Regularization Constraints Research Articles

Consensus Multi-view subspace clustering based on Graph Filtering

Multi-view subspace clustering has attracted an increasing amount of attention because it can capture information from multiple views as well as avoid the curse of dimensionality. The existing methods cannot simultaneously achieve both the effective reduction of negative impact of noise and the high-quality consensus representation within a unified framework. To handle this issue, this paper proposes a novel Consensus Multi-view subspace clustering based on Graph Filtering, named CMGF. First, CMGF learns a latent data space by using view-specific k-order filters to reduce noise and redundant information. Then, CMGF obtains the spectral embedding matrix of each view by imposing graph regularization constraint. Ultimately, to generate a consensus representation, we integrate the spectral embedding matrix of each view by using an adaptively weighted scheme. Experimental results on ten real-word datasets show that the proposed method outperforms state-of-the-art baselines significantly. Experiments also demonstrate that the graph filtering employed in CMGF enhances the smoothness of the data and improves the distinctiveness of the cluster structure.

Robust image segmentation and bias field correction model based on image structural prior constraint

In this paper, we propose an advanced variational model for image segmentation and bias correction. In contrast to the majority of existing level set segmentation models that only consider illumination bias fields, we additionally consider the impact of image reflectance on segmentation accuracy. Our method is capable of effectively segmenting images with blurry edge structures affected by non-uniform illumination. In order to enhance segmentation efficiency, we directly segment the underlying structures of the images, construct spatial prior and apply adaptive regularization constraints on the structural component. Therefore, in the process of segmentation, the proposed algorithm can accurately identify object boundaries without being affected by the environment. Besides, the GL operator is applied to enhance the robustness of the model against noise. Furthermore, we use the alternating direction method of multipliers and the operator splitting algorithm for numerical solution. The experimental results obtained from various sorts of images illustrate that our model outperforms many leading-edge level set models with regard to robustness, corrected results and accuracy.

Isometric Immersions and the Waving of Flags.

In this article we propose a novel geometric model to study the motion of a physical flag. In our approach, a flag is viewed as an isometric immersion from the square with values in satisfying certain boundary conditions at the flag pole. Under additional regularity constraints we show that the space of all such flags carries the structure of an infinite dimensional manifold and can be viewed as a submanifold of the space of all immersions. In the second part of the article we equip the space of isometric immersions with its natural kinetic energy and derive the corresponding equations of motion. This approach can be viewed in a spirit similar to Arnold's geometric picture for the motion of an incompressible fluid.

On sparse regression, Lp‐regularization, and automated model discovery

AbstractSparse regression and feature extraction are the cornerstones of knowledge discovery from massive data. Their goal is to discover interpretable and predictive models that provide simple relationships among scientific variables. While the statistical tools for model discovery are well established in the context of linear regression, their generalization to nonlinear regression in material modeling is highly problem‐specific and insufficiently understood. Here we explore the potential of neural networks for automatic model discovery and induce sparsity by a hybrid approach that combines two strategies: regularization and physical constraints. We integrate the concept of Lp regularization for subset selection with constitutive neural networks that leverage our domain knowledge in kinematics and thermodynamics. We train our networks with both, synthetic and real data, and perform several thousand discovery runs to infer common guidelines and trends: L2 regularization or ridge regression is unsuitable for model discovery; L1 regularization or lasso promotes sparsity, but induces strong bias that may aggressively change the results; only L0 regularization allows us to transparently fine‐tune the trade‐off between interpretability and predictability, simplicity and accuracy, and bias and variance. With these insights, we demonstrate that Lp regularized constitutive neural networks can simultaneously discover both, interpretable models and physically meaningful parameters. We anticipate that our findings will generalize to alternative discovery techniques such as sparse and symbolic regression, and to other domains such as biology, chemistry, or medicine. Our ability to automatically discover material models from data could have tremendous applications in generative material design and open new opportunities to manipulate matter, alter properties of existing materials, and discover new materials with user‐defined properties.

Multi-constraint non-negative matrix factorization for community detection: orthogonal regular sparse constraint non-negative matrix factorization

Community detection is an important method to analyze the characteristics and structure of community networks, which can excavate the potential links between nodes and further discover subgroups from complex networks. However, most of the existing methods only unilaterally consider the direct link topology without comprehensively considering the internal and external characteristics of the community as well as the result itself, which fails to maximize the access to the network information, thus affecting the effectiveness of community detection. To compensate for this deficiency, we propose a new community detection method based on multi-constraint non-negative matrix factorization, named orthogonal regular sparse constraint non-negative matrix factorization (ORSNMF). Based on the network topology, the ORSNMF algorithm models the differences of the outside of the community, the similarities of the nodes inside the community, and the sparseness of the community membership matrices at the same time, which together guides the iterative learning process to better reflect the underlying information and inherent attributes of the community structure in order to improve the correct rate of dividing subgroups. An algorithm with convergence guarantee is also proposed to solve the model, and finally a large number of comparative experiments are conducted, and the results show that the algorithm has good results.

