A Class of Novel Kernel Functions

2008 ◽  
pp. 188-192
Author(s):  
Xinfei Liao ◽  
Limin Tao
Keyword(s):  
Kernel Functions

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

The Spinning Quality Control Management Based on Decision Making by Data Mining Techniques

2018 ◽  
Vol 7 (1) ◽  
pp. 72
Author(s):  
Khalid AA Abakar ◽  
Chongwen Yu
Keyword(s):  
Data Mining ◽  
Kernel Functions ◽  
Support Vector ◽  
Ann Model ◽  
Data Mining Techniques ◽  
Yarn Quality ◽  
Yarn Properties ◽  
Svm Model ◽  
Rbf Kernel

This work demonstrated the possibility of using the data mining techniques such as artificial neural networks (ANN) and support vector machine (SVM) based model to predict the quality of the spinning yarn parameters. Three different kernel functions were used as SVM kernel functions which are Polynomial and Radial Basis Function (RBF) and Pearson VII Function-based Universal Kernel (PUK) and ANN model were used as data mining techniques to predict yarn properties. In this paper, it was found that the SVM model based on Person VII kernel function (PUK) have the same performance in prediction of spinning yarn quality in comparison with SVM based RBF kernel. The comparison with the ANN model showed that the two SVM models give a better prediction performance than an ANN model.

A New Approach for Predicting the Value of Gene Expression: Two-way Collaborative Filtering

2019 ◽  
Vol 14 (6) ◽  
pp. 480-490 ◽  
Author(s):  
Tuncay Bayrak ◽  
Hasan Oğul
Keyword(s):  
Gene Expression ◽  
Regression Model ◽  
Collaborative Filtering ◽  
High Throughput Sequencing ◽  
Mean Squared Error ◽  
Experimental Studies ◽  
Kernel Functions ◽  
Feature Representation ◽  
Sequencing Analysis ◽  
Computational Systems Biology

Background: Predicting the value of gene expression in a given condition is a challenging topic in computational systems biology. Only a limited number of studies in this area have provided solutions to predict the expression in a particular pattern, whether or not it can be done effectively. However, the value of expression for the measurement is usually needed for further meta-data analysis. Methods: Because the problem is considered as a regression task where a feature representation of the gene under consideration is fed into a trained model to predict a continuous variable that refers to its exact expression level, we introduced a novel feature representation scheme to support work on such a task based on two-way collaborative filtering. At this point, our main argument is that the expressions of other genes in the current condition are as important as the expression of the current gene in other conditions. For regression analysis, linear regression and a recently popularized method, called Relevance Vector Machine (RVM), are used. Pearson and Spearman correlation coefficients and Root Mean Squared Error are used for evaluation. The effects of regression model type, RVM kernel functions, and parameters have been analysed in our study in a gene expression profiling data comprising a set of prostate cancer samples. Results: According to the findings of this study, in addition to promising results from the experimental studies, integrating data from another disease type, such as colon cancer in our case, can significantly improve the prediction performance of the regression model. Conclusion: The results also showed that the performed new feature representation approach and RVM regression model are promising for many machine learning problems in microarray and high throughput sequencing analysis.

A Comprehensive Investigation of Ensembles of Gaussian-Based and Gradient-Based Transformed Reliability Analyses: When and How to Use Them

2016 ◽  
Author(s):  
Po Ting Lin ◽  
Wei-Hao Lu ◽  
Shu-Ping Lin
Keyword(s):  
Design Optimization ◽  
Design Space ◽  
Optimization Problems ◽  
Nonlinear Problems ◽  
Kernel Functions ◽  
Sensitivity Analyses ◽  
Normal Space ◽  
Highly Nonlinear ◽  
Standard Normal ◽  
Gradient Based

In the past few years, researchers have begun to investigate the existence of arbitrary uncertainties in the design optimization problems. Most traditional reliability-based design optimization (RBDO) methods transform the design space to the standard normal space for reliability analysis but may not work well when the random variables are arbitrarily distributed. It is because that the transformation to the standard normal space cannot be determined or the distribution type is unknown. The methods of Ensemble of Gaussian-based Reliability Analyses (EoGRA) and Ensemble of Gradient-based Transformed Reliability Analyses (EGTRA) have been developed to estimate the joint probability density function using the ensemble of kernel functions. EoGRA performs a series of Gaussian-based kernel reliability analyses and merged them together to compute the reliability of the design point. EGTRA transforms the design space to the single-variate design space toward the constraint gradient, where the kernel reliability analyses become much less costly. In this paper, a series of comprehensive investigations were performed to study the similarities and differences between EoGRA and EGTRA. The results showed that EGTRA performs accurate and effective reliability analyses for both linear and nonlinear problems. When the constraints are highly nonlinear, EGTRA may have little problem but still can be effective in terms of starting from deterministic optimal points. On the other hands, the sensitivity analyses of EoGRA may be ineffective when the random distribution is completely inside the feasible space or infeasible space. However, EoGRA can find acceptable design points when starting from deterministic optimal points. Moreover, EoGRA is capable of delivering estimated failure probability of each constraint during the optimization processes, which may be convenient for some applications.

