Double Regularization Research Articles

Multi-sensor data fusion-enabled lightweight convolutional double regularization contrast transformer for aerospace bearing small samples fault diagnosis

Aiming at the problems of low information utilization and lack of feature mining capability in multi-sensor fusion networks, this study presents a multi-sensor data fusion-enabled lightweight convolutional double regularization contrast transformer for aerospace bearing small samples fault diagnosis. Firstly, a metric termed integrated cliff entropy is devised to assign weights to vibration signals from diverse sensor channels. It aims to enhance the cyclic impulse characteristics within the fused signals, thereby facilitating more precise fault identification. Secondly, a lightweight Diwaveformer architecture is constructed as the backbone of contrast learning. It enables the global and local features of faulty signals to be comprehensively extracted with less computational effort. Finally, a double contrast loss is constructed to optimize the distribution of intra-class and inter-class features to improve the fault identification ability of the network with small samples. Additionally, a discard regularization method is designed to remove the projection head during the contrast learning process, further advancing the model lightweight. Our method achieved accuracies of 95.54% and 92.56% on two aerospace bearing datasets with extremely sparse training samples, which proved its superior performance.

The Double Regularization Method for Capacity Constrained Optimal Transport

The Double Regularization Method for Capacity Constrained Optimal Transport

An efficient one-step proximal method for EIT sparse reconstruction based on nonstationary iterated Tikhonov regularization

ABSTRACT Image reconstruction of EIT mathematically is a seriously ill-posed inverse problem, which is easily affected by measurement noise. This fact leads to a relatively low spatial resolution, particularly in the accuracy of identifying object boundaries. This paper concerns with reconstructing a finite number of simple and small inclusions equipped with the homogeneous background conductivity. The sparsity with respect to the inclusions in the spacial representation domain is apriori assumed. We try to reexamine the multi-parameter constraints on mixing between -norm and -norm for attaining the sparse reconstruction as well as simultaneously enhancing the stability. On the basis of the reference approximation reconstructed by nonstationary iterated Tikhonov regularization (NITR) method, we propose a novel one-step proximal sparsity-promoting approach by one induced proximal shrink operator, abbreviated as one-step PNITR method. The proposed one-step PNITR method consists of twofold: one first performs NITR with mth iteration to generate the reference approximation, and then performs one-step proximal shrinkage processing and one forcing constraint function on it to obtain the final sparsity-promoting reconstruction. For the latter, the former aims to not only enhance higher reliability but also guarantee the sparsity. The proposed method can benefit from the double regularization effect. It is supposed to further improve the imaging quality in terms of sharpening the edges and reducing the artefacts. To validate the advantage of the proposed method, numerical simulations with synthetic data have been carried out. Also, qualitative and quantitative comparisons are conducted. Results indicate that the proposed approach can lead to substantial improvements in EIT image resolution. The performed numerical simulations show that our method is promising.

A sparse negative binomial classifier with covariate adjustment for RNA-seq data

Supervised machine learning methods have been increasingly used in biomedical research and clinical practice. In transcriptomic applications, RNA-seq data have become dominating and have gradually replaced traditional microarray, due to their reduced background noise and increased digital precision. Most existing machine learning methods are, however, designed for continuous intensities of microarray and are not suitable for RNA-seq count data. In this paper we develop a negative binomial model via generalized linear model framework with double regularization for gene and covariate sparsity to accommodate three key elements: adequate modeling of count data with overdispersion, gene selection and adjustment for covariate effect. The proposed sparse negative binomial classifier (snbClass) is evaluated in simulations and two real applications of multidisease postmortem brain tissue RNA-seq data and cervical tumor miRNA-seq data to demonstrate its superior performance in prediction accuracy and feature selection.

