Gaussian Radial Basis Function Kernel Research Articles

Machine Learning Application of Generalized Gaussian Radial Basis Function and Its Reproducing Kernel Theory

Gaussian Radial Basis Function Kernels are the most-often-employed kernel function in artificial intelligence for providing the optimal results in contrast to their respective counterparts. However, our understanding surrounding the utilization of the Generalized Gaussian Radial Basis Function across different machine learning algorithms, such as kernel regression, support vector machines, and pattern recognition via neural networks is incomplete. The results delivered by the Generalized Gaussian Radial Basis Function Kernel in the previously mentioned applications remarkably outperforms those of the Gaussian Radial Basis Function Kernel, the Sigmoid function, and the ReLU function in terms of accuracy and misclassification. This article provides a concrete illustration of the utilization of the Generalized Gaussian Radial Basis Function Kernel as mentioned earlier. We also provide an explicit description of the reproducing kernel Hilbert space by embedding the Generalized Gaussian Radial Basis Function as an L2−measure, which is utilized in implementing the analysis support vector machine. Finally, we provide the conclusion that we draw from the empirical experiments considered in the manuscript along with the possible future directions in terms of spectral decomposition of the Generalized Gaussian Radial Basis Function.

Developing a novel image marker to predict the clinical outcome of neoadjuvant chemotherapy (NACT) for ovarian cancer patients

ObjectiveNeoadjuvant chemotherapy (NACT) is one kind of treatment for advanced stage ovarian cancer patients. However, due to the nature of tumor heterogeneity, the clinical outcomes to NACT vary significantly among different subgroups. Partial responses to NACT may lead to suboptimal debulking surgery, which will result in adverse prognosis. To address this clinical challenge, the purpose of this study is to develop a novel image marker to achieve high accuracy prognosis prediction of NACT at an early stage. MethodsFor this purpose, we first computed a total of 1373 radiomics features to quantify the tumor characteristics, which can be grouped into three categories: geometric, intensity, and texture features. Second, all these features were optimized by principal component analysis algorithm to generate a compact and informative feature cluster. This cluster was used as input for developing and optimizing support vector machine (SVM) based classifiers, which indicated the likelihood of receiving suboptimal cytoreduction after the NACT treatment. Two different kernels for SVM algorithm were explored and compared. A total of 42 ovarian cancer cases were retrospectively collected to validate the scheme. A nested leave-one-out cross-validation framework was adopted for model performance assessment. ResultsThe results demonstrated that the model with a Gaussian radial basis function kernel SVM yielded an AUC (area under the ROC [receiver characteristic operation] curve) of 0.806 ± 0.078. Meanwhile, this model achieved overall accuracy (ACC) of 83.3%, positive predictive value (PPV) of 81.8%, and negative predictive value (NPV) of 83.9%. ConclusionThis study provides meaningful information for the development of radiomics based image markers in NACT treatment outcome prediction.

Gaussian RBF kernels via Fock spaces: quaternionic and several complex variables settings

In this paper, we study two extensions of the complex-valued Gaussian radial basis function (RBF) kernel and discuss their connections with Fock spaces in two different settings. First, we introduce the quaternionic Gaussian RBF kernel constructed using the theory of slice hyperholomorphic functions. Then, we consider the case of Gaussian RBF kernels in several complex variables.

Spatiotemporally Mapping Non-Grain Production of Winter Wheat Using a Developed Auto-Generating Sample Algorithm on Google Earth Engine