scholarly journals LNG Tank Sloshing Simulation of Multidegree Motions Based on Modified 3D MPS Method

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Chunhui Wang ◽  
Chunyu Guo ◽  
Fenglei Han
Keyword(s):  
Free Surface ◽  
Weighted Average ◽  
Kernel Functions ◽  
Computational Stability ◽  
Mps Method ◽  
Fluid Sloshing ◽  
Particle Hydrodynamics ◽  
Moving Particle ◽  
Lng Tank ◽  
Stability And Accuracy

Modified 3D Moving Particle Semi-Implicit (MPS) method is used to complete the numerical simulation of the fluid sloshing in LNG tank under multidegree excitation motion, which is compared with the results of experiments and 2D calculations obtained by other scholars to verify the reliability. The cubic spline kernel functions used in Smoothed Particle Hydrodynamics (SPH) method are adopted to reduce the deviation caused by consecutive two times weighted average calculations; the boundary conditions and the determination of free surface particles are modified to improve the computational stability and accuracy of 3D calculation. The tank is under forced multidegree excitation motion to simulate the real conditions of LNG ships, the pressures and the free surfaces at different times are given to verify the accuracy of 3D simulation, and the free surface and the splashed particles can be simulated more exactly.

scholarly journals Classification of Prefrontal Cortex Activity Based on Functional Near-Infrared Spectroscopy Data upon Olfactory Stimulation

2021 ◽  
Vol 11 (6) ◽  
pp. 701
Author(s):  
Cheng-Hsuan Chen ◽  
Kuo-Kai Shyu ◽  
Cheng-Kai Lu ◽  
Chi-Wen Jao ◽  
Po-Lei Lee
Keyword(s):  
Prefrontal Cortex ◽  
Infrared Spectroscopy ◽  
Near Infrared Spectroscopy ◽  
Near Infrared ◽  
Kernel Functions ◽  
Olfactory Stimulation ◽  
Support Vector ◽  
Hemodynamic Response Function ◽  
Functional Near Infrared Spectroscopy ◽  
Data Set

The sense of smell is one of the most important organs in humans, and olfactory imaging can detect signals in the anterior orbital frontal lobe. This study assessed olfactory stimuli using support vector machines (SVMs) with signals from functional near-infrared spectroscopy (fNIRS) data obtained from the prefrontal cortex. These data included odor stimuli and air state, which triggered the hemodynamic response function (HRF), determined from variations in oxyhemoglobin (oxyHb) and deoxyhemoglobin (deoxyHb) levels; photoplethysmography (PPG) of two wavelengths (raw optical red and near-infrared data); and the ratios of data from two optical datasets. We adopted three SVM kernel functions (i.e., linear, quadratic, and cubic) to analyze signals and compare their performance with the HRF and PPG signals. The results revealed that oxyHb yielded the most efficient single-signal data with a quadratic kernel function, and a combination of HRF and PPG signals yielded the most efficient multi-signal data with the cubic function. Our results revealed superior SVM analysis of HRFs for classifying odor and air status using fNIRS data during olfaction in humans. Furthermore, the olfactory stimulation can be accurately classified by using quadratic and cubic kernel functions in SVM, even for an individual participant data set.

scholarly journals Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Fractional Order ◽  
Continuous Functions ◽  
Kernel Functions ◽  
Superior Performance ◽  
Image Description ◽  
Orthogonal Moments ◽  
Integer Order ◽  
Geometric Invariance ◽  
Order Continuous

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

scholarly journals Kernel Based Data-Adaptive Support Vector Machines for Multi-Class Classification

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 936
Author(s):  
Jianli Shao ◽  
Xin Liu ◽  
Wenqing He
Keyword(s):  
Machine Learning ◽  
Spatial Association ◽  
Class Imbalance ◽  
Imbalanced Data ◽  
Real Data ◽  
Kernel Functions ◽  
Support Vector ◽  
Classification Problems ◽  
Rare Class ◽  
Data Adaptive

Imbalanced data exist in many classification problems. The classification of imbalanced data has remarkable challenges in machine learning. The support vector machine (SVM) and its variants are popularly used in machine learning among different classifiers thanks to their flexibility and interpretability. However, the performance of SVMs is impacted when the data are imbalanced, which is a typical data structure in the multi-category classification problem. In this paper, we employ the data-adaptive SVM with scaled kernel functions to classify instances for a multi-class population. We propose a multi-class data-dependent kernel function for the SVM by considering class imbalance and the spatial association among instances so that the classification accuracy is enhanced. Simulation studies demonstrate the superb performance of the proposed method, and a real multi-class prostate cancer image dataset is employed as an illustration. Not only does the proposed method outperform the competitor methods in terms of the commonly used accuracy measures such as the F-score and G-means, but also successfully detects more than 60% of instances from the rare class in the real data, while the competitors can only detect less than 20% of the rare class instances. The proposed method will benefit other scientific research fields, such as multiple region boundary detection.

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