Target Subspace Research Articles

A subspace‐adaptive weights cubature method with application to the local hyperreduction of parameterized finite element models

AbstractThis article is concerned with quadrature/cubature rules able to deal with multiple subspaces of functions, in such a way that the integration points are common for all the subspaces, yet the (nonnegative) weights are tailored to each specific subspace. These subspace‐adaptive weights cubature rules can be used to accelerate computational mechanics applications requiring efficiently evaluating spatial integrals whose integrand function dynamically switches between multiple pre‐computed subspaces. One of such applications is local hyperreduced‐order modeling (HROM), in which the solution manifold is approximately represented as a collection of basis matrices, each basis matrix corresponding to a different region in parameter space. The proposed optimization framework is discrete in terms of the location of the integration points, in the sense that such points are selected among the Gauss points of a given finite element mesh, and the target subspaces of functions are represented by orthogonal basis matrices constructed from the values of the functions at such Gauss points, using the singular value decomposition (SVD). This discrete framework allows us to treat also problems in which the integrals are approximated as a weighted sum of the contribution of each finite element, as in the energy‐conserving sampling and weighting method of C. Farhat and co‐workers. Two distinct solution strategies are examined. The first one is a greedy strategy based on an enhanced version of the empirical cubature method (ECM) developed by the authors elsewhere (we call it the subspace‐adaptive weights ECM, SAW‐ECM for short), while the second method is based on a convexification of the cubature problem so that it can be addressed by linear programming algorithms. We show in a toy problem involving integration of polynomial functions that the SAW‐ECM clearly outperforms the other method both in terms of computational cost and optimality. On the other hand, we illustrate the performance of the SAW‐ECM in the construction of a local HROMs in a highly nonlinear equilibrium problem (large strains regime). We demonstrate that, provided that the subspace‐transition errors are negligible, the error associated to hyperreduction using adaptive weights can be controlled by the truncation tolerances of the SVDs used for determining the basis matrices. We also show that the number of integration points decreases notably as the number of subspaces increases, and that, in the limiting case of using as many subspaces as snapshots, the SAW‐ECM delivers rules with a number of integration points only dependent on the intrinsic dimensionality of the solution manifold and the degree of overlapping required to avoid subspace‐transition errors. The Python source codes of the proposed SAW‐ECM are openly accessible in the public repository https://github.com/Rbravo555/localECM.

NOODLE: Joint Cross-View Discrepancy Discovery and High-Order Correlation Detection for Multi-View Subspace Clustering

Benefiting from the effective exploration of the valuable topological pair-wise relationship of data points across multiple views, multi-view subspace clustering (MVSC) has received increasing attention in recent years. However, we observe that existing MVSC approaches still suffer from two limitations that need to be further improved to enhance the clustering effectiveness. Firstly, previous MVSC approaches mainly prioritize extracting multi-view consistency, often neglecting the cross-view discrepancy that may arise from noise, outliers, and view-inherent properties. Secondly, existing techniques are constrained by their reliance on pair-wise sample correlation and pair-wise view correlation, failing to capture the high-order correlations that are enclosed within multiple views. To address these issues, we propose a novel MVSC framework via joi N t cr O ss-view discrepancy disc O very an D high-order corre L ation d E tection ( NOODLE ), seeking an informative target subspace representation compatible across multiple features to facilitate the downstream clustering task. Specifically, we first exploit the self-representation mechanism to learn multiple view-specific affinity matrices, which are further decomposed into cohesive factors and incongruous factors to fit the multi-view consistency and discrepancy, respectively. Additionally, an explicit cross-view sparse regularization is applied to incoherent parts, ensuring the consistency and discrepancy to be precisely separated from the initial subspace representations. Meanwhile, the multiple cohesive parts are stacked into a three-dimensional tensor associated with a tensor-Singular Value Decomposition (t-SVD) based weighted tensor nuclear norm constraint, enabling effective detection of the high-order correlations implicit in multi-view data. Our proposed method outperforms state-of-the-art methods for multi-view clustering on six benchmark datasets, demonstrating its effectiveness.