Spatiotemporally mapping winter wheat is imperative for informing and shaping global food security policies. Traditional mapping methods heavily rely on sufficient and reliable samples obtained through labor-intensive fieldwork and manual sample collection. However, these methods are time-consuming, costly, and lack timely and continuous data collection. To address these challenges and fully leverage remote sensing big data and cloud computing platforms like Google Earth Engine (GEE), this paper developed an algorithm for Auto-Generating Winter Wheat Samples for mapping (AGWWS). The AGWWS utilizes historical samples to determine the optimal migration threshold by measuring Spectral Angle Distance (SAD), Euclidean Distance (ED), and Near-Infrared band Difference Index (NIRDI). This facilitates the auto-generation of winter wheat sample sets for the years 2000, 2005, 2010, 2015, and 2021. Approximately two-thirds of the samples were allocated for training, with the remaining one-third used for validating the mapping method, employing the One-Class Support Vector Machine (OCSVM). The Huang–Huai–Hai (HHH) Plain, a major winter wheat production region, was selected to perform the algorithm and subsequent analysis on. Different combinations of the hyper-parameters, gamma and nu, of the OCSVM based on the Gaussian Radial Basis Function Kernel were tested for each year. Following correlation analysis between the winter wheat area derived from the generated maps and the national statistical dataset at the city level, the map with the highest corresponding R2 was chosen as the AGWWS map for each year (0.77, 0.77, 0.80, 0.86, and 0.87 for 2000, 2005, 2010, 2015, and 2021, respectively). The AGWWS maps ultimately achieved an average Overall Accuracy of 81.65%. The study then explores the Non-Grain Production of Winter Wheat (NGPOWW) by analyzing winter wheat change maps from 2000–2005, 2005–2010, 2005–2010, and 2015–2021 in the HHH Plain. Despite an overall increase in the total planted area of winter wheat, the NGPOWW phenomena has led to concerning winter wheat planting marginalization. Compensatory winter wheat areas are notably situated in mountainous and suburban cultivated lands with low qualities. Consequently, despite the apparent expansion in planted areas, winter wheat production is anticipated to be adversely affected. The findings highlight the necessity for improved cultivated land protection policies monitoring the land quality of the compensation and setting strict quota limits on occupations.

Implementation of a non-linear SVM classification for seizure EEG signal analysis on FPGA

An automatic detection method for disease diagnosis plays an important role in the medical field. A computer-aided diagnosis (CAD) system for seizure detection using electroencephalogram (EEG) data is significant in protecting patients' lives. This paper presents machine learning algorithm-based seizure detection approach implemented in both software and hardware using EEG recordings. The input EEG signal is subjected to pre-processing, decomposition using wavelet transform and classification by a support vector machine (SVM) classifier. The maximum and variance statistical values of the decomposed EEG sub-bands are computed to generate a feature vector, while classification accuracy and computational complexity are taken into account. Gaussian Radial Basis Function (RBF) kernel based Non-Linear SVM (NLSVM) is used in this proposed approach to solve both two-class and three-class classification problems. In three-class classification, the one-against-one (OAO) technique is used. The competency of the proposed technique is evaluated using two distinct datasets provided by Bonn University, Germany & Neurology and Sleep Centre, New Delhi. The adequate parameters of the NLSVM classifier model are determined by using MATLAB software in the training phase and the best performing NLSVM model is selected for implementation on the Field-Programmable Gate Array (FPGA). The proposed seizure detection method is implemented with Verilog code and examined on a Xilinx Zynq-7000 XC7Z020 FPGA board to evaluate its performance. The experimental results show that the proposed method with a minimal number of features achieved a good performance metric for seizure detection and is comparable with that of the state-of-the-art methods.

Sentiment Analysis of 2024 Presidential Candidates Election Using SVM Algorithm

Elections for presidential candidates are held every 5 years with various candidates, especially on Twitter, arguments about political matters often occur that many Twitter users participate in discussions about the election for presidential candidate. Therefore, this study focuses on sentiment analysis to infer user responses to the presidential election and validate it by looking for a correlation between electability survey results and Twitter sentiment data using Pearson Correlation. In sentiment analysis model, the 10-Fold Cross Validation method is used to find the best model from a dataset with a division of training data and test data with 90:10 split. Then the alphabetic data will be converted into numeric data using the TF-IDF weighting method. To validate the best model, Confusion Matrix is used to get the best f1-score. The model is using Support vector machine algorithm with the Gaussian RBF (Radial Basis Function) kernel. The results of the analysis are compared with the results of the news portal electability survey which contains the 3 candidates using Pearson Correlation. This study produces the best fold for each data on each presidential candidate with the f1-score to find the best model for each fold. In the Peason Correlation result, the higher positive sentiment of each presidential candidate, the higher electability survey data. For further research, research can be discuss about hyper tuning parameters and using other kernels on Support vector machine algorithm.

