Regularization Method Research Articles

A Family of Hyper-parameter Estimators Linking EB and SURE for Kernel-based Regularization Methods

A Family of Hyper-parameter Estimators Linking EB and SURE for Kernel-based Regularization Methods

Infectious bovine rhinotracheitis: Unveiling the hidden threat to livestock productivity and global trade.

An infectious disease called infectious bovine rhinotracheitis (IBR) can lead to a number of disorders affecting cattle's respiratory system. The disease is caused by bovine alphaherpesvirus type 1 (BoAHV-1). Based on antigenic and genetic characteristics, BoAHV-1 strains are divided into subtypes 1.1, 1.2a, 1.2b, and 1.3. IBR is currently widespread throughout the world, with the exception of a few nations that have achieved eradication. The most significant characteristic of this illness is that, after a clinical or subclinical infection, the virus typically establishes a latent condition that can later be reactivated in the presence of stress, immunosuppressive conditions/substances, or other diseases. Primarily, the virus spreads by direct or indirect contact between animals. It may also be transmitted via the reproductive system, causing infectious balanoposthitis or vulvovaginitis. Most virus subtypes are associated with reproductive failure, such as fetal or embryonic resorption and abortions. The virus may also be transmitted through semen, which could lead to genital transfer. Bovine herpesvirus type 1 (BoHV-1) infection produces a variety of lesions. Lesion in the mucosal surface usually consists of white necrotic material. Regular methods for diagnosing BoHV-1 infections include isolation in cell culture, enzyme linked immunosorbent assay, virus neutralisation test, and methods based on identification of nucleic acids, like PCR. The interplay of several host, pathogen, environmental, and management factors affects the spread of IBR. Through its impacts on health and fitness, IBR can lead to production losses. In order to minimize the severity of clinical signs and stop the infection from spreading, the veterinarian may advise that sick or at-risk animals be placed under immediate isolation and vaccinated (such as intranasal vaccination, including the use of both killed and live attenuated virus vaccines) as soon as an IBR diagnosis is obtained.

Improving procedures for obtaining Sanger sequences from old herbarium specimens

Because DNA degrades over time, extracting DNA of sufficient quality for sequencing is presumed to be more difficult from older than younger herbarium specimens. Although massive parallel sequencing techniques have clear advantages when it comes to sequencing ancient DNA, Sanger sequencing is still in frequent use, prompting us to test and improve its application on herbarium specimens. During molecular phylogenetic investigations of the subfamily Lamioideae (Lamiaceae) and subgroups, we extracted DNA from 651 herbarium specimens collected between 1826 and 2006 using regular mini-prep methods. The aim was to obtain DNA of sufficient quality for Sanger sequencing of various plastid and nuclear genetic markers. Here, we report successful Sanger sequencing of the commonly used plastid marker, rps16, as a conservative measure of DNA quality, and logistic regression to investigate the relationship between age of the material and DNA quality. Our result indicates that the upper age limit for obtaining DNA suitable for Sanger,sequencing from herbarium specimens using regular mini-prep DNA extraction methods has not been reached. After simple modifications to the regular DNA miniprep and PCR procedures, at least one genetic marker was successfully sequenced for about 90 % of the specimens tested, the oldest being 168 years old. Jointly, despite the technique’s drawbacks, these results demonstrate a high success rate of Sanger sequencing of herbarium specimens.

Quantitative Light-Induced Fluorescence (QLF) in Assessing the Efficacy of Dental Floss as An Adjunct to Toothbrushing

Objectives: The objective of this was to determine the of adjunctive usage of interdental mechanical aids along with educational, preventive and motivational actions on plaque reduction using Quantitative Light- induced Fluorescence (QLF-D) in motivated and non- motivated individuals. Materials and Method: 25 dental students were selected for this study, clinical indices, and QLF-D scores were recorded for all, after which they were divided into two groups. All the participants were given standardized toothbrushes and toothpaste. One group was asked to follow the regular oral hygiene methods while the other group was asked to use toothbrushes and floss along with instructions to use them for three weeks. After said period, the participants reported to the clinic and clinical indices and QLF-D scores were recorded again. The data was collected and subjected to statistical analysis. Results: The statistically significant intragroup difference was noted in groups. When comparing the plaque reduction three weeks post-intervention, the Simple Plaque Score (SPS) score showed a significant difference, whereas, the red fluorescence did not show any significant difference. Conclusion: According to the results obtained, we can conclude that patient education using QLF-D was effective as interdental plaque can be visualized by the patients and effectively cleaned using interdental aids like floss, which is difficult with clinical indices alone. So QLF- D can be an effective educational and motivational tool.