Model robustness for feedback stabilization of open quantum systems

This paper builds upon and expands the findings presented in Liang et al. (2021). Our focus lies in scenarios where initial states and model parameters remain unknown. In contrast to prior research, we consider multiple measurement channels, addressing the challenge of global exponential stabilization towards a chosen target subspace. Under quantum non-demolition conditions, our analysis establishes essential tools for achieving feedback stabilization. Furthermore, we explore the utilization of a simplified filter as a viable alternative to full state estimator. While the effectiveness of this simplified filter was numerically examined in Cardona et al. (2020), our paper offers a comprehensive proof of its applicability in feedback stabilization. Furthermore, our analysis may serve as an inspiration for demonstrating the validation of the robust feedback stabilization through generic approximate filters.

Adaptive graph-guided joint soft clustering and distribution alignment for cross-load and cross-device rotating machinery fault transfer diagnosis

Domain adaptation (DA) is an effective solution for addressing the domain shift problem. However, existing DA techniques usually directly match the distributions of the data in the original feature space, where some of the features may be distorted by a large domain shift. Besides, geometric and clustering structures of the data, which play a significant role in revealing hidden failure patterns, are not considered in traditional DA methods. To tackle the above issues, a new joint soft clustering and distribution alignment with graph embedding (JSCDA-GE) method is proposed. Specifically, weighted subspace alignment is proposed to align bases of source and target subspaces by combining instance reweighting and subspace alignment strategies. Then, JSCDA-GE formulates an objective function by incorporating dynamic distribution alignment, soft large margin clustering, and GE in a unified structural risk minimization framework. Ultimately, JSCDA-GE aims to learn a generalization classifier for fault diagnosis. Its effectiveness and superiority have been confirmed through 36 tasks on 2 bearing databases.

A generic impulsive controller for Hamiltonian time-independent systems

In a recent work Briozzo (2021) the author introduced an impulsive Floquet controller for periodic orbits in time-periodic Hamiltonian systems, which expresses the control law analytically in terms of the linearized dynamics about the reference orbit and makes full use of the center manifold enhancing performance by minimizing the energy of the actual orbit in the co-moving frame of the reference one. The purpose of the present work is to introduce an equivalent controller for Hamiltonian linear time-periodic systems obtained by linearization of a general time-independent Hamiltonian one about a periodic orbit, so incorporating the presence of a shear manifold associated to energy conservation and the ensuing non-isolation of periodic orbits. Like its preceding version, the controller defines a target subspace akin to the sliding surface of sliding mode controllers, onto which the system state vector is repeatedly sent by control impulses, and is generic in the sense that the target subspace and the control law are explicitly given for any possible decomposition of state space into a shear manifold and saddle, centre, or saddle-focus ones.

Robust Tracking of Multiple Targets Subspace Based on Distributed Array Networks

Robust subspace tracking is a real-time solution for suppressing harsh interference and estimating the target subspace in complex electromagnetic environments. In this paper, a robust and decentralized subspace tracking method is proposed. The multi-sensor array is divided into a number of nodes, each attached with a processor and no central processing unit (CPU) is deployed. In order to reduce the impact of burst pulse, a robust real-time update algorithm of the subspace is designed through the weighted least squares method. The optimization model established in this paper is robust to synchronization error. Then a subspace real-time update algorithm is proposed based on the average consensus (AC) method that integrates the information of distributed arrays. The computational complexity and convergence properties of the proposed algorithm are also investigated. Simulation results show that the proposed approach converges to the subspace estimation error by an order of magnitude compared with the single-node algorithm.

