competitiveness even against gradient-dominant algorithms. Furthermore, we applied the proposed algorithm to the robot dynamic manipulation problem, achieving a close-optimal solution that eludes gradient-dominant approaches. This paper delves into the inherent capabilities and establishes the generalization of a metaheuristic algorithm within non-Euclidean functional landscapes. The source code will be available at https://github.com/lingping-fuzzy/metaheuristic-manifold-optimization.

Bilayer Intelligent Omni-Surface-Assisted Full-Duplex Systems: Simultaneous Self-Interference Cancellation and Sum Rate Maximization.

Recently, reconfigurable intelligent surfaces (RISs) have attracted increasing attentions in the design of full-duplex (FD) systems due to their novel capability of propagation environment reconfiguration. However, in conventional RIS-assisted FD systems, the beamforming for self-interference cancellation (SIC) and sum rate maximization (SRM) are highly coupled during RIS optimization, which significantly degrades the system performance. To tackle this issue, we exploit a novel bilayer intelligent omni-surface (BIOS) structure in FD systems. Compared with the conventional RIS designs, the BIOS provides independent beams on both sides, thus enabling more flexible achievement of SRM and SIC. For the BIOS-assisted FD system, we first formulate an optimization problem to achieve SRM and efficient SIC simultaneously. Then, we exploit the relationship between the SRM and mean square error (MSE), and propose a weighted MSE minimization with SIC algorithm to solve the problem. Specifically, we jointly design the beamforming at the base station and the BIOS with manifold optimization while guaranteeing an SIC constraint. Furthermore, we theoretically derive a lower band for the BIOS size required for efficient SIC in FD systems. Simulation results indicate that the BIOS outperforms the conventional RIS designs in FD systems, and verify the accuracy of the derived lower bound for the BIOS size.

Phase response constrained symbol‐level waveform design for dual‐functional radar‐communication systems

AbstractIn this letter, a novel algorithm is proposed to design symbol‐level waveform for dual‐functional radar‐communication (DFRC) systems with low range sidelobe. Different from current schemes design waveform at the block level, a phase response constraint is introduced at the symbol level to provide an additional degree of freedom to decrease the range sidelobe in the pulse compression procedure, which is highly desired in radar systems. In particular, the phase response at the target direction is constrained to be similar to the given reference phase, and the matching error between the designed beampattern and the desired one is minimized subject to the constant modulus constraint. Furthermore, to guarantee the quality of service for communication, constructive interference is exploited at the symbol level for each communication user. An alternating direction method of multipliers algorithm is also proposed to solve the resulting nonconvex optimization problem with tractable subproblems solved sufficiently by the manifold optimization and standard quadratic problem. Numerical simulation results demonstrate the performance of the proposed method.

Unified Manifold Optimization for Double-IRS-Aided MIMO Communication

Unified Manifold Optimization for Double-IRS-Aided MIMO Communication

Backbone curve tailoring via Lyapunov subcenter manifold optimization

We present a technique for the direct optimization of conservative backbone curves in nonlinear mechanical systems. The periodic orbits on the conservative backbone are computed analytically using the reduced dynamics of the corresponding Lyapunov subcenter manifold (LSM). In this manner, we avoid expensive full-system simulations and numerical continuation to approximate the nonlinear response. Our method aims at tailoring the shape of the backbone curve using a gradient-based optimization with respect to the system’s parameters. To this end, we formulate the optimization problem by imposing constraints on the frequency-amplitude relation. Sensitivities are computed analytically by differentiating the backbone expression and the corresponding LSM. At each iteration, only the reduced-order model construction and sensitivity computation are performed, making our approach robust and efficient.