Multi-label Feature Selection based on Label-specific features and Manifold Learning

Each instance in multi-label data is associated with multiple labels, and there are irrelevant or redundant features in its feature space, which leads to the performance degradation of multi-label learning algorithms. Multi-label feature selection selects representative features from the feature space to improve the accuracy of the model. Due to the high cost of labels and the difficulty of data collection, there will be some missing labels in the data set, which affects the accuracy of feature selection. To solve this problem, a multi-label feature selection algorithm based on label-specific features and manifold learning is proposed. The algorithm uses the linear relationship between the features and labels in known label samples to build a linear regression model for learning label-specific features. By using the nonlinear relation between instances and the nonlinear relation between features, we can precisely learn the label-specific features. We use the Laplacian feature mapping method to construct the instance manifold model and the feature manifold model, which are also used as the regular term constraint weight matrix. The final model can not only complete the missing labels, but also select sparse and representative features. The feature selection is carried out by analyzing the weight of the feature given by the final model. Experiments were conducted to verify the effectiveness of the proposed algorithm under different label deletion rates on four evaluation indexes.

Alternating projection combined with fast gradient projection (FGP-AP) method for intensity-only measurement optical diffraction tomography in LED array microscopy.

Optical diffraction tomography (ODT) is a powerful label-free measurement tool that can quantitatively image the three-dimensional (3D) refractive index (RI) distribution of samples. However, the inherent "missing cone problem," limited illumination angles, and dependence on intensity-only measurements in a simplified imaging setup can all lead to insufficient information mapping in the Fourier domain, affecting 3D reconstruction results. In this paper, we propose the alternating projection combined with the fast gradient projection (FGP-AP) method to compensate for the above problem, which effectively reconstructs the 3D RI distribution of samples using intensity-only images captured from LED array microscopy. The FGP-AP method employs the alternating projection (AP) algorithm for gradient descent and the fast gradient projection (FGP) algorithm for regularization constraints. This approach is equivalent to incorporating prior knowledge of sample non-negativity and smoothness into the 3D reconstruction process. Simulations demonstrate that the FGP-AP method improves reconstruction quality compared to the original AP method, particularly in the presence of noise. Experimental results, obtained from mouse kidney cells and label-free blood cells, further affirm the superior 3D imaging efficacy of the FGP-AP method.

A regularized constrained two-stream convolution augmented Transformer for aircraft engine remaining useful life prediction

Remaining Useful Life (RUL) prediction is of great significance for maintaining the reliability and safety of industrial equipment. To address the challenges faced by existing methods in simultaneously extracting local and global degradation information from monitoring data. This paper proposes a Two-Stream Convolution Augmented Transformer (TACT) model based on L2 regularization constraint. Specifically, we design the parallel multi-scale Convolution Neural Network (CNN) and Transformer module to combine the local modeling ability of CNN and the global modeling ability of Transformer to improve the overall architecture of RUL prediction model. Moreover, the two-stream network based on the parallel structure also realizes the synchronous extraction of different time steps and sensor features in the sequence. Then, in the process of model training, the prediction reliability constraint is fused, the delay prediction constraint term is introduced, and the L2 regularization loss function is constructed. Finally, extensive experiments on the commercial modular aero-propulsion system simulation (C-MAPSS) show that our model provides competitive performance in terms of Root-Mean-Square Error (RMSE) and Score metrics. Compared to the state-of-the-art method based on Recurrent Neural Network (RNN) or CNN and its variants, Score is reduced by at least 2.71% and RMSE by at least 3.13%. Compared to the Transformer-based improved method, the Score is decreased by at least 4.54% and the RMSE is decreased by at least 2.78%. The effectiveness of the proposed method is demonstrated.

Aberration pre-correction for a simple optical system of HMDs.