Deep Learning–based Dynamic User Alignment in Social Networks

Academics and businesses are paying intense attention to social network alignment, which centers various social networks around their shared members. All studies to date treat the social network as static and ignore its innate dynamism. In reality, an individual's discriminative pattern is embedded in the dynamics of social networks, and this information may be used to improve social network alignment. This study finds that these dynamics can reveal more apparent patterns better suited to lining up the social web of things (SWoT). The correlation between the user structure and attributes for each social network must be maintained to combine the binary dynamics and make the original synthetic embedding representation. Finally, the initial embedding of each network is projected to a target subspace as part of the semi-supervised spatial transformation learning process. The Dynamic Social Network Alignment approach outperforms the current mainstream algorithm by 10% in this article's extensive series of trials using real-world datasets. The findings of this study show that this alignment of enormous networks addresses the volume, variety, velocity, and veracity (or 4Vs) of vast networks. To improve the efficacy and resilience of an adversarial network alignment, adversarial learning techniques can be applied. The results show that the model with structure, attribute, and time information performs the best, while the model without attribute information comes in second, the model without time information performs mediocrely, and the model without structure information performs the worst.

A unified framework for visual domain adaptation with covariance matching

In the field of Machine Learning, it is widely acknowledged that training and test data should ideally stem from the same source and distribution. However, in the real world, this is not always feasible. Domain Adaptation (DA) techniques address this issue by adapting a classifier trained on annotated source domain data on unannotated target domain data while minimizing the impact of domain shift. Many recent DA approaches concentrate on learning a latent feature space that remains invariant to domain shift by mitigating various statistical and geometrical divergences. Although these methods have demonstrated effectiveness, they frequently overlook a crucial aspect of learning a domain-invariant discriminative latent feature space across diverse domains. To address this issue, we propose a novel framework called Unified Framework for Visual Domain Adaptation with Covariance Matching (UDACM) that aims to learn a domain invariant and class discriminative latent feature space by incorporating multiple objectives such as maximizing target domain variance, minimizing distribution and subspace divergence, performing manifold learning, preserving discriminative information of both the source and target domains, and measuring and matching covariance simultaneously. In our proposed framework, the measuring and matching of covariance play a crucial role in ensuring the learning of discriminative latent feature space by aligning the within-class and between-class covariance matrices of the source and target domains simultaneously. Detailed experiments demonstrate the outperformance of UDACM on baseline datasets such as CMU-PIE, Office+Caltech10, USPS+MNIST, VLCS, and Office–Home, compared to various established primitive, shallow, and deep domain adaptation methods on several image classification tasks.

Joint optimization of FDA-MIMO antenna selection and frequency offset to maximize SINR

The structured sparse multiple-input multiple-output frequency diverse array (FDA-MIMO) radar has range, angle estimation, and resolution advantages. However, the structured sparse array is not the optimal array structure with the max output signal-to-interference-noise ratio (SINR). In order to obtain the optimal FDA-MIMO structure, this paper maximizes the output SINR of the array by optimizing the array antenna selection and frequency offset. Because there is a coupling relationship between frequency offset and array antenna selection, and it is difficult to optimize them simultaneously, we divide the problem into two subproblems. According to the spatial separation coefficient (SCC), we propose the array antenna selection method using the angle of target and interference subspace and the frequency offset optimization approach using the constant modulus beamforming idea and particle swarm optimization algorithm. Then we join the two approaches to conduct alternate iterative optimization. By comparing the optimum FDA-MIMO with other structures of FDA-MIMO, we confirm the effectiveness and superiority of the optimum FDA-MIMO.

Fast uncertainty reduction of chemical kinetic models with complex spaces using hybrid response-surface networks