Semi-supervised multi-sensor information fusion tailored graph embedded low-rank tensor learning machine under extremely low labeled rate

This paper investigates a demanding and meaningful task of intelligent fault diagnosis, in which multi-sensors signals are fused for semi-supervised analysis with few labeled fault data. Exploring effective strategies to solve this task from an industrial or academic perspective remains a challenging and resource-consuming task. To this issue, this study develops a new low-rank tensor-based semi-supervised classifier, called graph embedded low-rank tensor learning machine (GE-LRTLM), which can effectively alleviate the foregoing difficulties and increase the diagnosis precision in engineering applications. First, multi-sensor and multi-channel vibration signals are converted into the pixel matrices that are stacked as the multi-sensor information fusion feature tensors, making the coupling relationship between multi-sensor signals remained and achieving a reasonable fusion of multi-source features. Additionally, an advanced tensor decomposition method, tensor nuclear norm (TNN), is introduced in GE-LRTLM model to obtain the low-rank structure information of each feature tensor, implementing the extraction of the most important feature and patterns from the tensor data while ensuring that the tensor data structure remains unchanged. Ultimately, the manifold regularization and tensor-based graph construction method are introduced to obtain potential label information from unlabeled samples, achieving better description of the geometry similarity and distribution of tensor data. Numerous semi-supervised experiments are conducted across multiple datasets, and the results demonstrate that the proposed method can achieve a classification accuracy of 97% even when the number of labeled samples is extremely limited. Simultaneously, it also verifies that the combination of the constructed labeled and unlabeled multi-sensor information fusion tensor samples can promote the improvement of model accuracy.

On a Backward Problem for the Rayleigh–Stokes Equation with a Fractional Derivative

The Rayleigh–Stokes equation with a fractional derivative is widely used in many fields. In this paper, we consider the inverse initial value problem of the Rayleigh–Stokes equation. Since the problem is ill-posed, we adopt the Tikhonov regularization method to solve this problem. In addition, this paper not only analyzes the ill-posedness of the problem but also gives the conditional stability estimate. Finally, the convergence estimates are proved under two regularization parameter selection rules.

A model of homographs automatic identification for the Belarusian language

Objectives. А prototype system for automated removal of homonyms in Belarusian and Russian electronic texts is described. This is due to the urgent problem of automatic text processing at the morphological level, the process of which is complicated by the inflection of the Belarusian language with a diverse and rich system of morphological characteristics of parts of speech.Methods. The work uses regular homographs identification methods and knowledge-based methods.Results. Methods and approaches for designing systems for automatic detection of homographs are proposed. An algorithm for identifying homographs on the basis of knowledge-based method has been developed. An effective and fast-acting prototype for their removal in Russian and Belarusian has been implemented.Conclusion. A working prototype of the homograph search is presented, which is the first resource for removing ambiguity for the Belarusian language in open access.

Regularized coupling multiscale method for thermomechanical coupled problems

The coupling effects in multiphysics processes are often neglected in designing multiscale methods. The coupling may be described by a non-positive definite operator, which in turn brings significant challenges in multiscale simulations. In the paper, we develop a regularized coupling multiscale method based on the generalized multiscale finite element method (GMsFEM) to solve coupled thermomechanical problems, and it is referred to as the coupling generalized multiscale finite element method (CGMsFEM). The method consists of defining the coupling multiscale basis functions through local regularized coupling spectral problems in each coarse-grid block, which can be implemented by a novel design of two relaxation parameters. Compared to the standard GMsFEM, the proposed method can not only accurately capture the multiscale coupling correlation effects of multiphysics problems but also greatly improve computational efficiency with fewer multiscale basis functions. In addition, the convergence analysis is also established, and the optimal error estimates are derived, where the upper bound of errors is independent of the magnitude of the relaxation coefficient. Several numerical examples for periodic, random microstructure, and random material coefficients are presented to validate the theoretical analysis. The numerical results show that the CGMsFEM shows better robustness and efficiency than uncoupled GMsFEM.

