Local Kernel Research Articles

Noise reduction in magnitude diffusion-weighted images using spatial similarity and diffusion redundancy.

Diffusion-weighted imaging (DWI) has significant value in clinical application, which however suffers from a serious low signal-to-noise ratio (SNR) problem, especially at high spatial resolution and/or high diffusion sensitivity factor. Here, we propose a denoising method for magnitude DWI. The method consists of two modules: pre-denoising and post-filtering, the former mines the diffusion redundancy by local kernel principal component analysis, and the latter fully mines the non-local self-similarity using patch-based non-local mean. Validated by simulation and in vivo datasets, the experiment results show that the proposed method is capable of improving the SNR of the whole brain, thus enhancing the performance for diffusion metrics estimation, crossing fiber discrimination, and human brain fiber tractography tracking compared with the different three state-of-the-art comparison methods. More importantly, the proposed method consistently exhibits superior performance to comparison methods when used for denoising diffusion data acquired with sensitivity encoding (SENSE). The proposed denoising method is expected to show significant practicability in acquiring high-quality whole-brain diffusion data, which is crucial for many neuroscience studies.

Local kernel renormalization as a mechanism for feature learning in overparametrized convolutional neural networks

Empirical evidence shows that fully-connected neural networks in the infinite-width limit (lazy training) eventually outperform their finite-width counterparts in most computer vision tasks; on the other hand, modern architectures with convolutional layers often achieve optimal performances in the finite-width regime. In this work, we present a theoretical framework that provides a rationale for these differences in one-hidden-layer networks; we derive an effective action in the so-called proportional limit for an architecture with one convolutional hidden layer and compare it with the result available for fully-connected networks. Remarkably, we identify a completely different form of kernel renormalization: whereas the kernel of the fully-connected architecture is just globally renormalized by a single scalar parameter, the convolutional kernel undergoes a local renormalization, meaning that the network can select the local components that will contribute to the final prediction in a data-dependent way. This finding highlights a simple mechanism for feature learning that can take place in overparametrized shallow convolutional neural networks, but not in shallow fully-connected architectures or in locally connected neural networks without weight sharing.

A Nonparametric Model for High-Frequency Energy Prices

Abstract This paper proposes an efficient approach for modelling a high frequency continuous time diffusion process for the dynamics of crude oil. While various applications of continuous time models are considered in the literature, the results on choosing the right model are mixed. We employ a very general non-parametric approach to capture the dynamics of the crude oil market proxied by United States Oil (USO) exchange traded fund. This approach is purely data driven and does not require specification of the drift or the diffusion coefficient function. The proposed nonparametric kernel-based estimation procedure relies on the local polynomial kernel regression, where the choice of a bandwidth parameter plays a significant role. We demonstrate that besides offering a convenient way of estimating the continuous-time models for energy prices, our estimation procedure performs well when dealing with predicting USO prices out-of-sample. The analysis is extended by incorporating possible jump diffusion, where the assumption of continuity of the stochastic process is relaxed and a jump component is added to the diffusion process. In addition, we extend our model by adding possible seasonalities in the underlying dynamics, which requires decomposing the price by means of the Maximum Overlap Discrete Wavelet Transform (MODWT) algorithm and applying nonparametric kernel-based estimation procedure to modelling of the deseasonalized prices.

A Comprehensive Study on Heterogeneous Media with Spherical Cavity: The Higher-Order Fractional Triple-Phase-Lag Thermoelasticity with Local Kernels

Fractional calculus has recently been successfully integrated into thermoelastic theories. While many existing models rely on fractional operators with anomalous kernels, this study introduces a new approach that derives triple-phase-lag (TPL) thermoelastic thermal conductivity using higher-order fractional derivatives with local, nonanomalous kernels. By applying the Taylor series expansion of higher-order fractional derivatives, as proposed by Caputo and Fabrizio, this model offers enhanced approximations for heat flux, temperature gradients, and thermal displacement. Unlike previous models, it incorporates nonlocal effects, phase lags, and higher-order time derivatives, providing a more comprehensive understanding of the interactions between heat and mechanical forces on materials. The model’s effectiveness is demonstrated by its application to an infinite, heterogeneous thermoelastic medium with a spherical cavity, where it was analyzed under various parameters, including higher-order fractional time derivatives and the heterogeneity index. Results show that an increase in the heterogeneity index intensifies the temperature gradient, leading to greater temperature variations throughout the medium. This effect is attributed to the inhomogeneous properties of the material, which influence thermal conduction and heat transfer processes.

