Gaussian Weighting Function Research Articles

An Ensemble Framework of Multi-ratio Undersampling-based Imbalanced Classification

Class imbalance is commonly observed in real-world data, and it is problematic in that it degrades classification performance due to biased supervision. Undersampling is an effective resampling approach to the class imbalance. The conventional undersampling-based approaches involve a single fixed sampling ratio. However, different sampling ratios have different preferences toward classes. In this paper, an undersampling-based ensemble framework, MUEnsemble, is proposed. This framework involves weak classifiers of different sampling ratios, and it allows for a flexible design for weighting weak classifiers in different sampling ratios. To demonstrate the principle of the design, in this paper, a uniform weighting function and a Gaussian weighting function are presented. An extensive experimental evaluation shows that MUEnsemble outperforms undersampling-based and oversampling-based state-of-the-art methods in terms of recall, gmean, F-measure, and ROC-AUC metrics. Also, the evaluation showcases that the Gaussian weighting function is superior to the uniform weighting function. This indicates that the Gaussian weighting function can capture the different preferences of sampling ratios toward classes. An investigation into the effects of the parameters of the Gaussian weighting function shows that the parameters of this function can be chosen in terms of recall, which is preferred in many real-world applications.

A Comparative Study of Nonparametric Kernel estimators with Gaussian Weight Function

Nowadays, Parametric methods become unfavorable by researchers because of the restrictions on using them and losing the flexibility in estimating and analysis the data. Therefore, the researchers preferred the nonparametric method which proved their efficiency and capable to analysis the data without of predetermined assumptions. Consequently, the data and their included information are becoming who determine the functional shape for the studied population and there are no parameters instead of the observations. The objective of estimating the nonparametric regression function is to approximate the regression function to the real regression function. On the other hand, COVID-19 pandemic nowadays speared in all the countries one of them is Iraq. The function of infection speared have been studied in different countries but not in Iraq. Therefore, the aim of our research is to apply three nonparametric Kernel estimators with Gaussian weighted function to model and forecast the number of infections of COVID-19 in Iraq. R software and the data represent the daily number of COVID-19 infections for the period 23/2/2020 to 21/6/2020 are used to apply many models and choose the appropriate one. The results of applying three nonparametric Kernel model that the Priestley-Chao model is the appropriate one in all the sample sizes and other conditions

Geographically and Temporally Weighted Regression Model with Gaussian Kernel Weighted Function and Bisquare Kernel Weighted Function

The Geographically and Temporally Weighted Regression (GTWR) model is a development of the Geographically Weighted Regression (GWR) model. Estimation of parameters in the GTWR model uses Weighted Least Square (WLS). The purpose of this study is to build two GTWR models using the Gaussian kernel weight function and the Bisquare kernel weight function on the percentage of poor people in East Java Province in 2010-2015. Each weighted function produces 228 different models at each location and time. The GTWR method with the Gaussian Kernel weight function produces parameter estimates at the observation location in the range between 0.7796 to 48.1435. Meanwhile, the parameter estimation of the GTWR model with the Kernel Bisquare weight function ranges from 0.7828 to 48.1444. The two weight functions can model the percentage of poor people in East Java Province in 2010-2015, with R2 values of 98.994% and 98.987%, respectively.

Analysis on evolution characteristics of spatial expansion pattern of urban agglomeration construction land based on environmental characteristics

The feature extraction accuracy and efficiency of traditional urban agglomeration construction land spatial expansion pattern evolution characteristics analysis methods still need to be further improved. Therefore, an analysis method of urban agglomeration construction land spatial expansion pattern evolution characteristics based on environmental characteristics is proposed. This method uses Gaussian weighting function to select remote sensing image feature points of urban agglomeration construction land and extract urban environmental features. According to the extraction results, the expansion parameters of urban agglomeration construction land are calculated, and the evolution characteristic analysis function is constructed. Experimental results show that the proposed method analyse the evolution of the characteristics, can be effectively extracting features of the evolution pattern of city group extension, and has a high efficiency, the maximum efficiency of the analysis and the extraction accuracy of 96% and 98%, respectively.

New bounds for soft margin estimator via concavity of Gaussian weighting function

In the present article, we elaborate on the notion to obtain bounds for the soft margin estimator of “Identification of Patient Zero in Static and Temporal Network-Robustness and Limitations”. To achieve these bounds for the soft margin estimator, we utilize the concavity of the Gaussian weighting function and well-known Jensen’s inequality. To acquire some more general bounds for the soft margin estimator, we consider some general functions defined on rectangles. We also use the behavior of the Jaccard similarity function to extract some handsome bounds for the soft margin estimator.