Indonesian Society’s Sentiment Analysis Against the COVID-19 Booster Vaccine

The COVID-19 pandemic is still occurring in various countries, including Indonesia. This pandemic is caused by the coronavirus, which has mutated into multiple virus variants, such as Delta and Omicron. As of 9 February 2022, 4,626,936 people were confirmed positive for COVID-19 in Indonesia. This number continues to rise. The Indonesian government has prevented the spread of these virus variants by introducing booster vaccines to the public. However, this vaccination program has caused various sentiments among Indonesians. To optimize efforts to combat COVID-19, the government needs to know these sentiments immediately. Based on these problems, the researcher proposes the application of machine learning technology to develop a system that can analyze the sentiments of the Indonesians toward the booster vaccine. This research has several stages: data collection, data labeling, text preprocessing, feature extraction, and application of the support vector machine (SVM) algorithm using various kernels, namely the linear kernel, Gaussian radial basis function (RBF) kernel, and polynomial kernel. Furthermore, the results of the system were tested for accuracy using a 10-fold cross validation and confusion matrix. The dataset used was 681 tweets with the hashtag “vaksinbooster.” The dataset consists of two classes: negative (0) and positive (1). The results showed that the data were positive for the booster vaccine, as evidenced by the higher number of positive tweets, with 554 data, compared to 127 negative tweets. In addition, the dataset was divided into training data of 545 and testing data of 136. In addition, the test results of this study revealed that the SVM algorithm with the polynomial kernel, which was evaluated with 10-fold cross validation, yielded the highest level of accuracy, namely 79.22%.

Study on the Relationship between the Spatial Distribution of Shared Bicycle Travel Demand and Urban Built Environment

As a green and sustainable trip mode, shared bicycles play an essential role in completing short-distance trips in cities. This paper proposes a method to analyze the impact of the urban built environment on the distribution of shared bicycles in a small-scale space. First, the Fishnet function of ArcGIS is utilized to divide the study area into grids of 500 m × 500 m. Then, three indicators are proposed to describe the characteristics of the urban built environment, including point of information (POI) comprehensive index, the intensity of public transportation coverage, spatial accessibility, providing them the ways to be assigned to the grids. Finally, the multivariable linear regression model and support vector regression (SVR) models are applied to reveal the impacts of built environment factors on the spatial distribution of shared bicycles. Results show that SVR models based on linear kernel function, Gaussian radial basis kernel function, and Polynomial kernel function can achieve better analysis results. The SVR model based on the Gaussian radial basis function shows higher explanatory power (adjusted R2 = 0.978) than the multivariable linear regression model (adjusted R2 = 0.847). This paper can aid in understanding the demand and supply of shared bicycles and help operators or governments to improve service quality.

Evaluation of Corporate Social Responsibility and Core Competitiveness Based on GA-SVM Model

Abstract The author proposes a model evaluation based on the GA-SVM model to better understand the evaluation of the company’s relationship and core competitiveness. The system index is reduced by relative gray analysis, the support vector machine model is optimized by a genetic algorithm, and the specific algorithm steps are introduced. Select models from the top 100 enterprises in China’s construction industry in 2020 published by China Construction Industry Market, using relative gray to reduce the measure, and then use the genetic algorithm support vector machine (GA-SVM) model for the training model to achieve the evaluation of the core competencies of the target construction technique business. The experimental results show that the relative error of prediction of the GA-SVM(Genetic algorithm-support vector machine) model for the evaluation of the competitive core of the business is not more than 5, which meets the should be made of accurate predictions. Therefore, choosing the Gaussian radial basis kernel function (RBF) as the kernel function of the GA-SVM intelligent evaluation model is good. It proves that the GA-SVM model can analyze the relationship between the role and the important competition.