Efficiency of the TEMJOUHERT date palm kernel as activated carbon in wastewater treatment for the Ghardaia region

This study aims to determine the potential for using activated carbon prepared by local agricultural waste for the treatment of wastewater loaded with organic pollutants. The activated carbon was prepared by chemical activation using phosphoric acid H3PO4 at an “85%” concentration, from local date kernels TEMJOUHERT (TMG) from the Ghardaïa region, Algeria. The activated carbon synthesis yield is equal to 28.56%. The adsorbent prepared was characterized by determining its physical and chemical characteristics, in particular the bulk density, the ash content, the iodine number, the surface functions by the Boehm method and the pH at the point of zero charge. Thus the textural properties are determined by scanning electron microscopy SEM and the Burnauer-emmett-Teller (BET). The surface area and micropore volumes of activated carbon TMG; were found to be 639.9190 m2/g and 0.420779 cm3/g respectively. All the results obtained from the treatment of wastewater from the Atteuf "kef doukhane area in the Ghardaia region. are clear that: the best pollutant removal rates are 84.75% for PO3-4; 85.21% for COD and 74.55% for NH4+ by activated carbons; using a mass of 1g of adsorbent per 100 ml of water, 90 min contact time and 250rpm stirring speed.

Analysis of Spatial Agglomeration Characteristics of Logistics Enterprises in Henan Province based on Poi

As an important industry connecting urban and rural areas and serving production and life, logistics enterprises, as the micro-foundation of the development of logistics industry, have a profound impact on the spatial reconstruction of regional economic and social development. National Development and Reform Commission issued the "Fourteenth Five-Year Plan" modern logistics development and "Fourteenth Five-Year Plan" modern circulation system construction planning "put forward new requirements for the development of logistics industry, emphasizing the optimization of logistics spatial layout and speed up the construction of national logistics hub, especially pointed out that to make up for the shortcomings of the central and western regions. As an important base for the development of China's logistics industry, the spatial layout of logistics enterprises in Henan province not only affects the high-quality development of the logistics industry in the province, but also plays an important role in the improvement of the national logistics network. In this paper, based on POI data, the mean nearest neighbor method, local Moran scatter plot analysis and kernel density visualization technology are used to analyze the spatial agglomeration characteristics of logistics enterprises in 157 counties in Henan Province. It is found that the spatial distribution of logistics enterprises in Henan Province has gradually evolved from multi-point dispersion to a single-core and multi-core collaborative model with Zhengzhou as the core, and presents a significant spatial positive correlation and agglomeration trend. This change has improved the logistics efficiency and promoted the strengthening of regional economic ties. At the same time, the agglomeration trend of logistics enterprises in Henan Province continues to strengthen, from the initial agglomeration in the core area to the diversified diffusion pattern, showing the continuous optimization and reconstruction of logistics network in the province.

Automatic identification of MS lesions based on local steering kernel features and sparse dictionary training

Automatic identification of MS lesions based on local steering kernel features and sparse dictionary training

DPC clustering algorithm based on K-nearest neighbors and kernel density estimation

Clustering by fast search and find of density peaks (DPC) is a density-based clustering algorithm. This algorithm does not require iteration and too many parameter settings, but it cannot identify cluster centers with small cluster density because the local structure of the data is not considered when calculating the local density. To address the above problems, a DPC clustering algorithm (KKDPC) based on K-reciprocal Neighbors (KN) and Kernel Density Estimation (KDE) is proposed. First, the number of reciprocal neighbors and local kernel density of data points are obtained by nearest neighbor and kernel density estimation methods ; second, the number of K reciprocal neighbors is added to the local kernel density to obtain a new local density; finally, the relative distance is obtained according to the local density of the data points, and the cluster center is selected and the non-center point is allocated by constructing a decision graph. Experiments are conducted using artificial and real data sets, and compared with seven clustering algorithms: DPC, DBSCAN, K-means, FCM, DPC-KNN, DPC-NN, and DPC-FWSN. The performance of the KKDPC clustering algorithm is verified by calculating the adjusted mutual information (AMI), adjusted Rand index (ARI), and normalized mutual information (NMI). The experimental results show that this method can more accurately identify the cluster center and effectively improve the clustering accuracy.