Response-surface (RS) surrogate approaches permit efficient inverse uncertainty quantification (UQ) of combustion kinetic models, wherein the uncertainty of reaction rates is reduced from observed targets. For kinetic models with parameters characterized by large uncertainty factors, strong nonlinearities, and reaction couplings (e.g., reduced mechanisms of real fuels; such models are referred to be “complex” in this work), the global RS is difficult to approximate, precluding conventional surrogate approaches. This paper proposes a framework that is extendable to such systems, termed Hybrid Response Surface Networks followed by a Stochastic Gradient Descent Ensemble (HRSN-SGDE). This technique focuses on mapping the local RS of just the uncertain spaces in the vicinity of the observed target, referred to as the rate target subspace. Two neural network surrogates are considered: a classifier that predicts the probability of data residing in the rate target subspace and a local RS surrogate which maps the RS of this subspace. A hybrid surrogate loss function is then defined using these surrogates to optimize uncertain rates repeatedly to get an ensemble of solutions representing the constrained rate space. HRSN-SGDE is demonstrated on a complex jet fuel model developed using the hybrid chemistry (HyChem) approach with a low temperature chemistry sub-model using a series of ignition delay times as targets. Results show that the method's local RS objective enables efficient and accurate construction of the surrogates through active learning-based sampling. Also, the unique formulation of the surrogate loss function enables optimization that is robust to suboptimal local minima and faster than evolutionary algorithms by several orders of magnitude. It is shown that HRSN-SGDE method is highly efficacious and suitable to conducting inverse UQ on such complex kinetic models.

Multi-Source Discriminant Subspace Alignment for Cross-Domain Speech Emotion Recognition

Cross-domain speech emotion recognition (SER) is an effective strategy to improve the generalization ability of emotion classification models, which is an important research direction in speech signal processing. However, since the speech signals are non-stationary, it is difficult to train a robust classifier from single-source emotional corpus. To solve this shortcoming, we propose a novel method named multi-source discriminant subspace alignment (MDSA) for cross-domain SER. In MDSA, we first conduct linear discriminant analysis (LDA) in the multi-source domain. Then, the instances in the multi-source discriminant subspace are used to linearly reconstruct the instances in the target subspace. At the same time, the reconstruction contribution of each source discriminant subspace is determined by adaptive weights. Furthermore, the multi-source discriminant subspace is aligned by reducing the loss between projections, which can make our model more robust. In this way, MDSA considers both the alignment of cross-domain data distribution and the structural information of cross-domain instances. Finally, extensive experiments are conducted on five standard emotional corpora, i.e., Berlin, IEMOCAP, CVE, EMOVO, and TESS, and the results demonstrate the proposed MDSA is superior to several state-of-the-art transfer learning algorithms in terms of performance. The codes are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/shaokai1209/MDSA.</uri>

Spectral–Spatial Prototype Learning-Based Nearest Neighbor Classifier for Hyperspectral Images

Due to the Hughes phenomenon, hyperspectral image (HSI) classification under small sample size situation is still a key challenging problem. To alleviate this issue, we propose a novel spectral–spatial prototype learning-based nearest neighbor classifier (SSPLNN) for HSI in this article. The local spectral–spatial neighbor set is first constructed for each sample based on both spectral similarity and spatial structural context to accurately explore the local spectral–spatial information. Then, a spectral–spatial prototype learning model is designed to learn a set of spectral–spatial prototypes, which can optimally utilize both the similarity and variance of samples within each spectral–spatial set and excavate the unseen spectral–spatial variations. The learned spectral–spatial prototypes offer more complementary information to improve the classification accuracy remarkably under small sample size situation. In addition, a linear discriminative projection is simultaneously learned to make each test local spectral–spatial set to be optimally classified to the same class with its nearest neighbor (NN) spectral–spatial prototype set in the projected target subspace. Finally, the NN classifier based on measuring the minimum geometric distance between the projected test spectral–spatial set and the projected spectral–spatial prototype sets is employed to determine the label. Experimental results demonstrate that the proposed SSPLNN method outperforms several well-known classification methods by a large margin on three widely analyzed HSI datasets.