DETERMINATION OF THE TEMPERATURE CONDUCTIVITY COEFFICIENT a GRAPHICAL METHOD BASED ON NOMOGRAM FOR A SEMI-CONFINED ROD

The article presents a technique and formula for calculating the thermal diffusivity of solids using nomograms of temperature changes. The paper describes a technique by which the final formulas are simplified to algebraic equations using the relative temperature θM of heating a semi-restricted rod from the end.Known equations for solving direct problems of heat conduction using regular modes of the 1-st, 2-nd and 3-rd kind, in which the final formulas are simplified.The article provides methods and formulas for calculating the coefficient of thermal conductivity using nomograms.The method uses the maximum of the first derivative of θM and tabular values of the function erf (1/(2 x Fo )), which is a solution to the direct problem of thermal conductivity. The temperature at a specific point of the rod is measured – x1 and time –τ1 with start of heatingent of thermal conductivity of solid bodies using nomograms of temperature changes.The work describes a method by which the final formulas are simplified to algebraic equations using the relative temperature θM of heating a semirestricted rod from the end. Known equations for solving direct heat conduction problems using regular regimes of the 1-st, 2-nd and 3-rd kind, in which the final formulas are simplified. In work Kondratiev H.M. notes: "The theory of the regular thermal regime is one of the sections of the study of heat transfer insolids. The theory of the regular mode considers the process of cooling or heating not throughout, but only at the stage that has ceased to be affected by the initial state of the body.In work of Lykov O.V. «Theory of thermal conductivity» the solution of the problem is done by three methods: classical, operational and the method of Fourier transformation. Not all methods of pulsed heating are related to these types of regular mode, but it can be used due to the simple form of the exponent. In this work, the proposed method does not belong to regular mode methods. It is done by solving the inverse problem with the help of a well-developed graphic nomogram.According to the accepted classification, the problem is solved under boundary conditions of the 1-st kind, in which the surface temperature is specified as a function of time. Considered a simpler case when surface of the bodyremains constant throughout the heat exchange process.This is achieved with the help of special devices that maintain a constant temperature of a semi-restricted rod with thermal insulation of the side surface.

Stochastic linear regularization methods: random discrepancy principle and applications

The a posteriori stopping rule plays a significant role in the design of efficient stochastic algorithms for various tasks in computational mathematics, such as inverse problems, optimization, and machine learning. Through the lens of classical regularization theory, this paper describes a novel analysis of Morozov’s discrepancy principle for the stochastic generalized Landweber iteration and its continuous analog of generalized stochastic asymptotical regularization. Unlike existing results relating to convergence in probability, we prove the strong convergence of the regularization error using tools from stochastic analysis, namely the theory of martingales. Numerical experiments are conducted to verify the convergence of the discrepancy principle and demonstrate two new capabilities of stochastic generalized Landweber iteration, which should also be valid for other stochastic/statistical approaches: improved accuracy by selecting the optimal path and the identification of multi-solutions by clustering samples of obtained approximate solutions.

DSST: A dual student model guided student–teacher framework for semi-supervised medical image segmentation

Numerous semi-supervised learning methods are emerging in medical image segmentation to reduce the dependency of deep learning models on pixel-level annotation data. Consistency regularization methods based on the Student–Teacher structure have achieved brilliant results in this domain. However, the current structures are unable to resolve the tight weight coupling satisfactorily between the teacher and student model, which leads to a decrease in the segmentation performance. In this paper, we propose a novel and practical semi-supervised learning framework, Dual-Student-Single-Teacher (DSST), to alleviate this problem. Particularly, the DSST framework consists of three segmentation models with the identical structure but different initial parameters, one serves as the teacher model and others as the student models, which employs an alternating manner to update the teacher model parameters. For the DSST framework, we present different supervised modes to sufficiently explore the enhancement of consistency regularization for model segmentation performance. Furthermore, we also introduce abundant and efficient input and feature perturbations for the proposed method. Finally, we evaluate our framework in three public medical image segmentation tasks, including Pancreas-CT, LA dataset, and cardiac segmentation on the ACDC dataset. Extensive experiments demonstrate that, compared with eight other superior semi-supervised methods, the DSST method obtains state-of-the-art segmentation performance and is an effective and generalizable framework. Code is available at https://github.com/LBL0704/DSST.

Multiscale dilated dense network for hyperspectral image classification

Hyperspectral image has rich spectral information and can accurately reflect the real condition of ground objects, so it is widely used. However, there are huge challenges in hyperspectral image, such as few training samples, the phenomena of “the foreign matter same spectrum” and “the same thingdifferent spectrum” can not be distinguished. The hyperspectral image classification method based on convolutional neural network can solve the above problems and achieve good classification performance. Most classification methods based on convolutional neural network only extract the deep semantic information at the end of the network, ignoring the shallow details. At the same time, Methods of this type increase the receptive field by designing deep network structure, which is prone to gradient vanishing. To solve the above two problems, a multiscale dilated dense network is proposed for hyperspectral image classification. Firstly, hyperspectral data cubes with different neighborhood sizes are selected as network inputs to construct a multi-channel network structure with different scale inputs. Secondly, a multiscale feature mapping module with fusion of dilated convolution is designed. Different numbers of dilated convolution are used to increase the model's receptive field without increasing network parameters, and spatial-spectral features of different scales are fused. Skip connections are added between the designed modules to fully combine the shallow and deep features of the network, without skip connections in the modules, reduce the computation of the overall network. Finally, the resulting features are input into the fully connected layer and softmax to complete the classification. In addition, in order to prevent the network from overfitting, we add dropout regularization method after the fully connected layer to improve the generalization ability of the model. Experiments are conducted on three publicly available datasets, Indian Pines, University of Pavia and Salinas, with accuracy rates of 99.28%, 99.48% and 99.25%, respectively. The experimental results show that compared with the classification methods based on convolutional neural network, the proposed method can effectively extract multiscale features of hyperspectral image and enhance the expression ability of spatial-spectral fusion features, and the classification performance is better.

