Kernel Function Value Research Articles

A Novel Combined Regularization for Identifying Random Load Sources on Coal‐Rock Structure

This study discusses the practical engineering problem of determining random load sources on coal‐rock structures. A novel combined regularization technique combining mollification method (MM) and discrete regularization (DR), which was called MM‐DR technique, was proposed to reconstruct random load sources on coal‐rock structures. MM‐DR technology is compared with DR, Tikhonov regularization (TR), and maximum entropy regularization (MER) in load reconstruction. The results show that the reconstructed random load sources are more consistent with the real load sources using MM‐DR technique combined with particle swarm optimization (PSO) and L‐curve method, which was named as PSO‐L method, and selecting optimal ω value of kernel function is beneficial to overcome the ill‐posed of random load sources reconstruction and to obtain the stable and approximate solutions. The method proposed in this study provides a theoretical basis for the recognition of coal‐rock interface.

Efficient Algorithms for Kernel Aggregation Queries

Kernel functions support a broad range of applications that require tasks like density estimation, classification, regression or outlier detection. For these tasks, a common online operation is to compute the weighted aggregation of kernel function values with respect to a set of points. However, scalable aggregation methods are still unknown for typical kernel functions (e.g., Gaussian kernel, polynomial kernel, sigmoid kernel and additive kernels) and weighting schemes. In this paper, we propose a novel and effective bounding technique, by leveraging index structures, to speed up the computation of kernel aggregation. In addition, we extend our technique to additive kernel functions, including X2, intersection, JS and Hellinger kernels, which are widely used in different communities, e.g., computer vision, medical science, Geoscience etc. To handle the additive kernel functions, we further develop the novel and effective bound functions to efficiently evaluate the kernel aggregation. Experimental studies on many real datasets reveal that our proposed solution KARL achieves at least one order of magnitude speedup over the state-of-the-art for different types of kernel functions.

Denoising using Self Adaptive Radial Basis Function

This paper presents an adaptive form of the Radial basis function neural network to correct the noisy image in a unified way without estimating the existing noise model in the image. Proposed method needs a single noisy image to train the adaptive radial basis function network to learn the correction of the noisy image. The gaussian kernel function is applied to reconstruct the local disturbance appeared because of the noise. The proposed adaptiveness in the radial basis function network is compared with the fixed form of spreadness and the center value of kernel function. The proposed solution can correct the image suffered from different varieties of noises like speckle noise, Gaussian noise, salt & pepper noise separately or combination of noises. Various standard test images are considered for test purpose with different levels of noise density and performance of proposed algorithm is compared with adaptive wiener filter.

Denoising using Self Adaptive Radial Basis Function

This paper presents an adaptive form of the Radial basis function neural network to correct the noisy image in a unified way without estimating the existing noise model in the image. Proposed method needs a single noisy image to train the adaptive radial basis function network to learn the correction of the noisy image. The gaussian kernel function is applied to reconstruct the local disturbance appeared because of the noise. The proposed adaptiveness in the radial basis function network is compared with the fixed form of spreadness and the center value of kernel function. The proposed solution can correct the image suffered from different varieties of noises like speckle noise, Gaussian noise, salt & pepper noise separately or combination of noises. Various standard test images are considered for test purpose with different levels of noise density and performance of proposed algorithm is compared with adaptive wiener filter.

Consistent shepard interpolation for SPH-based fluid animation

We present a novel technique to correct errors introduced by the discretization of a fluid body when animating it with smoothed particle hydrodynamics (SPH). Our approach is based on the Shepard correction, which reduces the interpolation errors from irregularly spaced data. With Shepard correction, the smoothing kernel function is normalized using the weighted sum of the kernel function values in the neighborhood. To compute the correction factor, densities of neighboring particles are needed, which themselves are computed with the uncorrected kernel. This results in an inconsistent formulation and an error-prone correction of the kernel. As a consequence, the density computation may be inaccurate, thus the pressure forces are erroneous and may cause instabilities in the simulation process. We present a consistent formulation by using the corrected densities to compute the exact kernel correction factor and, thereby, increase the accuracy of the simulation. Employing our method, a smooth density distribution is achieved, i.e., the noise in the density field is reduced by orders of magnitude. To show that our method is independent of the SPH variant, we evaluate our technique on weakly compressible SPH and on divergence-free SPH. Incorporating the corrected density into the correction process, the problem cannot be stated explicitly anymore. We propose an efficient and easy-to-implement algorithm to solve the implicit problem by applying the power method. Additionally, we demonstrate how our model can be applied to improve the density distribution on rigid bodies when using a well-known rigid-fluid coupling approach.