Noncoercive Variational–Hemivariational Inequalities: Existence, Approximation by Double Regularization, and Application to Nonmonotone Contact Problems

Noncoercive Variational–Hemivariational Inequalities: Existence, Approximation by Double Regularization, and Application to Nonmonotone Contact Problems

Periodic orbits for double regularization of piecewise smooth systems with a switching manifold of codimension two

<p style='text-indent:20px;'>In this paper we consider an <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> dimensional piecewise smooth dynamical system. This system has a co-dimension 2 switching manifold <inline-formula><tex-math id="M2">\begin{document}$ \Sigma $\end{document}</tex-math></inline-formula> which is an intersection of two hyperplanes <inline-formula><tex-math id="M3">\begin{document}$ \Sigma_1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \Sigma_2 $\end{document}</tex-math></inline-formula>. We investigate the relation between periodic orbit of PWS system and periodic orbit of its double regularized system. If this PWS system has an asymptotically stable sliding periodic orbit(including type Ⅰ and type Ⅱ), we establish conditions to ensure that also a double regularization of the given system has a unique, asymptotically stable, periodic orbit in a neighbourhood of <inline-formula><tex-math id="M5">\begin{document}$ \gamma $\end{document}</tex-math></inline-formula>, converging to <inline-formula><tex-math id="M6">\begin{document}$ \gamma $\end{document}</tex-math></inline-formula> as both of the two regularization parameters go to <inline-formula><tex-math id="M7">\begin{document}$ 0 $\end{document}</tex-math></inline-formula> by applying implicit function theorem and geometric singular perturbation theory.</p>

Multi-Frame Super-Resolution Reconstruction Algorithm of Optical Remote Sensing Images Based on Double Regularization Terms and Unsupervised Learning

High-resolution images have always been in urgent need in the fields of surveying, mapping, military and civilian. In this paper, first, based on anisotropic nonlinear diffusion tensor, a diffusion tensor regularization term which can make full use of direction selection smoothing property was constructed. Based on the improved gradient vector field (GVF), a regularization term which can constrain the continuity of gradient vectors for high-resolution and low-resolution images was constructed. On the basis of these, a multi-frame super-resolution reconstruction algorithm based on double regularization terms was proposed and verified by simulation. Second, combining PCA with adaptive dictionary learning, two constraints of reconstruction regularity based on improved nonlocal means and kernel regression were proposed for experimental verification, and an improved K-means clustering algorithm for initial centre selection of spatial characteristic measure clustering was proposed to enhance the stability of the algorithm. Then high-resolution image generated by learning method was used as the initial input of multi-frame reconstruction of optical remote sensing images. The experimental results show that the reconstruction algorithm based on partial differential equation and unsupervised learning achieves both subjective and objective results for the realization of super-resolution reconstruction of optical remote sensing images.

Vehicle Face Recognition Algorithm Based on Weighted Nonnegative Matrix Factorization with Double Regularization Terms

Vehicle Face Recognition Algorithm Based on Weighted Nonnegative Matrix Factorization with Double Regularization Terms

Scalable double regularization for 3D Nano-CT reconstruction

Nano-CT (computerized tomography) has emerged as a non-destructive high-resolution cross-sectional imaging technique to effectively study the sub-μm pore structure of shale, which is of fundamental importance to the evaluation and development of shale oil and gas. Nano-CT poses unique challenges to the inverse problem of reconstructing the 3D structure due to the lower signal-to-noise ratio (than Micro-CT) at the nano-scale, increased sensitivity to the misaligned geometry caused by the movement of object manipulator, limited sample size, and a larger volume of data at higher resolution. We propose a scalable double regularization (SDR) method to utilize the entire dataset for simultaneous 3D structural reconstruction across slices through total variation regularization within slices and L1 regularization between adjacent slices. SDR allows information borrowing both within and between slices, contrasting with the traditional methods that usually build on slice by slice reconstruction. We develop a scalable and memory-efficient algorithm by exploiting the systematic sparsity and consistent geometry induced by such Nano-CT data. We illustrate the proposed method using synthetic data and two Nano-CT imaging datasets of Jiulaodong (JLD) shale and Longmaxi (LMX) shale acquired in the Sichuan Basin. These numerical experiments show that the proposed method substantially outperforms selected alternatives both visually and quantitatively.

Inference of compressed Potts graphical models.