DYMatch: Semi-Supervised Learning with Dynamic Pseudo Labeling and Feature Consistency

A considerable number of approaches based on consistency regularization and pseudo-labeling have been proposed in Semi-supervised Learning (SSL) so far. These approaches significantly enhance the SSL methods by effectively utilizing large amount of unlabeled data to improve the model’s performance. However, existing methods may fail to utilize the unlabeled data more efficiently, mainly due to the challenges faced in pseudo-label estimation. In this paper, we begin by analyzing the impact of the pseudo-label estimation method on training the SSL model. Furthermore, we emphasize that an effective pseudo-label estimation method should reflect the difference of recognition performance among samples from different categories, and also ensure the maintenance of both high-quantity and high-quality pseudo-labels during each training iteration. Based on above analysis, we propose DYMatch, an innovative SSL method employing a dynamic estimation process. Firstly, a dynamic pseudo-label estimation method based on Gaussian mixture model is proposed to dynamically estimate the confidence threshold on different categories. Secondly, a feature-correlation consistency regularization method is introduced to further enhance the learning on unlabeled data. The experimental results show that DYMatch is a simple and effective SSL method, especially when the labeled data is limited.

Sparse smooth group [formula omitted] regularization method for convolutional neural networks

Deep convolutional neural networks (CNNs) have successfully addressed numerous challenging real-world problems and are known to be more complex and powerful classifiers. However, finding a simple CNN architecture to properly estimate an unknown solution is still a challenging problem. With the objective of regularizing networks at the group level instead of individual ones, we propose the sparse smooth Group L0∘L1/2 regularization method, which is formulated as a composition of L0 and L1/2 regularizers. In doing so, both the L0 and L1/2 regularization terms are nonsmooth, which leads to difficulties in the training process. To overcome this issue, we propose a novel smooth function approximating the L1/2 regularizer. Additionally, we use an existing smooth indicator function to approximate the L0 regularizer. Numerical simulation results on a range of benchmark datasets and various CNN architectures demonstrate the effectiveness of the proposed method. It outperforms well-known group sparse regularization algorithms in several aspects, particularly in achieving superior group and weight sparsity.

Sparse-firing regularization methods for spiking neural networks with time-to-first-spike coding

The training of multilayer spiking neural networks (SNNs) using the error backpropagation algorithm has made significant progress in recent years. Among the various training schemes, the error backpropagation method that directly uses the firing time of neurons has attracted considerable attention because it can realize ideal temporal coding. This method uses time-to-first-spike (TTFS) coding, in which each neuron fires at most once, and this restriction on the number of firings enables information to be processed at a very low firing frequency. This low firing frequency increases the energy efficiency of information processing in SNNs. However, only an upper limit has been provided for TTFS-coded SNNs, and the information-processing capability of SNNs at lower firing frequencies has not been fully investigated. In this paper, we propose two spike-timing-based sparse-firing (SSR) regularization methods to further reduce the firing frequency of TTFS-coded SNNs. Both methods are characterized by the fact that they only require information about the firing timing and associated weights. The effects of these regularization methods were investigated on the MNIST, Fashion-MNIST, and CIFAR-10 datasets using multilayer perceptron networks and convolutional neural network structures.

Discrete Legendre spectral projection-based methods for Tikhonov regularization of first kind Fredholm integral equations

In this paper, we apply the discrete Legendre Galerkin and multi-Galerkin methods to find the approximate solution of the Tikhonov regularized equation of the Fredholm integral equations of the first kind. We evaluate the error bounds for the approximate solutions with the exact solution in the infinity norm. We provide an a priori parameter choice strategy to find the convergence rates under the infinity norm. Since smoothness of the solution is not known in applied problems, we discuss an adaptive parameter choice rule to choose the regularization parameter, and then using this regularization parameter, we obtain the order of convergence in infinity norm. We give test examples to justify the theoretical estimates.