A Distributed Gaussian Weight Function based Deep Spectral Cluster Learning and Enhanced Deep Patch Level Classifier for Detection of Diabetic Retinopathy

A Distributed Gaussian Weight Function based Deep Spectral Cluster Learning and Enhanced Deep Patch Level Classifier for Detection of Diabetic Retinopathy

Simulation of macrosegregation in direct-chill casting—A model based on meshless diffuse approximate method

A multiphysics numerical model has been developed for prediction of macrosegregation in direct-chill casting. The model uses volume averaged mass, momentum, energy, and species conservation equations to simulate the solidification of axisymmetric aluminium-alloy billets. The boundary conditions for the heat transfer include the effects of hot top, mould chill, and direct chill. The volume averaged conservation equations are solved with the explicit local meshless diffuse-approximate method. The approximation coefficients are evaluated on subdomains containing 14 nodes with the second order polynomial basis and the Gaussian weight function. Problems with instabilities due to strong convection are successfully eliminated with an adaptive shift of the weight function and evaluation position in the upstream direction. The automatic adaptive generation of computational node arrangement decreases the calculation time and in a straightforward way enables investigation of the complex flow for geometrically different inflow structures, including sharp and curved edges. The model is used for casting simulation of an Al-5.25wt%Cu alloy billet with a 120 mm radius for various inlet designs. The effect of inlet geometry on the temperature, solid fraction, melt flow, and macrosegregation is investigated. The described developments represent a first meshless numerical approach for simulation of macrosegregation of an important industrial process.

Topological and Dynamical Properties of Composition Operators

We study various properties of composition operators acting between generalized Fock spaces $\mathcal{F}_\varphi^p$ and $\mathcal{F}_\varphi^q$ with weight functions $\varphi$ grow faster than the classical Gaussian weight function $\frac{1}{2}|z|^2$ and satisfy some mild smoothness conditions. We have shown that if $p\neq q,$ then the composition operator $C_\psi: \mathcal{F}_\varphi^p \to \mathcal{F}_\varphi^q $ is bounded if and only if it is compact. This result shows a significance difference with the analogous result for the case when $C_\psi$ acts between the classical Fock spaces or generalized Fock spaces where the weight functions grow slower than the Gaussian weight function. We further described the Schatten $\mathcal{S}_p(\mathcal{F}_\varphi^2)$ class, normal, unitary, cyclic and supercyclic composition operators. As an application, we characterized the compact differences, the isolated and essentially isolated points, and connected components of the space of the operators under the operator norm topology.

Effect of the leakage location pattern on the speed of recovery in water supply networks

The International Water Association states that Non-Revenue Water is an efficient indicator of the performance of a water company that has been implemented internationally. The volume of water loss expressed as Non-Revenue Water at the global level shows a high number. Every year more than 32 billion m3 of treated water is lost due to leakage from the distribution network. There are four pillars in the network leakage management strategy include management of pressure, speed of recovery, active leakage control, and asset management. These components influence how leakage is managed and affect the volume and value of economic leakage - in a distribution network of water companies. The current annual volume of physical losses tends to increase along with the expansion service area of the distribution network. The rate of increase can be inhibited by the right strategy combining the four components into an effective leakage management strategy. This study analyzes the distribution pattern of leakage points in water distribution pipelines in Malang City, and how much they affect the speed of recovery. The data in this study consist of 5449 pipeline leakage points which include spatial and attributes data. The method used in this study is the Spatial Point Process. The results of the analysis show that the distribution pattern of leakage is an inhomogeneous pattern. It is found that the parameters of the model -with Euclidean distance- the leakage pattern affects the occurrence of leakage and the Geographical Weighted Regression model -with fixed Gaussian Kernel Weight Function with Manhattan distance- the leakage pattern affects the speed of recovery.

Multi-Level Features Extraction for Discontinuous Target Tracking in Remote Sensing Image Monitoring.

Many techniques have been developed for computer vision in the past years. Features extraction and matching are the basis of many high-level applications. In this paper, we propose a multi-level features extraction for discontinuous target tracking in remote sensing image monitoring. The features of the reference image are pre-extracted at different levels. The first-level features are used to roughly check the candidate targets and other levels are used for refined matching. With Gaussian weight function introduced, the support of matching features is accumulated to make a final decision. Adaptive neighborhood and principal component analysis are used to improve the description of the feature. Experimental results verify the efficiency and accuracy of the proposed method.