A fully locally selective large kernel network for traffic video detection

Vision Transformer (ViT) are widely used in the field of traffic video inspection because of their wide sensing field and strong global context-capturing capability. However, the ViT model has inadequate local detail feature extraction and high computational complexity. Convoluted neural networks(CNN) are commonly used as a means of video image detection. Although it is more flexible and less computationally complex in the extraction of local details, the fixed-size kernel limits it. It is difficult to effectively utilize the full local context information, resulting in the difficulty of effectively extracting the tiny targets with uneven scale distribution in the region. It is prone to leakage and misdetection of small targets. In view of this, this study proposes a new fully localized selective large kernel network (FL-SLKNet). The network effectively captures specific targets and background information through a fully localized feature extraction method, thus making small targets in the region more distinctive features. On this basis, the Adaptive Expansion Residual Module (AERM) is proposed, which solves the problem of image resolution degradation due to sensory field expansion by combining point-by-point convolution and expansion convolution and utilizing residual connections to supplement the lost information. In order to effectively identify tiny targets in the local area, this study proposes the Multi-Scale Frequency Domain Encoder (MSFDEncoder); this encoder utilizes a high-frequency branch to capture local details and a low-frequency branch to focus on the global structure, effectively capturing granular features of targets at various scales. Experimental results on the VisDrone2019-DET and BDD-100K datasets indicate that FL-SLKNet outperforms other advanced models in traffic video detection, with an increase of 3.3% and 3.4% in mAP0.5 compared to the RT-DETR model. Meanwhile, the detection performance of FL-SLKNet is excellent compared with the YOLO series on the SZ Actual Traffic Video dataset. In addition, in the rainy and hazy simulation scenarios, FL-SLKNet’s mAP0.5 improves by 5.5% and 2.6% compared to the RT-DETR model, and the extreme weather robustness performance is better.

Distributed learning for kernel mode–based regression

AbstractWe propose a parametric kernel mode–based regression built on the mode value, which provides robust and efficient estimators for datasets containing outliers or heavy‐tailed distributions. To address the challenges posed by massive datasets, we integrate this regression method with distributed statistical learning techniques, which greatly reduces the required amount of primary memory and simultaneously accommodates heterogeneity in the estimation process. By approximating the local kernel objective function with a least squares format, we are able to preserve compact statistics for each worker machine, facilitating the reconstruction of estimates for the entire dataset with minimal asymptotic approximation error. Additionally, we explore shrinkage estimation through local quadratic approximation, showcasing that the resulting estimator possesses the oracle property through an adaptive LASSO approach. The finite‐sample performance of the developed method is illustrated using simulations and real data analysis.

Maximum Local Density-Driven Non-overlapping Radial Basis Function Support Kernel Neural Network

The learning and optimization of kernels in the radial basis function neural network (RBFNN) are crucial. However, in existing methods, there are issues of overfitting when learning kernel parameters. The learned kernels are also sensitive to outliers. This paper proposes a general kernel learning strategy for RBFNN called non-overlapping maximum local density support kernel learning (MLD-SKL), which contains two modules, the non-overlapping maximum local density (MLD) kernel learning module and support kernel learning (SKL) module. In the MLD kernel learning stage, the candidate set of kernels is incrementally determined based on the local density of samples. Meanwhile, it is required that the coverage ranges of kernels from different classes do not overlap with each other. This module is effective in reducing the impact of outliers. In the SKL stage, kernel importance indicator is defined to measure the importance of kernels. The learned support kernels are utilized to construct a maximum local density-driven non-overlapping radial basis function support kernel neural network (MLD-RBFSKNN). The RBFNN constructed through MLD-SKL exhibits a more compact structure. The experiments demonstrate that the proposed MLD-RBFSKNN improves accuracy in recognition task. Furthermore, while achieving superior recognition performance, the final constructed network also has the minimum number of kernels.

Interval-Censored Linear Quantile Regression

Censored quantile regression has emerged as a prominent alternative to classical Cox’s proportional hazards model or accelerated failure time model in both theoretical and applied statistics. While quantile regression has been extensively studied for right-censored survival data, methodologies for analyzing interval-censored data remain limited in the survival analysis literature. This article introduces a novel local weighting approach for estimating linear censored quantile regression, specifically tailored to handle diverse forms of interval-censored survival data. The estimation equation and the corresponding convex objective function for the regression parameter can be constructed as a weighted average of quantile loss contributions at two interval endpoints. The weighting components are nonparametrically estimated using local kernel smoothing or ensemble machine learning techniques. To estimate the nonparametric distribution mass for interval-censored data, a modified EM algorithm for nonparametric maximum likelihood estimation is employed by introducing subject-specific latent Poisson variables. The proposed method’s empirical performance is demonstrated through extensive simulation studies and real data analyses of two HIV/AIDS datasets. Supplementary materials for this article are available online.