We consider the problem of inferring a graphical Potts model on a population of variables. This inverse Potts problem generally involves the inference of a large number of parameters, often larger than the number of available data, and, hence, requires the introduction of regularization. We study here a double regularization scheme, in which the number of Potts states (colors) available to each variable is reduced and interaction networks are made sparse. To achieve the color compression, only Potts states with large empirical frequency (exceeding some threshold) are explicitly modeled on each site, while the others are grouped into a single state. We benchmark the performances of this mixed regularization approach, with two inference algorithms, adaptive cluster expansion (ACE) and pseudolikelihood maximization (PLM), on synthetic data obtained by sampling disordered Potts models on Erdős-Rényi random graphs. We show in particular that color compression does not affect the quality of reconstruction of the parameters corresponding to high-frequency symbols, while drastically reducing the number of the other parameters and thus the computational time. Our procedure is also applied to multisequence alignments of protein families, with similar results.

Hand Vein Recognition Algorithm Based on NMF with Sparsity and Clustering Property Constraints in Feature Mapping Space

Most of the existed vein features are lack of robustness to light intensity variation, and some algorithms rely on the specified vein data sets, which leads to the limitation of real applications. To solve the problems, we propose a novel vein recognition algorithm based on Nonnegative matrix factorization (NMF) with double regularization terms. The innovations of our algorithm are mainly reflected in the following two aspects: in order to improve feature robustness, a novel feature mapping function is designed to map the initial Histogram of oriented gradient (HOG) feature to a new space; to enhance the recognition performance, an effective NMF model is presented, which not only reduces feature dimension, but also optimizes the feature sparsity and clustering property simultaneously. Experiments show that the proposed algorithm can achieve satisfactory results in terms of False rejection rate (FRR) and False acceptance rate (FAR), which indicates that our algorithm is valuable for other classification problems.

Slow–fast systems and sliding on codimension 2 switching manifolds

ABSTRACTIn this work, we consider piecewise smooth vector fields X defined in , where Σ is a self-intersecting switching manifold. A double regularization of X is a 2-parameter family of smooth vector fields , satisfying that converges uniformly to X in each compact subset of when . We define the sliding region on the non-regular part of Σ as a limit of invariant manifolds of . Since the double regularization provides a slow–fast system, the GSP-theory (geometric singular perturbation theory) is our main tool.

A Global Optimization Method for Specular Highlight Removal From a Single Image

The presence of specular highlight is a critical issue for both natural and medical images such as those produced by laparoscopes, which can lead to erroneous visual tracking, stereo reconstruction, and image segmentation. Specular highlight removal from a single image is necessary for image analysis and applications. Due to the differences between natural and medical image scenes, existing literature to address this issue has only been effective on natural images or medical images with textureless regions. To overcome this limitation, we propose a global optimization method for specular highlight removal from a single image based on a dichromatic reflection model. In addition to introducing modified illumination chromaticity, the proposed method consists of two novel steps: one for estimating diffuse chromaticity by correcting hue and saturation on highlighted regions, and the other for estimating diffuse and specular reflection coefficients using convex optimization with double regularization. The estimated diffuse chromaticity is proven to approximate the true diffuse chromaticity and the proposed optimization algorithm is guaranteed to find the optimal diffuse coefficients. Experimental results show that the proposed method can effectively remove specular highlights from both natural images and endoscopic images with texture detail preservation. To further demonstrate the efficacy of our proposed method, an application of stereo reconstruction using a public dataset illustrates that our highlight removal method can enhance surface reconstruction accuracy from 1.10mm RMSD to 0.69mm RMSD.

Double Regularization Matrix Factorization Recommendation Algorithm

With the development of social networks, the research of integrated social information recommendation models has received extensive attention. However, most existing social recommendation models are based on the matrix factorization technique which ignore the impact of the relationships between items on users’ interests, resulting in a decline of recommendation accuracy. To solve this problem, this paper proposes a double regularization matrix factorization recommendation algorithm. The algorithm first uses attribute information and manifold learning to calculate similarity. Then, the matrix factorization model is constrained through the regularization of item association relations and user social relations. Experimental results on real datasets show that the proposed method can effectively alleviate problems such as cold start and data sparsity in the recommender system and improve the recommendation accuracy compared with those of existing methods.