Unified Noise Reduction using Adaptive Radial Basis Function

The images captured by SAR and sonar are blurred and corrupted more by speckle noise and also other types of noise like Gaussian noise and salt & pepper noise. Denoising all types of noises to get perfect image is a vital challenge, earlier works on the same mode addressed with one filter for one noise, there is no one common or unified filter which can denoise all types of noise. Therefore in this paper, we have designed a filter which not only removes speckle noise, but also combination of other noises. Here IUNR (Intelligent Unified Noise Reduction) algorithm is proposed which is based on neural network called adaptive radial basis function acts as a unified filter for Denoising. Proposed method needs a single noisy image to train the adaptive radial basis function neural network to learn the correction of the noisy image. The Gaussian kernel function is applied to reconstruct the local disturbance appeared because of the noise. The proposed adaptive radial basis function network is compared with the fixed form which has fixed spread and the center value of kernel function. This method can correct the image suffered from different varieties of noises like speckle noise, salt & pepper noise and Gaussian noise separately or combination of noise. Various standard test images are considered for test purpose with different levels of noise density and performance of proposed algorithm is compared with adaptive wiener filter.

Laplacian Embedded Infinite Kernel Model for Semi-Supervised Classification

Promoted by its convexity and low time complexity, Laplacian embedded support vector regression (LapESVR) model based on manifold regularization (MR) has assumed an important role in semi-supervised classification. Conventionally, the LapESVR model is based on a single kernel function that is intrinsically capable of describing one feature mapping relation only. However, when the data to be processed is from a complex dataset where multiple features of the data are required to be treated, the classification performance using the LapESVR based on a single kernel substantially degrade, indicating that the classification requirement in this case is beyond the capability of the LapESVR. In addition, the processing data is often subject to the impact of abnormal data samples; therefore, in practice assigning a fixed value that is related to the average distance of the processing data as the parameter value of kernel function of the LapESVR is by no means optimal. To solve the problems as mentioned regarding the LapESVR, this paper proposes a Laplacian embedded infinite kernel regression (LapEIKR) model. The proposed model combines the multiple kernels linearly to improve its ability of characterization of the processing data, typical in semi-supervised classification of complex datasets, with multiple features. Further, the parameter setting of the multiple kernels of the LapEIKR model is turned into an optimization problem by formulating a corresponding minimum objective function and an iterative algorithm, and then the values of the settings are facilitated to be obtained by a formulated calculation, assuming the optimal values with respect to the designed objective function. Comparative experiments on the UCI datasets, benchmark datasets and Caltech256 datasets show that the proposed LapEIKR model is improving in terms of adaptivity and efficiency.

Linear diffusion-wave channel routing using a discrete Hayami convolution method

Summary The convolution of an input with a response function has been widely used in hydrology as a means to solve various problems analytically. Due to the high computation demand in solving the functions using numerical integration, it is often advantageous to use the discrete convolution instead of the integration of the continuous functions. This approach greatly reduces the amount of the computational work; however, it increases the possibility for mass balance errors. In this study, we analyzed the characteristics of the kernel function for the Hayami convolution solution to the linear diffusion-wave channel routing with distributed lateral inflow. We propose two ways of selection of the discrete kernel function values: using the exact point values or using the center-averaged values. Through a hypothetical example and the applications to Asotin Creek, WA and the Clearwater River, ID, we showed that when the point kernel function values were used in the discrete Hayami convolution (DHC) solution, the mass balance error of channel routing is dependent on the number of time steps on the rising limb of the Hayami kernel function. The mass balance error is negligible when there are more than 1.8 time steps on the rising limb of the kernel function. The fewer time steps on the rising limb, the greater risk of high mass balance errors. When the average kernel function values are used for the DHC solution, however, the mass balance is always maintained, since the integration of the discrete kernel function is always unity.

Chinese Question Classification Based on Question Property Kernel

Support vector machine have been widely used in classification tasks, however, the structure of the question is ignored while using the standard kernel function in the question classification. To solve the problem, a question property kernel function which combines syntactic dependency relationship and POS (part of speech) is proposed in this paper. Firstly we extract the term, POS, dependency relationship of "HED" words and dependency relationship of "question words" from questions. And then we adopt the value of kernel function by computing the dependency relationship of the term, POS, and the dependency path which the two terms shared. At last we get the support vectors by SMO algorithm. The results of experiments show that the kernel function proposed in this paper which implicated the effective utilization of the question structure can improves the accuracy of the classification.

Using support vector machine with a hybrid feature selection method to the stock trend prediction

In this paper, we developed a prediction model based on support vector machine (SVM) with a hybrid feature selection method to predict the trend of stock markets. This proposed hybrid feature selection method, named F- score and Supported Sequential Forward Search (F_SSFS), combines the advantages of filter methods and wrapper methods to select the optimal feature subset from original feature set. To evaluate the prediction accuracy of this SVM-based model combined with F_SSFS, we compare its performance with back-propagation neural network (BPNN) along with three commonly used feature selection methods including Information gain, Symmetrical uncertainty, and Correlation-based feature selection via paired t-test. The grid-search technique using 5-fold cross-validation is used to find out the best parameter value of kernel function of SVM. In this study, we show that SVM outperforms BPN to the problem of stock trend prediction. In addition, our experimental results show that the proposed SVM-based model combined with F_SSFS has the highest level of accuracies and generalization performance in comparison with the other three feature selection methods. With these results, we claim that SVM combined with F_SSFS can serve as a promising addition to the existing stock trend prediction methods.