Adaptivity in Local Kernel Based Methods for Approximating the Action of Linear Operators

Adaptivity in Local Kernel Based Methods for Approximating the Action of Linear Operators

Conformal anomalies and renormalized stress tensor correlators for nonconformal theories

We analyze the proposal of defining the Weyl anomaly for classically nonconformal theories as gmn⟨Tmn⟩−⟨gmnTmn⟩, originally put forward by Duff, in the case of a scalar field with quartic self-interaction in 4d. We work in the context of dimensional regularization in curved background to two loops (first order in the coupling). We review the original regularized but not renormalized prescription and its ambiguities; we argue that it cannot be extended to the interacting theory as it fails to provide a finite result. We then propose an alternative prescription via renormalized expectation values. At one loop, our candidate reproduces the local heat kernel result, while its extension to interacting theories contains nonlocal contributions. Published by the American Physical Society 2024

Local stability in kidney exchange programs

When each patient of a kidney exchange program has a preference ranking over its set of compatible donors, questions naturally arise surrounding the stability of the proposed exchanges. We extend recent work on stable exchanges by introducing and underlining the relevance of a new concept of locally stable, or L-stable, exchanges. We show that locally stable exchanges in a compatibility digraph are exactly the so-called local kernels (L-kernels) of an associated blocking digraph (whereas the stable exchanges are the kernels of the blocking digraph), and we prove that finding a nonempty L-kernel in an arbitrary digraph is NP-complete. Based on these insights, we propose several integer programming formulations for computing an L-stable exchange of maximum size. We conduct numerical experiments to assess the quality of our formulations and to compare the size of maximum L-stable exchanges with the size of maximum stable exchanges. It turns out that nonempty L-stable exchanges frequently exist in digraphs which do not have any stable exchange. All the above results and observations carry over when the concept of (locally) stable exchanges is extended to the concept of (locally) strongly stable exchanges.

LSIAC-MRA for nonuniform meshes and applications to mesh adaptivity

In this article we consider the extension of the (L)SIAC-MRA enhancement procedure to nonuniform meshes. We demonstrate that error reduction can be obtained on perturbed quadrilateral and Delaunay meshes, and investigate the effect of limited resolution and its impact on the procedure for various function types. We show that utilizing mesh-based localized kernel scalings, which were shown to reduce approximation errors for LSIAC filters, improve the performance of the LSIAC-MRA enhancement procedure. Lastly, we demonstrate the usefulness of enhanced approximations generated by (L)SIAC-MRA in mesh adaptivity applications, and show that SIAC reconstruction can be used in identification of regions of high error in steady-state DG approximations.

Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency

In this paper, for a wide class of nonparametric regression models, new local linear kernel estimators are proposed that are uniformly consistent under close-to-minimal and visual conditions on design points. These estimators are universal in the sense that their designs can be either fixed and not necessarily satisfying the traditional regularity conditions, or random, while not necessarily consisting of independent or weakly dependent random variables. With regard to the design elements, only dense filling of the regression function domain with the design points without any specification of their correlation is assumed. This study extends the dense data methodology and main results of the authors’ previous work for the case of regression functions of several variables.

Generalized single index modeling of longitudinal data with multiple binary responses.

In health and clinical research, medical indices (eg, BMI) are commonly used for monitoring and/or predicting health outcomes of interest. While single-index modeling can be used to construct such indices, methods to use single-index models for analyzing longitudinal data with multiple correlated binary responses are underdeveloped, although there are abundant applications with such data (eg, prediction of multiple medical conditions based on longitudinally observed disease risk factors). This article aims to fill the gap by proposing a generalized single-index model that can incorporate multiple single indices and mixed effects for describing observed longitudinal data of multiple binary responses. Compared to the existing methods focusing on constructing marginal models for each response, the proposed method can make use of the correlation information in the observed data about different responses when estimating different single indices for predicting response variables. Estimation of the proposed model is achieved by using a local linear kernel smoothing procedure, together with methods designed specifically for estimating single-index models and traditional methods for estimating generalized linear mixed models. Numerical studies show that the proposed method is effective in various cases considered. It is also demonstrated using a dataset from the English Longitudinal Study of Aging project.

Seismic Anisotropy From 6C Ground Motions of Ambient Seismic Noise

AbstractWe propose a new approach capable of measuring local seismic anisotropy from 6C (three‐component translation and three‐component rotation) amplitude observations of ambient seismic noise data. Our recent theory demonstrates that the amplitude ratio of 6C cross‐correlation functions (CCFs) enables retrieving the local phase velocity. This differs from conventional velocity extraction methods based on the travel time. Its local sensitivity kernel beneath the 6C seismometer allows us to study anisotropy from azimuth‐dependent CCFs, avoiding path effects. Such point measurements have great potential in planetary exploration, ocean bottom observations, or volcanology. We apply this approach to a small seismic array at Pion Flat Observatory (PFO) in southern California, array‐deriving retrieves rotational ground motions from microseismic noise data. The stress‐induced anisotropy is well resolved and compatible with other tomography results, providing constraints on the origin of depth‐dependent seismic anisotropy.

Two-stage regression spline modeling based on local polynomial kernel regression

Two-stage regression spline modeling based on local polynomial kernel regression