Decomposition and Regularization of the Solution of Ill-Posed Inverse Problems in the Processing of Measurement Information. Part 2. Application of Theory to a Practical Problem

Application of the theory of double decomposition (physical and canonical) and two-sided regularization (of the left and right sides of a system of linear equations) to the solution of one of the ill-posed inverse problems of space geodesy is considered. The problem is related to transformation of the coordinates of the ground points of local satellite geodetic networks to the state reference frame. A variant of the Helmert decomposed model along with an adaptive algorithm for regularization of the solution of an ill-posed inverse problem are proposed.

New approach to identify the initial condition in degenerate hyperbolic equation

ABSTRACTThis paper deals with the determination of an initial condition in degenerate hyperbolic equation from final observations. With the aim of reducing the execution time, this inverse problem is solved using an approach based on double regularization: a Tikhonov’s regularization and regularization in equation by viscose-elasticity. So, we obtain a sequence of weak solutions of degenerate linear viscose-elastic problems. Firstly, we prove the existence and uniqueness of each term of this sequence. Secondly, we prove the convergence of this sequence to the weak solution of the initial problem. Also we present some numerical experiments to show the performance of this approach.

Double regularization methods for robust feature selection and SVM classification via DC programming

In this work, two novel formulations for embedded feature selection are presented. A second-order cone programming approach for Support Vector Machines is extended by adding a second regularizer to encourage feature elimination. The one- and the zero-norm penalties are used in combination with the Tikhonov regularization under a robust setting designed to correctly classify instances, up to a predefined error rate, even for the worst data distribution. The use of the zero norm leads to a nonconvex formulation, which is solved by using Difference of Convex (DC) functions, extending DC programming to second-order cones. Experiments on high-dimensional microarray datasets were performed, and the best performance was obtained with our approaches compared with well-known feature selection methods for Support Vector Machines.

Double regularization medical CT image blind restoration reconstruction based on proximal alternating direction method of multipliers

To solve the problem of CT image degradation, a double regularization CT image blind restoration reconstruction method was proposed. The objective function including both a clear image and point spread function was established. To avoid the over-smoothing phenomenon and protect the detail, the objective function includes two constraint regularization terms. They are total variation (TV) and wavelet sparsity respectively. The objective function was solved by the alternating direction multiplier method (ADMM), and the optimal solution was obtained. Firstly, the CT image blind restoration reconstruction was decomposed into two sub-problems: reconstructed image estimation and point spread function estimation. Furthermore, each sub-problem can be solved by the proximal alternating direction method of multipliers. Finally, the CT image blind restoration reconstruction was realized. The experimental results show that the proposed algorithm takes into account the degradation effect of projection data, and the proposed algorithm is superior to other existing algorithms in the subjective visual effect. At the same time, in the aspect of objective evaluation, the proposed algorithm improves the objective image quality metrics such as peak signal-to-noise ratio (PSNR), structural similarity index metric (SSIM), and universal image quality index (UIQI).

Control for well-posedness about a class of non-Newtonian incompressible porous medium fluid equations

Considering the non-Newtonian fluid equation of incompressible porous media, using the properties of operator semigroup and measure space and the principle of squeezed image, Fourier analysis and a priori estimate in the measurement space are used to discuss the non-compressible porous media, the properness of the solution of the equation, its gradual behavior and its topological properties. Through the diffusion regularization method and the compressed limit compact method, we study the overall decay rate of the solution of the equation in a certain space when the initial value is sufficient. The decay estimation of the solution of the incompressible seepage equation is obtained, and the asymptotic behavior of the solution is obtained by using the double regularization model and the Duhamel principle.

Hyperspectral Image Superresolution Based on Double Regularization Unmixing

This letter proposes a novel double regularization unmixing-based method for hyperspectral image (HSI) superresolution. The proposed cost function contains two data-fidelity terms, the endmember regularization term and the abundance regularization term. Since the double regularization unmixing terms are able to exploit the spatial structure information of endmember and abundance, respectively, the nonnegative factorization (spectral unmixing) error is minimized. As a result, the performance of the proposed HSI superresolution method can be enhanced in terms of noise suppression and the special structure information preservation of reconstruction images. Finally, the associated optimization problem is effectively solved by an alternating direction optimization algorithm. Simulation results illustrate that the proposed method has a better performance than the state-of-the-art methods in terms of both visual effectiveness and quality indices.