Guided wave signal‐based sensing and classification for small geological structure

AbstractSensing, Computing and Communication Integration (SC2) is widely believed as a new enabling technology. A non‐negative tensor sparse factorisation (NTSF) algorithm based on tensor analysis is proposed for sensing and classification of Small Geological Structure in coal mines. Utilising this method, advanced detection of geological anomalies hidden in coal seams was achieved. The morphological properties of geological anomalies in coal seams and the propagation characteristics of guided waves were first thoroughly studied. A three‐dimensional (3D) medium geometry model was developed for a complicated coal seam with Goaf, collapse column, scouring zone, and tiny fault based on COMSOL Multiphysics. On this model, the third‐order tensors data was constructed. Then, the TUCKER‐based NTSF algorithm was employed for feature extraction and classification. To achieve multi‐dimensional feature, the two‐dimensional data in the form of a matrix is collected, and a multiplicative update method is introduced to update the algorithm iteratively. Finally, the Support Vector Machine (SVM) multi‐classifier with Gaussian radial basis kernel function is selected for classification of Small Geological Structure. The experimental results show that the classification accuracy based on the NTSF and SVM is as high as 97.33%, which demonstrates that the proposed algorithm is suitable for Sensing and Classification of Small Geological Structure in coal mines.

Wear Parameter Diagnostics of Industrial Milling Machine with Support Vector Regression

Modern industrial machine applications often contain data collection functions through automation systems or external sensors. Yet, while the different data collection mechanisms might be effortless to construct, it is advised to have a well-balanced consideration of the possible data inputs based on the machine characteristics, usage, and operational environment. Prior consideration of the collected data parameters reduces the risk of excessive data, yet another challenge remains to distinguish meaningful features significant for the purpose. This research illustrates a peripheral milling machine data collection and data pre-processing approach to diagnose significant machine parameters relevant to milling blade wear. The experiences gained from this research encourage conducting pre-categorisation of data significant for the purpose, those being manual setup data, programmable logic controller (PLC) automation system data, calculated parameters, and measured parameters under this study. Further, the results from the raw data pre-processing phase performed with Pearson Correlation Coefficient and permutation feature importance methods indicate that the most dominant correlation to recognised wear characteristics in the case machine context is perceived with vibration excitation monitoring. The root mean square (RMS) vibration signal is further predicted by using the support vector regression (SVR) algorithm to test the SVR’s overall suitability for the asset’s health index (HI) approximation. It was found that the SVR algorithm has sufficient data parameter behaviour forecast capabilities to be used in the peripheral milling machine prognostic process and its development. The SVR with Gaussian radial basis function (RBF) kernel receives the highest scoring metrics; therefore, outperforming the linear and polynomial kernels compared as part of the study.

Automated recognition of asymmetric gait and fatigue gait using ground reaction force data.

Introduction: The purpose of this study was to evaluate the effect of running-induced fatigue on the characteristic asymmetry of running gait and to identify non-linear differences in bilateral lower limbs and fatigued gait by building a machine learning model. Methods: Data on bilateral lower limb three-dimensional ground reaction forces were collected from 14 male amateur runners before and after a running-induced fatigue experiment. The symmetry function (SF) was used to assess the degree of symmetry of running gait. Statistical parameter mapping (Paired sample T-test) algorithm was used to examine bilateral lower limb differences and asymmetry changes pre- and post-fatigue of time series data. The support vector ma-chine (SVM) algorithm was used to recognize the gait characteristics of both lower limbs before and after fatigue and to build the optimal algorithm model by setting different kernel functions. Results: The results showed that the ground reaction forces were asymmetrical (SF > 0.5) both pre-and post-fatigue and mainly concentrated in the medial-lateral direction. The asymmetry of the medial-lateral direction increased significantly after fatigue (p < 0.05). In addition, we concluded that the polynomial kernel function could make the SVM model the most accurate in classifying left and right gait features (accuracy of 85.3%, 82.4%, and 82.4% in medial-lateral, anterior-posterior and vertical directions, respectively). Gaussian radial basis kernel function was the optimal kernel function of the SVM algorithm model for fatigue gait recognition in the medial-lateral and vertical directions (accuracy of 54.2% and 62.5%, respectively). Moreover, polynomial was the optimal kernel function of the anterior-posterior di-rection (accuracy = 54.2%). Discussion: We proved in this study that the SVM algorithm model depicted good performance in identifying asymmetric and fatigue gaits. These findings can provide implications for running injury prevention, movement monitoring, and gait assessment.