Head-mounted displays (HMDs) are becoming increasingly popular as a crucial component of virtual reality (VR). However, contemporary HMDs enforce a simple optical structure due to their constrained form factor, which impedes the use of multiple lens elements that can reduce aberrations in general. As a result, they introduce severe aberrations and imperfections in optical imagery, causing visual fatigue and degrading the immersive experience of being present in VR. To address this issue without modifying the hardware system, we present a novel, to the best of our knowledge, software-driven approach that compensates for the aberrations in HMDs in real time. Our approach involves pre-correction that deconvolves an input image to minimize the difference between its after-lens image and the ideal image. We characterize the specific wavefront aberration and point spread function (PSF) of the optical system using Zernike polynomials. To achieve higher computational efficiency, we improve the conventional deconvolution based on hyper-Laplacian prior by adopting a regularization constraint term based on L2 optimization and the input-image gradient. Furthermore, we implement our solution entirely on a graphics processing unit (GPU) to ensure constant and scalable real-time performance for interactive VR. Our experiments evaluating our algorithm demonstrate that our solution can reliably reduce the aberration of the after-lens images in real time.

Wavelet-Improved Score-Based Generative Model for Medical Imaging.

The score-based generative model (SGM) has demonstrated remarkable performance in addressing challenging under-determined inverse problems in medical imaging. However, acquiring high-quality training datasets for these models remains a formidable task, especially in medical image reconstructions. Prevalent noise perturbations or artifacts in low-dose Computed Tomography (CT) or under-sampled Magnetic Resonance Imaging (MRI) hinder the accurate estimation of data distribution gradients, thereby compromising the overall performance of SGMs when trained with these data. To alleviate this issue, we propose a wavelet-improved denoising technique to cooperate with the SGMs, ensuring effective and stable training. Specifically, the proposed method integrates a wavelet sub-network and the standard SGM sub-network into a unified framework, effectively alleviating inaccurate distribution of the data distribution gradient and enhancing the overall stability. The mutual feedback mechanism between the wavelet sub-network and the SGM sub-network empowers the neural network to learn accurate scores even when handling noisy samples. This combination results in a framework that exhibits superior stability during the learning process, leading to the generation of more precise and reliable reconstructed images. During the reconstruction process, we further enhance the robustness and quality of the reconstructed images by incorporating regularization constraint. Our experiments, which encompass various scenarios of low-dose and sparse-view CT, as well as MRI with varying under-sampling rates and masks, demonstrate the effectiveness of the proposed method by significantly enhanced the quality of the reconstructed images. Especially, our method with noisy training samples achieves comparable results to those obtained using clean data. Our code at https://zenodo.org/record/8266123.

Video stabilization based on low‐rank constraint and trajectory optimization

AbstractVideo stabilization plays a pivotal role in enhancing video quality by eliminating unwanted jitter in shaky videos. This paper introduces a novel video stabilization algorithm that leverages low‐rank constraint and trajectory optimization to effectively eliminate undesirable motion and generate stabilized videos. In the proposed algorithm, a low‐rank constraint regularization term is incorporated to enhance the smoothness of motion trajectories. Additionally, a predictive path smoothness term is integrated to ensure the consistency of motion across neighbouring frames. To address the problem of excessive cropping resulting from aggressive smoothing, a flexible local window strategy that emphasizes local motion relationships within the trajectories is introduced. The experimental results show that, compared to other excellent video stabilization algorithms, the proposed algorithm improves the stability metric by approximately 2.3%. Furthermore, in the stabilized videos generated by the algorithm, an approximate improvement of 2.18 dB in average image temporal fidelity and a 5.7% increase in average structural similarity between adjacent frames are achieved. The code that implements the proposed method is publicly accessible at https://github.com/CZS0319/VS_Low‐Rank_Constraint_Trajectory_Optimization.

A spatially adaptive regularization based three-dimensional reconstruction network for quantitative susceptibility mapping

Objective. Quantitative susceptibility mapping (QSM) is a new imaging technique for non-invasive characterization of the composition and microstructure of in vivo tissues, and it can be reconstructed from local field measurements by solving an ill-posed inverse problem. Even for deep learning networks, it is not an easy task to establish an accurate quantitative mapping between two physical quantities of different units, i.e. field shift in Hz and susceptibility value in ppm for QSM. Approach. In this paper, we propose a spatially adaptive regularization based three-dimensional reconstruction network SAQSM. A spatially adaptive module is specially designed and a set of them at different resolutions are inserted into the network decoder, playing a role of cross-modality based regularization constraint. Therefore, the exact information of both field and magnitude data is exploited to adjust the scale and shift of feature maps, and thus any information loss or deviation occurred in previous layers could be effectively corrected. The network encoding has a dynamic perceptual initialization, which enables the network to overcome receptive field intervals and also strengthens its ability to detect features of various sizes. Main results. Experimental results on the brain data of healthy volunteers, clinical hemorrhage and simulated phantom with calcification demonstrate that SAQSM can achieve more accurate reconstruction with less susceptibility artifacts, while perform well on the stability and generalization even for severe lesion areas. Significance. This proposed framework may provide a valuable paradigm to quantitative mapping or multimodal reconstruction.