Manifold Optimization-Based Data Detection Algorithm for Multiple-Input–Multiple-Output Orthogonal Frequency-Division Multiplexing Systems under Time-Varying Channels

Recently, multiple-input–multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems have gained significant attention in the field of wireless communications. The utilization of the Riemannian manifold has become prevalent in MIMO-OFDM systems. However, the existing data detection algorithms for MIMO-OFDM systems are mostly designed for block fading channels. Additionally, these algorithms often suffer from high computational complexity. In this paper, we propose a data detection algorithm on the basis of Riemannian manifold optimization for MIMO-OFDM systems under time-varying channels. The core concept of this algorithm is to optimize the transmitted signals by solving the manifold optimization problem in the case of time-varying channels. In order to reduce the computational complexity of the algorithm, we improve the proposed algorithm by dividing the transmitted signals into multiple subframes for solving the optimization problem separately and using the pilots to maintain the performance of the algorithm. In the simulation, the performance of multiple proposed algorithms and the forced-zero detection algorithm under different parameter settings are compared. The simulation results show that the proposed algorithm demonstrates good bit error rate and computational complexity performances.

Secure energy efficiency maximization for joint ITS and IRS assisted satellite downlink communications

AbstractSatellite communications (SatCom) have been viewed as a promising technique to achieve ubiquitous global coverage in next‐generation wireless systems. This article investigates the secure energy efficient downlink transmission for SatCom where an intelligent transmissive surface‐aided transmitter is deployed at the satellite to perform energy efficient beamforming and an intelligent reflecting surface as well as a cooperative jammer are deployed on the ground to enhance the secure performance. The aim is to maximize the secure energy efficiency by jointly designing ITS beamforming, IRS phase shift, jammer precoding vector, and transmit power allocation. To develop a low‐complexity solution,first, an approximated concave lower bound of the non‐concave objective function is derived by utilizing Dinkelbach's method and a novel successive convex approximation technique. Then the reformulated problem is decoupled using alternating optimization algorithm and the subproblems are solved by adopting Riemannian manifold optimization, element‐wise block coordinate descent, Lagrange dual method and Karush–Kuhn–Tucker conditions. At last, simulation results demonstrate the effectiveness of the proposed scheme.

Massive MIMO secure beamforming design via manifold optimization combined with momentum

Secure beamforming with constant modulus has been regarded as a promising solution in enhancing the physical-layer security by intelligently designing the antenna phase of massive multiple-input multiple-output (MIMO) devices. The resulting problem is non-convex and NP-hard due to the constant modulus constraint (CMC). Existing methods mainly solve the problem by relaxing the constraints or the objective function, which inevitably introduces the relaxation error. We notice that the complex circle manifold (CCM), where complex numbers maintain a constant modulus, naturally satisfies the CMC. Further, considering the iteration points as high-dimensional particle points, the optimization process on the CCM can be regarded as the motion of the particle on the high-dimensional plane formed by the manifold. Based on this feature, we propose the manifold optimization method combining momentum (MOCM). Concretely, the original problem is first transformed into an unconstrained problem on the complex circle manifold. Then, the descent direction is derived to solve the problem by incorporating momentum into gradient information, which speeds up the convergence process. Simulation results show that the proposed method is 1 bps/Hz higher than existing works.

Improving Robustness of Intent Detection Under Adversarial Attacks: A Geometric Constraint Perspective.

Deep neural networks (DNNs)-based natural language processing (NLP) systems are vulnerable to being fooled by adversarial examples presented in recent studies. Intent detection tasks in dialog systems are no exception, however, relatively few works have been attempted on the defense side. The combination of linear classifier and softmax is widely used in most defense methods for other NLP tasks. Unfortunately, it does not encourage the model to learn well-separated feature representations. Thus, it is easy to induce adversarial examples. In this article, we propose a simple, yet efficient defense method from the geometric constraint perspective. Specifically, we first propose an M-similarity metric to shrink variances of intraclass features. Intuitively, better geometric conditions of feature space can bring lower misclassification probability (MP). Therefore, we derive the optimal geometric constraints of anchors within each category from the overall MP (OMP) with theoretical guarantees. Due to the nonconvex characteristic of the optimal geometric condition, it is hard to satisfy the traditional optimization process. To this end, we regard such geometric constraints as manifold optimization processes in the Stiefel manifold, thus naturally avoiding the above challenges. Experimental results demonstrate that our method can significantly improve robustness compared with baselines, while retaining the excellent performance on normal examples.