Choosing shape parameters for regression in reproducing kernel Hilbert space and variable selection

The Gaussian radial basis function (RBF) is a widely used kernel function in kernel-based methods. The parameter in RBF, referred to as the shape parameter, plays an essential role in model fitting. In this paper, we propose a method to select the shape parameters for the general Gaussian RBF kernel. It can simultaneously serve for variable selection and regression function estimation. For the former, asymptotic consistency is established; for the latter, the estimation is as efficient as if the true or optimal shape parameters are known. Simulations and real examples are used to illustrate the method's performance of prediction by comparing it with other popular methods.

Copy-Move Geometric Tampering Estimation Through Enhanced SIFT Detector Method

Digital picture forgery detection has recently become a popular and significant topic in image processing. Due to advancements in image processing and the availability of sophisticated software, picture fabrication may hide evidence and hinder the detection of such criminal cases. The practice of modifying original photographic images to generate a forged image is known as digital image forging. A section of an image is copied and pasted into another part of the same image to hide an item or duplicate particular image elements in copy-move forgery. In order to make the forgeries real and inconspicuous, geometric or post-processing techniques are frequently performed on tampered regions during the tampering process. In Copy-Move forgery detection, the high similarity between the tampered regions and the source regions has become crucial evidence. The most frequent way for detecting copy-move forgeries is to partition the images into overlapping square blocks and utilize Discrete cosine transform (DCT) components as block representations. Due to the high dimensionality of the feature space, Gaussian Radial basis function (RBF) kernel based Principal component analysis (PCA) is used to minimize the dimensionality of the feature vector representation, which improves feature matching efficiency. In this paper, we propose to use a novel enhanced Scale-invariant feature transform (SIFT) detector method called as RootSIFT, combined with the similarity measures to mark the tampered areas in the image. The proposed method outperforms existing state-of-the-art methods in terms of matching time complexity, detection reliability, and forgery location accuracy, according to the experimental results. The F1 score of the proposed method is 92.3% while the literature methods are around 90% on an average.

Experimental study on step characteristics of inchworm linear micro-actuator

Few studies have quantitatively analyzed the relationship among the step distance, the driving voltage, and driving frequency of the inchworm linear microactuator, which cannot achieve accurate control of the micro-actuator. What’s more, the parameter setting rule is not clear. In this paper, the relationship model among step distance, voltage, and frequency is studied through theoretical derivation and experimental analysis. The parameter setting conditions of the drive signal are analyzed, and the waveform is modified to improve the stability of the micro-actuator. The theoretical model of micro-driver step prediction is established by using the non-linear Support Vector Machine (SVM) regression theory and Gaussian radial basis kernel function and verified by experiments.

Performance Investigation of Principal Component Analysis for Intrusion Detection System Using Different Support Vector Machine Kernels

The growing number of security threats has prompted the use of a variety of security techniques. The most common security tools for identifying and tracking intruders across diverse network domains are intrusion detection systems. Machine Learning classifiers have begun to be used in the detection of threats, thus increasing the intrusion detection systems’ performance. In this paper, the investigation model for an intrusion detection systems model based on the Principal Component Analysis feature selection technique and a different Support Vector Machine kernels classifier is present. The impact of various kernel functions used in Support Vector Machines, namely linear, polynomial, Gaussian radial basis function, and Sigmoid, is investigated. The performance of the investigation model is measured in terms of detection accuracy, True Positive, True Negative, Precision, Sensitivity, and F-measure to choose an appropriate kernel function for the Support Vector Machine. The investigation model was examined and evaluated using the KDD Cup’99 and UNSW-NB15 datasets. The obtained results prove that the Gaussian radial basis function kernel is superior to the linear, polynomial, and sigmoid kernels in both used datasets. Obtained accuracy, Sensitivity, and, F-measure of the Gaussian radial basis function kernel for KDD CUP’99 were 99.11%, 98.97%, and 99.03%. for UNSW-NB15 datasets were 93.94%, 93.23%, and 94.44%.