Acoustic Shooting and Bounce Ray Method for Calculating Echoes of Complex Underwater Targets

The acoustic scattering characteristics of a target are of great significance to the design of underwater acoustic detection systems. With the improvement in underwater weapon detection ability, the precision and accuracy of underwater target echo characteristic simulations are required to be higher and higher. The traditional underwater target simulation based on bright spot can no longer meet the needs of an underwater acoustic detection system for targeting fine feature recognition. This paper proposes a calculation using the fine complex underwater target echo bounce beam line method, in addition to the establishment of a bandwidth signal time domain calculation model and the integral dimension reduction to accelerate the algorithm on the basis of thorough target subspace division, combined with the geometrical acoustics method (GA) and physical acoustics (PA) for the pipeline space beam propagation tracking and aperture sound field to solve and realize the acoustic scattering characteristic calculation of a complex underwater target. Finally, the proposed method was verified by the Benchmark standard submarine. The accuracy and computational efficiency of the PA acceleration method are given, and the integrity of the target information calculated by the method is verified by acoustic ISAR imaging analysis. The simulation results show that the pipeline method of bouncing an acoustic beam is suitable for the simulation of complex underwater, target-wide band fine echoes.

Fast trajectory planning and control of a lab-scale 3D gantry crane for a moving target in an environment with obstacles

In this work, the real-time optimal trajectory planning, together with a cascaded tracking controller, is presented for a three-dimensional (3D) gantry crane in an environment with static obstacles and a dynamically moving target considering dynamic constraints and control input limits. State-of-the-art trajectory optimization-based approaches require long computation times and cannot quickly respond to changes in the target state. The focus of this paper lies on a novel trajectory planning algorithm, which consists of two steps. First, an offline trajectory planner is implemented to compute a time-optimal, collision-free, and dynamically feasible trajectory database that connects all possible initial states of the gantry crane from a predefined starting subspace to the target states in a target subspace. Second, based on linear constrained quadratic programming, the online trajectory replanner makes use of this trajectory database to generate an optimal trajectory in real time that accounts for all changes in the target state. Additionally, a trajectory tracking controller is developed to take into account the dynamic constraints of the gantry crane and to compensate for possible model inaccuracies, disturbances, and other non-modeled effects. Both simulation and experimental results are presented to demonstrate the performance of the proposed trajectory (re)planning algorithm and the control concept.

Robust STAP Detection Based on Volume Cross-Correlation Function in Heterogeneous Environments

The performance of moving target detection in heterogeneous environments with the traditional space-time adaptive processing (STAP) may degrade when the real clutter environments deviate from the prior assumption on the clutter distribution. In this letter, a new detector for STAP applications based on volume cross-correlation function (VCF), namely VCF-STAP, is proposed to achieve robust performance of moving target detection in heterogeneous environments. In the new VCF-STAP, the VCF is used to form a distance measure between the sample signal subspace and the target subspace without modeling the clutter distribution. Then, a new robust STAP detection statistic is constructed using this distance measure. Simulation and experimental results show that the proposed VCF-STAP achieves robust performance of moving target detection in heterogeneous environments, especially it achieves much superior detection performance compared with existing STAP methods when the real clutter environments do not satisfy their prior assumptions. Besides, it is also shown that VCF-STAP has the constant false alarm rate (CFAR) property.

A Multistage Framework With Mean Subspace Computation and Recursive Feedback for Online Unsupervised Domain Adaptation.

In this paper, we address the Online Unsupervised Domain Adaptation (OUDA) problem and propose a novel multi-stage framework to solve real-world situations when the target data are unlabeled and arriving online sequentially in batches. Most of the traditional manifold-based methods on the OUDA problem focus on transforming each arriving target data to the source domain without sufficiently considering the temporal coherency and accumulative statistics among the arriving target data. In order to project the data from the source and the target domains to a common subspace and manipulate the projected data in real-time, our proposed framework institutes a novel method, called an Incremental Computation of Mean-Subspace (ICMS) technique, which computes an approximation of mean-target subspace on a Grassmann manifold and is proven to be a close approximate to the Karcher mean. Furthermore, the transformation matrix computed from the mean-target subspace is applied to the next target data in the recursive-feedback stage, aligning the target data closer to the source domain. The computation of transformation matrix and the prediction of next-target subspace leverage the performance of the recursive-feedback stage by considering the cumulative temporal dependency among the flow of the target subspace on the Grassmann manifold. The labels of the transformed target data are predicted by the pre-trained source classifier, then the classifier is updated by the transformed data and predicted labels. Extensive experiments on six datasets were conducted to investigate in depth the effect and contribution of each stage in our proposed framework and its performance over previous approaches in terms of classification accuracy and computational speed. In addition, the experiments on traditional manifold-based learning models and neural-network-based learning models demonstrated the applicability of our proposed framework for various types of learning models.