Local-crosscorrelation elastic full-waveform inversion

Full-waveform inversion (FWI) in its classic form is a method based on minimizing the [Formula: see text] norm of the difference between the observed and simulated seismic waveforms at the receiver locations. The objective is to find a subsurface model that reproduces the full waveform including the traveltimes and amplitudes of the observed seismic data. However, the widely used [Formula: see text]-norm-based FWI faces many issues in practice. The point-wise comparison of waveforms fails when the phase difference between the compared waveforms of the predicted and observed data is larger than a half-cycle. In addition, amplitude matching is impractical considering the simplified physics that we often use to describe the medium. To avoid these known problems, we have developed a novel elastic FWI algorithm using the local-similarity attribute. It compares two traces within a predefined local time extension; thus, is not limited by the half-cycle criterion. The algorithm strives to maximize the local similarities of the predicted and observed data by stretching/squeezing the observed data. Phases instead of amplitudes of the seismic data are used in the comparison. The algorithm compares two data sets locally; thus, it performs better than the global correlation in matching multiple arrivals. Instead of picking/calculating one stationary stretching/squeezing curve, we used a weighted integral to find all possible stationary curves. We also introduced a polynomial-type weighting function, which is determined only by the predefined maximum stretching/squeezing and is guaranteed to be smoothly varying within the extension range. Compared with the previously used Gaussian or linear weighting functions, our polynomial one has fewer parameters to play around with. A modified synthetic elastic Marmousi model and the North Sea field data are used to verify the effectiveness of the developed approach and also reveal some of its limitations.

Inverse Gaussian-beam common-reflection-point-stack imaging in crosswell seismic tomography

To solve problems in small-scale and complex structural traps, the inverse Gaussian-beam stack-imaging method is commonly used to process crosswell seismic wave reflection data. Owing to limited coverage, the imaging quality of conventional ray-based crosswell seismic stack imaging is poor in complex areas; moreover, the imaging range is small and with sever interference because of the arc phenomenon in seismic migration. Thus, we propose the inverse Gaussian-beam stack imaging, in which Gaussian weight functions of rays contributing to the geophones energy are calculated and used to decompose the seismic wavefield. This effectively enlarges the coverage of the reflection points and improves the transverse resolution. Compared with the traditional VSP-CDP stack imaging, the proposed methods extends the imaging range, yields higher horizontal resolution, and is more adaptable to complex geological structures. The method is applied to model a complex structure in the K-area. The results suggest that the wave group of the target layer is clearer, the resolution is higher, and the main frequency of the crosswell seismic section is higher than that in surface seismic exploration The effectiveness and robustness of the method are verified by theoretical model and practical data.

Improving Hyperspectral Anomaly Detection With a Simple Weighting Strategy

Numerous hyperspectral anomaly detection (AD) methods suffer from complex background compositions and subpixel objects due to their inadequate Gaussian-distributed representations for nonhomogeneous backgrounds or their low discrimination between subpixel anomalies and the background. To alleviate these issues, a novel hyperspectral AD weighting strategy based on tensor decomposition and cluster weighting is proposed in this letter. Equipped with this simple but effective strategy as a postprocess, the detection performances of generic AD methods can be significantly boosted. In this strategy, Tucker decomposition is adopted to remove the major background information. A parameter-adaptive $k$ -means clustering method is then applied on the decomposed anomaly/noise data cube to assemble homogeneous regions. After segmenting the clustering result into a number of nonoverlapping eight-connected domains, corresponding weights are assigned to large domains according to an improved Gaussian weight function. Finally, the resulting weight matrix is multiplied by the results of the detectors to achieve a performance boost. Experiments on two hyperspectral data sets validate the effectiveness of the proposed strategy.

Object registration in semi-cluttered and partial-occluded scenes for augmented reality

This paper proposes a stable and accurate object registration pipeline for markerless augmented reality applications. We present two novel algorithms for object recognition and matching to improve the registration accuracy from model to scene transformation via point cloud fusion. Whilst the first algorithm effectively deals with simple scenes with few object occlusions, the second algorithm handles cluttered scenes with partial occlusions for robust real-time object recognition and matching. The computational framework includes a locally supported Gaussian weight function to enable repeatable detection of 3D descriptors. We apply a bilateral filtering and outlier removal to preserve edges of point cloud and remove some interference points in order to increase matching accuracy. Extensive experiments have been carried to compare the proposed algorithms with four most used methods. Results show improved performance of the algorithms in terms of computational speed, camera tracking and object matching errors in semi-cluttered and partial-occluded scenes.

Efficient Correlation Tracking via Center-Biased Spatial Regularization.

Correlation filters (CFs) have been applied to visual tracking with success providing excellent performance in terms of accuracy and efficiency. The underlying periodic assumption of the training samples results in their great efficiency when using the fast Fourier transform (FFT), yet it also brings unwanted boundary effects. To address this issue, the recently proposed spatially-regularized discriminative CF (SRDCF) method introduces a Gaussian weight function to regularize the learning filter, yielding favorable performances in accuracy but high computational complexity because the objective of the SRDCF cannot achieve a closed solution via the FFT. Motivated by SRDCF, we present an efficient and effective CF-based tracker using center-biased constraint weights (CBCWs), which improve simultaneously speed and accuracy. Specifically, we first construct a CBCW function by exploiting the symmetry of the Fourier transform. The values of the constraint weights are real in both time and frequency domains, so that the optimization can be directly solved in the frequency domain without any data transformation, thereby greatly reducing its computational complexity. Moreover, according to the average peak-tocorrelation energy value of the CF response, we propose an efficient and effective filter update strategy to handle occlusions during tracking. Extensive experiments on the OTB-2013, OTB- 2015, and VOT2016 benchmarks demonstrate that the proposed tracker significantly outperforms the baseline SRDCF in terms of accuracy and efficiency. Moreover, the proposed method performs favorably against 16 other representative state-of-the-art methods regarding robustness and success rate.