Incorporation of measurement models in the IHCP: validation of methods for computing correction kernels

Thermocouples or other measuring devices are often imbedded into a solid to provide data for an inverse calculation. It is well-documented that such installations will result in erroneous (biased) sensor readings, unless the thermal properties of the measurement wires and surrounding insulation can be carefully matched to those of the parent domain. Since this rarely can be done, or doing so is prohibitively expensive, an alternative is to include a sensor model in the solution of the inverse problem. In this paper we consider a technique in which a thermocouple model is used to generate a correction kernel for use in the inverse solver. The technique yields a kernel function with terms in the Laplace domain. The challenge of determining the values of the correction kernel function is the focus of this paper. An adaptation of the sequential function specification method[1] as well as numerical Laplace transform inversion techniques are considered for determination of the kernel function values. Each inversion method is evaluated with analytical test functions which provide simulated "measurements". Reconstruction of the undisturbed temperature from the "measured" temperature and the correction kernel is demonstrated.

Forecasting financial condition of Chinese listed companies based on support vector machine

Due to the radical changing and specialty of Chinese capital market, it is challenging to develop a powerful financial distress prediction model. In this paper, we first analyzed the feasibility of Chinese special-treated companies as distressed sample by using statistical methods. Then we developed a prediction model based on support vector machines (SVM) for an unmatched sample of Chinese high-tech manufacture companies. The grid-search technique using 10-fold cross-validation is used to find out the best parameter value of kernel function of SVM. The experiment results show that the proposed SVM model outperforms conventional statistical methods and back-propagation neural network. In general, SVM provides a robust model with high prediction accuracy for forecasting financial distress of Chinese listed companies. It is also suggested that Chinese special-treated event adopted as cut-off line has some effect on the prediction accuracy of the models.

VOLTERRA FUNCTIONAL SECURE COMMUNICATION SYSTEMS

Two methods, based on nonlinear dynamics, are described for broad- and narrow-band communication systems. The first approach employs hyperchaotic discrete time series carrier sequences generated with mixed linear–nonlinear coupled differential equations [Irving & Dewson, 1997]. In this first approach it is assumed that the solution of the coupled ordinary differential equations can be represented as a multichannel Volterra functional expansion. Identification, synchronization and the potential unmasking of hyperchaotic communications systems, are achieved by generating a tractable hierarchy of ascending order time series moment equations by operating on a suitably truncated Volterra functional expansion. The estimated moment hierarchy facilitates the calculation of the coefficients of the coupled differential equations that generate the multichannel carrier that is to be modulated by the message. Due to its ability to easily and accurately estimate the coefficients of the governing differential equations the method is applied to the multichannel carrier sequences of data generated by a set of hyperchaotic equations. The inherent problem of resynchronization in chaotic communication systems cannot be avoided in general because of the evolutionary, time dependent, nature of the time series carriers used. This time dependence problem that results in repeated resynchronization can be avoided by considering an alternative and innovative approach that employs time series carrier sequences generated by an input–output multichannel Volterra kernel expansion [Dewson & Irving, 1996]. In this second method, mixed order multichannel Volterra kernel functions are used to generate the carrier sequence that is then modulated by the message. The Volterra kernel function values used to generate the carrier can be identified with the moment hierarchy method [Dewson & Irving, 1996] enabling the message to be deconvolved from the transmitted signal. The modulated nonlinear multichannel signal is transmitted to the receiver. The effect of transmission is to distort and corrupt the signal. In this work it is assumed that the distortions to the transmitted signal remain small, with the case where they become significant being treated elsewhere. First, the case where the signal is received free from both noise and distortion, for example the decryption of an encrypted e-mail, is first considered. Then signal reception in the presence of additive noise is considered. Each of the two proposed methods has been investigated to determine their accuracy and robustness in the presence of additive noise.

VES DIPOLE‐DIPOLE FILTER COEFFICIENTS

The conversion of sampled Schlumberger and dipole‐dipole vertical electrical sounding (VES) apparent resistivity values into raised kernel function values is an important step in the interpretation of these data. This conversion involves the convolution of the sampled values, uniformly spaced on a log distance scale, with a set of filter coefficients. For Schlumberger and dipole‐dipole configurations, these coefficients can be calculated directly from the Schlumberger filter function. Oscillations of the filter coefficients at large indices (distances) can be minimized by proper selection of the sampling interval, as suggested by Koefoed. The choice of an optimal sampling interval has a more pronounced effect on the accuracy of the inverse transform (raised kernel function into apparent resistivity) than on that of the forward transform. The accuracy of the inverse transform can be improved for nonoptimal sampling intervals by “phase perturbation” of the filter function. Both transforms are sensitive to aliasing, which can be severe for certain dipole‐dipole configurations.