Joint Hybrid Beamforming Design for Millimeter Wave Amplify-and-Forward Relay Communication Systems

Hybrid beamforming (HBF) has been regarded as one of the most promising technologies in millimeter Wave (mmWave) communication systems. In order to guarantee the communication quality in non-line-of-sight (NLOS) scenarios, joint HBF design for the mmWave amplify-and-forward (AF) relay communication system is studied in this paper. The ideal case is first considered where the mmWave half-duplex (HD) AF relay system operates with channel state information (CSI) accurately known. In order to tackle the non-convex problem, a manifold optimization (MO)-based alternating optimization algorithm is proposed, where an optimization problem containing only constant modulus constraints in Euclidean space can be converted to an unconstrained optimization problem in a Riemann manifold. Furthermore, considering more practical cases with estimation errors of CSI, we investigate the robust joint HBF design with the system operating in full-duplex (FD) mode to obtain higher spectral efficiency (SE). A null-space projection (NP) based self-interference cancellation (SIC) algorithm is developed to attenuate the self-interference (SI). Different from the traditional SI suppression algorithm, there’s no limit on the number of RF chains. Numerical results reveal that our proposed algorithms has a good convergence and can effectively deal with the influence of different CSI estimation errors. A significant performance improvement can be achieved in contrast with other approaches.

Multi-task collaborative method based on manifold optimization for automated test case generation based on path coverage

Automated test case generation based on path coverage is not only a large-scale black-box optimization problem, but also a key scientific problem in software automatic testing technology. Evolutionary algorithms and other search-based algorithms are representative methods for this problem. However, existing research mainly focuses on the multi-function case, where generating test cases for multiple functions is difficult due to the combinatorial explosion of the path number. In this paper, we propose a multi-task collaborative method based on manifold optimization by considering the topological manifold relationship between the test case space (decision space) and the program path space (target space). This method achieves the goal of collaborative optimization for different function coverage tasks by coordinating the allocation of computing resources and knowledge transfer mechanisms among them. To verify the effectiveness of the proposed method, we compare it with general solution methods for single-function automated test case generation based on path coverage, such as the manifold-inspired search-based algorithm. The experimental results show that the proposed method outperforms the compared single-function optimization algorithms especially on programs with strong coding similarities. This study verifies the feasibility of collaborative optimization methods for solving large-scale black-box optimization problems, such as the automated test case generation based on path coverage, and expands their application scenarios.

Efficiently Refining Beampattern in FDA-MIMO Radar via Alternating Manifold Optimization for Maximizing Signal-to-Interference-Noise Ratio

Joint transceiver beamforming is a fundamental and crucial research task in the field of signal processing. Despite extensive efforts made in recent years, the joint transceiver beamforming of frequency diverse array (FDA)-based multiple-input and multiple-output (MIMO) radar has received relatively less attention and is confronted with some tricky challenges, such as range–angle decoupling and the interaction between multiple performance metrics. In this paper, we initially derive the generalized ambiguity function of the FDA-MIMO radar to explore the intrinsic correlation between its waveform design and resolution. Following that, the joint beamforming optimization is formulated as a nonconvex bivariate quadratic programming problem (NBQP) with the aim of maximizing the Signal-to-Interference-Noise Ratio (SINR) of the FDA-MIMO radar system. Building upon this, we introduce an innovative alternating manifold optimization with nested iteration (AMO-NI) algorithm to address the NBQP. By incorporating manifold optimization into iterative updates of transmit waveform and receiving filter, the AMO-NI algorithm considers the interdependencies among the optimization variables. The algorithm efficiently and expeditiously finds global optimum solutions within a finite number of iterations. Compared with other methods, our approach yields a superior beampattern and higher SINR.