Integral constraint regularization method for fractional optimal control problem with pointwise state constraint

This paper investigates integral constraint regularization approximation of fractional optimal control problem with pointwise state constraint. Firstly the continuous first-order optimality condition is derived. In order to deal with the irregular multiplier, a regularized optimal control problem with finitely many integral state constraints is proposed based on integral constraint regularization method. The error between the original solution and the regularized solution is deduced. Continuous piecewise linear finite element combined with variational discretization approach is used to discretize the regularized optimal control problem. Finite element discretization error combined with the regularization error leads to the final error estimate. Finally, numerical examples are presented to verify the theoretical findings.

Segmental Regularized Constrained Inversion of Transient Electromagnetism Based on the Improved Sparrow Search Algorithm

The initial inversion model is typically established in a transient electromagnetic nonlinear inversion, assuming the accurate capture of the number of layers in the geoelectric model; however, this assumption leads to significantly poorer inversion results for complex models when obtaining the exact number of layers from available a priori information, which is challenging. This study proposes a segmented regularized inversion method to enhance inversion accuracy and stability under varying conditions. The process involves two key steps: Firstly, a segmented initial model is established based on preliminary information. The layering criteria and layer thickness threshold for each segment are set during inversion to reduce dependence on the accuracy of the preliminary information. Secondly, a segmented regularization constraint is added to the objective function to improve the efficiency and stability of the inversion, as numerous parameters can exacerbate the problem of inversion ambiguity. Subsequently, an improved sparrow search algorithm (ISSA) is utilized to optimize the inversion objective function. This enhances the efficiency of searching for the objective function and the algorithm’s ability to escape local optimal solutions. The proposed method is evaluated using one-dimensional and two-dimensional models with different initial models and inversion algorithms and applied to the inversion of on-site exploration data in a coal mining area in Chongqing. Comparative results demonstrate that the proposed segmented regularization method, based on the improved sparrow search algorithm, exhibits superior practicality and a higher fitting accuracy.

Low Rank Representation Subspace Clustering Algorithm Based on Hessian Regularization and Non Negative Constraints

Low Rank Representation Subspace Clustering Algorithm Based on Hessian Regularization and Non Negative Constraints

Imaging Upper-Mantle Anisotropy with Transdimensional Bayesian Monte Carlo Sampling

ABSTRACT Underdetermination is a condition affecting all problems in seismic imaging. It manifests mainly in the nonuniqueness of the models inferred from the data. This condition is exacerbated if simplifying hypotheses like isotropy are discarded in favor of more realistic anisotropic models that, although supported by seismological evidence, require more free parameters. Investigating the connections between underdetermination and anisotropy requires the implementation of solvers which explore the whole family of possibilities behind nonuniqueness and allow for more informed conclusions about the interpretation of the seismic models. Because these aspects cannot be investigated using traditional iterative linearized inversion schemes with regularization constraints that collapse the infinite possible models into a unique solution, we explore the application of transdimensional Bayesian Monte Carlo sampling to address the consequences of underdetermination in anisotropic seismic imaging. We show how teleseismic waves of P and S phases can constrain upper-mantle anisotropy and the amount of additional information these data provide in terms of uncertainty and trade-offs among multiple fields.

A fully coupled regularized mortar‐type finite element approach for embedding one‐dimensional fibers into three‐dimensional fluid flow

SummaryThe present article proposes a partitioned Dirichlet‐Neumann algorithm, that allows to address unique challenges arising from a novel mixed‐dimensional coupling of very slender fibers embedded in fluid flow using a regularized mortar‐type finite element discretization. The fibers are modeled via one‐dimensional (1D) partial differential equations based on geometrically exact nonlinear beam theory, while the flow is described by the three‐dimensional (3D) incompressible Navier‐Stokes equations. The arising truly mixed‐dimensional 1D‐3D coupling scheme constitutes a novel approximate model and numerical strategy, that naturally necessitates specifically tailored solution schemes to ensure an accurate and efficient computational treatment. In particular, we present a strongly coupled partitioned solution algorithm based on a Quasi‐Newton method for applications involving fibers with high slenderness ratios that usually present a challenge with regard to the well‐known added mass effect. The influence of all employed algorithmic and numerical parameters, namely the applied acceleration technique, the employed constraint regularization parameter as well as shape functions, on efficiency and results of the solution procedure is studied through appropriate examples. Finally, the convergence of the two‐way coupled mixed‐dimensional problem solution under uniform mesh refinement is demonstrated, a comparison to a 3D reference solution is performed, and the method's capabilities in capturing flow phenomena at large geometric scale separation is illustrated by the example of a submersed vegetation canopy.