“Spectral Method” for Determining a Kernel of the Fredholm Integral Equation of the First Kind of Convolution Type and Suppressing the Gibbs Effect

A set of one-dimensional (as well as one two-dimensional) Fredholm integral equations (IEs) of the first kind of convolution type is solved. The task for solving these equations is ill-posed (first of all, unstable); therefore, the Wiener parametric filtering method (WPFM) and the Tikhonov regularization method (TRM) are used to solve them. The variant is considered when a kernel of the integral equation (IE) is unknown or known inaccurately, which generates a significant error in the solution of IE. The so-called “spectral method” is being developed to determine the kernel of an integral equation based on the Fourier spectrum, which leads to a decrease of the error in solving the IE and image improvement. Moreover, the authors also propose a method for diffusing the solution edges to suppress the possible Gibbs effect (ringing-type distortions). As applications, the problems for processing distorted (smeared, defocused, noisy, and with the Gibbs effect) images are considered. Numerical examples are given to illustrate the use of the “spectral method” to enhance the accuracy and stability of processing distorted images through their mathematical and computer processing.

Retracted: Application Study of Sigmoid Regularization Method in Coke Quality Prediction

Retracted: Application Study of Sigmoid Regularization Method in Coke Quality Prediction

Non-negative Tucker decomposition with graph regularization and smooth constraint for clustering

Non-negative Tucker decomposition (NTD) and its graph regularized extensions are the most popular techniques for representing high-dimensional non-negative data, which are typically found in a low-dimensional sub-manifold of ambient space, from a geometric perspective. Therefore, the performance of the graph-based NTD methods relies heavily on the low-dimensional representation of the original data. However, most existing approaches treat the last factor matrix in NTD as a low-dimensional representation of the original data. This treatment leads to the loss of the original data’s multi-linear structure in the low-dimensional subspace. To remedy this defect, we propose a novel graph regularized Lp smooth NTD (GSNTD) method for high-dimensional data representation by incorporating graph regularization and an Lp smoothing constraint into NTD. The new graph regularization term constructed by the product of the core tensor and the last factor matrix in NTD, and it is used to uncover hidden semantics while maintaining the intrinsic multi-linear geometric structure of the data. The addition of the Lp smoothing constraint to NTD may produce a more accurate and smoother solution to the optimization problem. The update rules and the convergence of the GSNTD method are proposed. In addition, a randomized variant of the GSNTD algorithm based on fiber sampling is proposed. Finally, the experimental results on four standard image databases show that the proposed method and its randomized variant have better performance than some other state-of-the-art graph-based regularization methods for image clustering.

Propagation of nonlinear surface waves over non-periodic oscillatory bottom profiles

The effect of non-uniform, oscillating bottom profiles on a two-layer stable density stratification model has been examined using the method of weakly non-linear analysis. The study of bottom profiles in the context of two-layered stratified fluids has focused on three specific types: (a) profiles that exhibit a monotonically decreasing pattern, (b) profiles that decay exponentially, and (c) profiles that display Gaussian oscillations. The analysis of the second-order reflection and transmission coefficients for the nonlinear boundary value problem was conducted using a combination of the regular perturbation method and the Fourier transforms technique. The numerical findings pertaining to various physical parameters have been presented, demonstrating the impact of the Class I Bragg resonance in all three profiles and the elevation of the tails in the monotonically decreasing oscillatory profile. Specifically, the presence of high reflections due to the tail-lifting phenomenon is observed in a profile that exhibits a monotonically decreasing pattern, in contrast to the other profiles. The findings of the study indicate that interface modes demonstrate pronounced reflections when the density ratios are low, but divergent results are observed when the density ratios are high. As the density ratio R increases, there is a greater migration of wave energy from the interface mode to the surface mode, resulting in increased levels of reflection. As the value of R approaches 1, it is observed that lower frequencies exhibit significantly more pronounced internal mode reflections compared to surface mode. Several contrasting aspects can be observed in three oscillatory profiles when compared to periodic profiles. These aspects include the disappearance of zero reflection, also known as complete transmission, as well as the presence of oscillations. The findings of this study demonstrate that a monotonically oscillating decreasing profile can be considered as an efficacious Bragg breakwater. Furthermore, this study investigates the energy transfer that occurs during the movement of surface and internal waves across non-periodic oscillatory profiles. As a result, an energy balance relationship is derived, which specifically applies to surface and interface modes. This work has hydrodynamical relevance to wave propagation in coastal regions and to the hydrodynamics of tsunamis in the open ocean, both of which are affected by changes in the bathymetry of the fluid region.