Non-convex feature selection based on feature correlation representation and dual manifold optimization

The existing feature selection algorithms often utilize local structure of data, but do not fully mine internal structure and ignore potential correlation information between samples. To address the problems and fully utilize manifold information of data, this paper proposes non-convex feature selection based on feature correlation representation and dual manifold optimization (FDNFS). Firstly, FDNFS constructs feature graph of original data, which can obtain feature correlation representation to represent the interconnection information. Based on the obtained interconnection information, FDNFS unifies feature correlation representation learning and feature selection through feature transformation matrix, so that the interconnection information between data guides feature selection. Secondly, to make multivariate frameworks guide feature selection, FDNFS introduces self-representation on the improved sparse regression model. Using self-representation can make basis matrix and reconstruction coefficient matrix reconstruct original data more accurately. Next, in order to preserve local structure information abundantly, FDNFS has two-part manifold regularization on the pseudo-label matrix in sparse regression model and the reconstructed coefficient matrix in self-representation framework. This can fully use the manifold information of data. In addition, FDNFS imposes the non-convex constraints. It can ensure the sparsity of feature selection matrix. In turn, this can select features with lower redundancy, and then select a better feature subset. Finally, this paper adopts an iterative optimization method. FDNFS is compared with nine algorithms on seven datasets. The clustering results reflect better performance of FDNFS.

Phase-only beampattern synthesis for maximizing mainlobe gain via Riemannian Newton method

Beampattern synthesis with phase-only weights is extensively utilized in phased-array systems due to the virtue of low-cost and high power efficiency. It is always a non-convex optimization problem having constant modulus constraints (CMCs) and the performance significantly depends on the employed solvers. This paper discusses the phase-only beampattern synthesis for maximizing the mainlobe gain with the constraints on the mainlobe ripple and the relative sidelobe level. As CMC is equivalent to a complex circle manifold, the proposed beampattern synthesis is considered as a manifold optimization problem, and then decomposed into several subproblems under the framework of manifold alternating direction method of multipliers (ADMM). In particular, the subproblem for updating phase-only weights is efficiently tackled by a second-order Riemannian Newton method, which has faster convergence speed and no requirement on line search compared to widely-used first-order Riemannian manifold methods. The explicit convergence condition is derived and the computational complexity is also analyzed. Numerical results show that the proposed method has better performance on the mainlobe gain and sidelobe control accuracy, or less computational cost compared to several representative approaches, such as convex relaxation, standard ADMM, Riemannian gradient descent-based ADMM and Riemannian conjugate gradient methods.

Usage-aware representation learning for critical information identification in transportation networks

Extracting meaningful information from noisy high-dimensional data is attracting increasing attention as richer and higher resolution data is being collected and used for transportation system planning and management purposes. Discovering critical information via effective data representation learning not only helps reduce data dimension, it also enables a deeper understanding of the underlying properties of noisy data, which could then lead to better planning and operations decisions. In this study, we present a new perspective that, unlike most existing approaches in the general data science literature, the design of data representation should go beyond the data itself; it should incorporate an understanding of how the data is used in the domain-specific applications. We further argue that this design philosophy is particularly important for transportation data because of the high spatial correlations of transportation data brought by network interdependence. We propose a usage-aware representation learning framework by incorporating the information loss for downstream application into the data encoding-decoding process. The proposed approach is formulated as a Stiefel manifold optimization problem. The effectiveness of the proposed framework is demonstrated in two network applications: modeling transportation network flows and estimating network-level vehicular emissions. The performance of the learned representation from our approach is compared with existing approaches using multiple evaluation context, including data reconstruction quality, clustering, anomaly detection, and critical information identification, through case studies implemented in Sioux Falls, Boston, and San Jose networks. The good performance of our approach consistently observed in those experiments indicates the importance of incorporating the downstream data usage in the process of data representation learning.