Evaluation of Upland Rice Response to Water Stress Using Polyethylene Glycol (PEG -6000) at Germination and Early Seedling Stage

Water stress is one of the most important crop growth limiting factors which leads to low crop productivity and yield instability. Water stress affects crop growth and development, especially during the germination and seedling period. The experiment was conducted in the growth chamber at the seed physiology laboratory of the Department of Seed, Crop and Horticultural Sciences, University of Eldoret to evaluate sixteen upland rice varieties to water stress tolerance at germination and early seedling growth stage. These varieties were tested against four levels of water stress imposed by Polyethylene glycol 6000 (PEG - 6000) at 0%, 5%,10% and 15% concentration. The lay out of the experiment was complete randomized design (CRD) with three replications. Osmotic stress induced by PEG levels significantly (P<.001) reduced plant growth parameters. The result showed that the germination percentage, germination index, Relative seedling height (%), seedling dry weight, Seedling fresh weight, Seedling length, seedling vigor index and mean germination time of all tested rice varieties were found decreasing trends with increasing the levels of PEG from 0 to 15% concentration levels. Among all the sixteen varieties, NERICA rice varieties followed by MWUR, White rice, Kpatawee, and Komboka had an outstanding performed in terms of germination percentage, germination index, seedling height, seedling dry weight, root length and relative dry weight under water induced stress by using PEG concentration levels compared to other varieties. Therefore, these varieties could be useful in breeding programs and can be cultivated in arid and semi-arid environment or where water shortage is a regular constraint.

Joint constraints of guided filtering based confidence and nonlocal sparse tensor for color polarization super-resolution imaging.

This paper introduces a camera-array-based super-resolution color polarization imaging system designed to simultaneously capture color and polarization information of a scene in a single shot. Existing snapshot color polarization imaging has a complex structure and limited generalizability, which are overcome by the proposed system. In addition, a novel reconstruction algorithm is designed to exploit the complementarity and correlation between the twelve channels in acquired color polarization images for simultaneous super-resolution (SR) imaging and denoising. We propose a confidence-guided SR reconstruction algorithm based on guided filtering to enhance the constraint capability of the observed data. Additionally, by introducing adaptive parameters, we effectively balance the data fidelity constraint and the regularization constraint of nonlocal sparse tensor. Simulations were conducted to compare the proposed system with a color polarization camera. The results show that color polarization images generated by the proposed system and algorithm outperform those obtained from the color polarization camera and the state-of-the-art color polarization demosaicking algorithms. Moreover, the proposed algorithm also outperforms state-of-the-art SR algorithms based on deep learning. To evaluate the applicability of the proposed imaging system and reconstruction algorithm in practice, a prototype was constructed for color polarization image acquisition. Compared with conventional acquisition, the proposed solution demonstrates a significant improvement in the reconstructed color polarization images.

Utilizing the L-curve criterion for the inverse magnetostatic problem of Hall drift current estimation

Aiming at achieving the in-orbit diagnostic of Hall drift current, this study focuses on estimation through the indirect measurement methodology using a magnetic sensor array. It elaborates on the application of a pseudo-seminorm defined for the Hall drift current solution to address the inverse magnetostatic problems, which are formulated with a two-dimensional Tikhonov regularization constraint, and thereby offering a systematic approach to select regularization parameters. Our investigation discusses factors influencing the formation of the L-curve and the accuracy of the resultant solution obtained via the L-curve criterion. The results reveal that the formation of the defined pseudo-seminorm of the Hall drift current solution in the semi-logarithmic coordinate system is independent of the number of calibrating current elements or the number of magnetic sensors. This effectively resolves the issue of failing to generate an L-curve during regularization parameter selection. Furthermore, the study indicates that expanding the number of calibrating current elements—essentially increasing the unknown variables in the inverse magnetostatic equations—contributes to a significant enhancement in the accuracy of Hall drift current solutions. It also has extensibility to be applied to other areas where the contactless current measuring is required.