A generic impulsive controller for hamiltonian linear time-periodic systems

This work introduces an impulsive controller for Hamiltonian linear time-periodic systems obtained by linearization of a general time-periodic Hamiltonian one about a periodic orbit. The controller defines a target subspace akin to the sliding surface of sliding mode controllers, onto which the system state vector is periodically sent by control impulses, and is generic in the sense that the target subspace and the control law are explicitly given for any possible decomposition of state space into saddle, centre, or saddle-focus sub-manifolds. The novel treatment of the center manifold minimizes the system energy on it ensuring damping of oscillatory motions, which is proved crucial for controllability.

Smart image recognition system based on machine vision

This paper proposes an efficient and accurate method of two-dimensional code recognition for industrial actual projects, and develops a high-speed and batch two-dimensional code recognition system based on machine vision. Firstly, according to the position of the QR code in the target subspace, a method to locate the region of interest of each QR code by using geometric relationship and batch processing QR code is proposed. On this basis, Gaussian noise is added to simulate the possible noise in production practice, and the anti-noise ability of the system is evaluated. Finally, the relationship between system recognition rate and QR code movement speed is analyzed and the experimental results are compared. The experimental results show that the system can meet the requirement of real-time online detection.

Orthogonal Subspace Projection Target Detector for Hyperspectral Anomaly Detection

Orthogonal subspace projection (OSP) is a versatile hyperspectral imaging technique which has shown great potential in dimensionality reduction, target detection, spectral unmixing, etc. However, due to its inherent requirement of prior target knowledge, OSP has not been explored in anomaly detection. This article takes advantage of an unsupervised OSP-based algorithm, automatic target generation process (ATGP), and a recently developed OSP-go decomposition (OSP-GoDec) along with data sphering (DS) to make OSP applicable to anomaly detection. Its idea is to implement ATGP on the background (BKG) and target subspaces constructed from the low-rank matrix L and sparse matrix S generated by OSP-GoDec to derive an OSP-based anomaly detector (OSP-AD). In particular, OSP-AD also includes DS to remove BKG interference from the target subspace so as to enhance anomaly detection. Surprisingly, operating data samples on different constructions of the BKG subspace and the target subspace yields various versions of OSP-AD. Experiments show that given an appropriate construction of the BKG subspace and the target subspace, OSP-AD can be shown to outperform existing anomaly detectors including Reed-Xiaoli anomaly detector and collaborative representation-based anomaly detector (CRD).

Forbidden subspaces for level-1 quantum approximate optimization algorithm and instantaneous quantum polynomial circuits

We present a thorough investigation of problems that can be solved exactly with the level-1 Quantum Approximate Optimization Algorithm (QAOA). To this end we implicitly define a class of problem Hamiltonians that employed as phase separator in a level-1 QAOA circuit provide unit overlap with a target subspace spanned by a set of computational basis states. For one-dimensional target subspaces we identify instances within the implicitly defined class of Hamiltonians for which Quantum Annealing (QA) and Simulated Annealing (SA) have an exponentially small probability to find the solution. Consequently, our results define a first demarcation line between QAOA, QA and SA, and highlight the fundamental differences between an interference-based search heuristic such as QAOA and heuristics that are based on thermal and quantum fluctuations like SA and QA respectively. Moreover, for two-dimensional solution subspaces we are able to show that the depth of the QAOA circuit grows linearly with the Hamming distance between the two target states. We further show that there are no genuine solutions for target subspaces of dimension higher than $2$ and smaller than $2^n$. We also transfer these results to Instantaneous Quantum Polynomial (IQP) circuits.