An approach to the Gaussian RBF kernels via Fock spaces

We use methods from the Fock space and Segal–Bargmann theories to prove several results on the Gaussian RBF kernel in complex analysis. The latter is one of the most used kernels in modern machine learning kernel methods and in support vector machine classification algorithms. Complex analysis techniques allow us to consider several notions linked to the radial basis function (RBF) kernels, such as the feature space and the feature map, using the so-called Segal–Bargmann transform. We also show how the RBF kernels can be related to some of the most used operators in quantum mechanics and time frequency analysis; specifically, we prove the connections of such kernels with creation, annihilation, Fourier, translation, modulation, and Weyl operators. For the Weyl operators, we also study a semigroup property in this case.

TPE-RBF-SVM Model for Soybean Categories Recognition in Selected Hyperspectral Bands Based on Extreme Gradient Boosting Feature Importance Values

Soybeans with insignificant differences in appearance have large differences in their internal physical and chemical components; therefore, follow-up storage, transportation and processing require targeted differential treatment. A fast and effective machine learning method based on hyperspectral data of soybeans for pattern recognition of categories is designed as a non-destructive testing method in this paper. A hyperspectral-image dataset with 2299 soybean seeds in four categories is collected. Ten features are selected using an extreme gradient boosting algorithm from 203 hyperspectral bands in a range of 400 to 1000 nm; a Gaussian radial basis kernel function support vector machine with optimization by the tree-structured Parzen estimator algorithm is built as the TPE-RBF-SVM model for pattern recognition of soybean categories. The metrics of TPE-RBF-SVM are significantly improved compared with other machine learning algorithms. The accuracy is 0.9165 in the independent test dataset, which is 9.786% higher for the vanilla RBF-SVM model and 10.02% higher than the extreme gradient boosting model.

Monthly-scale runoff forecast model based on PSO-SVR

The current methods used in the Lubbog reservoir runoff forecast generally have shortcomings such as low forecast accuracy and low stability. Aiming at these problems, this paper constructs a PSO-SVR mid-and-long term forecast model, and it uses the particle swarm optimization algorithm (PSO) to find the penalty coefficient C, the insensitivity coefficient ε and the gamma parameter of the Gaussian radial basis kernel function of the support vector regression machine (SVR). The results demonstrates that the average relative errors of the PSO-SVR forecast model is relatively small, which are all within a reasonable range; the qualification rates for most monthly forecasts are above 80%. Experimental results indicate that compared with multiple regression analysis, the PSO-SVR model has a higher forecast accuracy, a stronger stability, and a higher credibility. It has a certain practical value and provides a reference for related research.

Prediction of Probabilistic Transient Stability Using Support Vector Machine

Transient stability assessment is an integral part of dynamic security assessment of power systems. Traditional methods of transient stability assessment, such as time domain simulation approach and direct methods, are appropriate for offline studies and thus, cannot be applied for online transient stability prediction, which is a major requirement in modern power systems. This motivated the requirement to apply an artificial intelligence-based approach. In this regard, supervised machine learning is beneficial for predicting transient stability status, in the presence of uncertainties. Therefore, this paper examines the application of a binary support vector machine-based supervised machine learning, for predicting the transient stability status of a power system, considering uncertainties of various factors, such as load, faulted line, fault type, fault location and fault clearing time. The support vector machine is trained using a Gaussian Radial Basis function kernel and its hyperparameters are optimized using Bayesian optimization. Results obtained for the IEEE 14-bus test system demonstrated that the proposed method offers a fast technique for probabilistic transient stability status prediction, with an excellent accuracy. DIgSILENT PowerFactory and MATLAB was utilized for transient stability time-domain simulations (for obtaining training data for support vector machine) and for applying support vector machine, respectively.