Development of meshless phase field method for two-phase flow

The purpose of the present paper is the development of meshless diffuse approximate method in connection with the phase field formulation for solution of two-phase flow problems. The numerical approach enables single-domain, fixed-node treatment of the involved moving boundaries. The problem is formulated for Newtonian fluids based on a physical model that involves a coupled set of Navier–Stokes and Cahn–Hilliard equations. Diffuse approximate method is structured with a second order polynomial basis, Gaussian weight function, adaptive upwind scheme and eleven-node local subdomain. The pressure-velocity coupling is performed by the incremental fractional step method and explicit time discretization is used to solve the governing equations. The method is demonstrated in axisymmetry for a problem of two co-flowing immiscible fluids with different material properties that yield dripping or jetting of the core fluid. An assessment of the novel method is carried out based on comparison of the present results with the finite volume method outcome. A sensitivity study of various process parameters is carried out and verified against the previously published results. The paper represents a pioneering development in simulation of two-phase flows by a meshless method.

Simulation of a macrosegregation benchmark with a meshless diffuse approximate method

PurposeThe purpose of this paper is to simulate a macrosegregation solidification benchmark by a meshless diffuse approximate method. The benchmark represents solidification of Al 4.5 wt per cent Cu alloy in a 2D rectangular cavity, cooled at vertical boundaries.Design/methodology/approachA coupled set of mass, momentum, energy and species equations for columnar solidification is considered. The phase fractions are determined from the lever solidification rule. The meshless diffuse approximate method is structured by weighted least squares method with the second-order monomials for trial functions and Gaussian weight functions. The spatial localization is made by overlapping 13-point subdomains. The time-stepping is performed in an explicit way. The pressure-velocity coupling is performed by the fractional step method. The convection stability is achieved by upstream displacement of the weight function and the evaluation point of the convective operators.FindingsThe results show a very good agreement with the classical finite volume method and the meshless local radial basis function collocation method. The simulations are performed on uniform and non-uniform node arrangements and it is shown that the effect of non-uniformity of the node distribution on the final segregation pattern is almost negligible.Originality/valueThe application of the meshless diffuse approximate method to simulation of macrosegregation is performed for the first time. An adaptive upwind scheme is successfully applied to the diffuse approximate method for the first time.

An effective two-dimensional linear discriminant analysis with locality preserving approach for image recognition

Linear discriminant analysis (LDA) is one of the most popular feature extraction methods in image recognition. Nevertheless, LDA always suffers from some undesired behaviors caused by globality, namely ignoring local geometric structure of images. To fully capture the geometric information, we propose a novel two-dimensional linear discriminant analysis with locality preserving (2DLP-LDA) approach, which can cover both within-class and between-class local geometric information. 2DLP-LDA re-characterizes the within-class scatter matrix by employing locality preserving projection technique and re-characterizes the between-class scatter matrix by introducing a Gaussian weighting function, making the samples from the same class moderately cluster, while the samples from different classes properly distribute in the reduced subspace. Encouraging experimental results on FERET face database as well as SEU bovine iris database show the effectiveness of the proposed approach.

Accurate B-spline-based 3-D interpolation scheme for digital volume correlation.

An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.

Robust Pedestrian Classification Based on Hierarchical Kernel Sparse Representation.

Vision-based pedestrian detection has become an active topic in computer vision and autonomous vehicles. It aims at detecting pedestrians appearing ahead of the vehicle using a camera so that autonomous vehicles can assess the danger and take action. Due to varied illumination and appearance, complex background and occlusion pedestrian detection in outdoor environments is a difficult problem. In this paper, we propose a novel hierarchical feature extraction and weighted kernel sparse representation model for pedestrian classification. Initially, hierarchical feature extraction based on a CENTRIST descriptor is used to capture discriminative structures. A max pooling operation is used to enhance the invariance of varying appearance. Then, a kernel sparse representation model is proposed to fully exploit the discrimination information embedded in the hierarchical local features, and a Gaussian weight function as the measure to effectively handle the occlusion in pedestrian images. Extensive experiments are conducted on benchmark databases, including INRIA, Daimler, an artificially generated dataset and a real occluded dataset, demonstrating the more robust performance of the proposed method compared to state-of-the-art pedestrian classification methods.