Nonlinear Support Vector Machine Visualization for Risk Factor Analysis Using Nomograms and Localized Radial Basis Function Kernels

Palm tree detection using remote sensing images has received increasing attention in recent years, concerning the issues of sustainability, productivity and profitability. There has been significant progress in the research of using machine learning techniques, especially convolutional neural networks (CNNs) for automatic palm tree detection. However, whether CNNs can actually outperform traditional human-engineered approaches in terms of classification accuracy and detection speed is yet unknown. In the present study, we have compared human-engineered features namely histogram of oriented gradients (HOG), local binary pattern (LBP) and scale-invariant feature transform (SIFT) with features extracted using pre-trained AlexNet model for detecting palm trees in high resolution images obtained via unmanned aerial vehicle (UAV). Support vector machines (SVM) with linear and non-linear kernels were used to classify feature vectors obtained by different feature extractors. Haar-like features used in Viola-Jones framework was also tested in the study. Results showed that features extracted from the fifth convolutional layer of AlexNet achieved the highest accuracy of 96.1% using SVM with RBF kernel as classifier, which surpassed the accuracy obtained by fully-connected CNN, namely 95.6%. The results also suggest that SVM classifier with radial basis function (RBF) kernel using LBP as features is the optimal combination as it achieved comparable accuracy but higher detection speed than CNN approaches.

Indonesia holds vast tourism potential, including Nusa Penida, Bali, renowned for its natural beauty. However, the adoption of modern technology to support tourism promotion and management remains limited. This study aims to compare the performance of Support Vector Machine (SVM) with Radial Basis Function (RBF) kernel and Random Forest algorithms in classifying images of three main tourist attractions in Nusa Penida: Angel’s Billabong, Broken Beach, and Kelingking Beach. The dataset consists of 450 images processed using the Histogram of Oriented Gradients (HOG) method for feature extraction. Two data split scenarios (80:20 and 70:30) were applied to evaluate the algorithms based on accuracy, precision, recall, and F1-score metrics. The experimental results revealed that SVM with RBF kernel outperformed Random Forest in all scenarios, achieving the best results in the 70% training and 30% testing data split with an accuracy of 0.967, precision of 0.969, recall of 0.967, and F1-score of 0.967. While Random Forest demonstrated stable performance, it remained inferior to SVM with RBF kernel. This study concludes that SVM with RBF kernel is superior for image classification tasks, offering opportunities for implementing artificial intelligence technologies to advance the tourism sector in Indonesia.

Objective: Delirium is an important syndrome found in patients in the intensive care unit (ICU), however, it is usually under-recognized during treatment. This study was performed to investigate whether delirious patients can be successfully distinguished from non-delirious patients by using heart rate variability (HRV) and machine learning. Approach: Electrocardiography data of 140 patients was acquired during daily ICU care, and HRV data were analyzed. Delirium, including its type, severity, and etiologies, was evaluated daily by trained psychiatrists. HRV data and various machine learning algorithms including linear support vector machine (SVM), SVM with radial basis function (RBF) kernels, linear extreme learning machine (ELM), ELM with RBF kernels, linear discriminant analysis, and quadratic discriminant analysis were utilized to distinguish delirium patients from non-delirium patients. Main results: HRV data of 4797 ECGs were included, and 39 patients had delirium at least once during their ICU stay. The maximum classification accuracy was acquired using SVM with RBF kernels. Our prediction method based on HRV with machine learning was comparable to previous delirium prediction models using massive amounts of clinical information. Significance: Our results show that autonomic alterations could be a significant feature of patients with delirium in the ICU, suggesting the potential for the automatic prediction and early detection of delirium based on HRV with machine learning.

Objective. The quantitative assessment of Parkinsonian tremor, e.g. (0, 1, 2, 3, 4) according to the Movement Disorder Society-Unified Parkinson’s Disease Rating Scale, is crucial for treating Parkinson’s disease. However, the tremor amplitude constantly fluctuates due to environmental and psychological effects on the patient. In clinical practice, clinicians assess the tremor severity for a short duration, whereas manual tremor labeling relies on the clinician’s physician experience. Therefore, automatic tremor quantification based on wearable inertial sensors and machine learning algorithms is affected by the manual labels of clinicians. In this study, an automatic modification method for the labels judged by clinicians is presented to improve Parkinsonian tremor quantitation. Approach. For the severe overlapping of dynamic feature range between different severities, an outlier modification algorithm (PCA-IQR) based on the combination of principal component analysis and interquartile range statistic rule is proposed to learn the blurred borders between different severity scores, thereby optimizing the labels. Afterward, according to the modified feature vectors, a support vector machine (SVM) with a radial basis function (RBF) kernel is proposed to classify the tremor severity. The classifier models of SVM with RBF kernel, k-nearest neighbors, and SVM with the linear kernel are compared. Main results. Experimental results show that the proposed method has high classification performance and excellent model generalization ability for tremor quantitation (accuracy: 97.93%, precision: 97.96%, sensitivity: 97.93%, F1-score: 97.94%). Significance. The proposed method may not only provide valuable assistance for clinicians to assess the tremor severity accurately, but also provides self-monitoring for patients at home and improve the assessment skills of clinicians.

Kernel functions are used in support vector machines (SVM) to compute inner product in a higher dimensional feature space. SVM classification performance depends on the chosen kernel. The radial basis function (RBF) kernel is a distance-based kernel that has been successfully applied in many tasks. This paper focuses on improving the accuracy of SVM by proposing a non-linear combination of multiple RBF kernels to obtain more flexible kernel functions. Multi-scale RBF kernels are weighted and combined. The proposed kernel allows better discrimination in the feature space. This new kernel is proved to be a Mercer’s kernel. Furthermore, evolutionary strategies (ESs) are used for adjusting the hyperparameters of SVM. Training accuracy, the bound of generalization error, and subset cross-validation on training accuracy are considered to be objective functions in the evolutionary process. The experimental results show that the accuracy of multi-scale RBF kernels is better than that of a single RBF kernel. Moreover, the subset cross-validation on training accuracy is more suitable and it yields the good results on benchmark datasets.

For hyperspectral image classification, feature extraction is a crucial pre-process for avoiding the Hughes phenomena. Some feature extraction methods such as linear discriminant analysis (LDA), nonparametric weighted feature extraction (NWFE), and their kernel versions, generalized discriminant analysis (GDA) and kernel nonparametric weighted feature extraction method (KNWFE) have been shown that they can improve the classification performance. However, for GDA and KNWFE, it is hard to find the suitable kernel parameters. Hence, although they have been published about 14 or 6 years, respectively, researchers rarely implement them for dealing with hyperspectral image classification problem. An automatic kernel parameter selection method (APS) was proposed to predetermine the appropriate radial basis function (RBF) kernel for support vector machine (SVM) and GDA. In this study, APS was applied to find the suitable RBF kernel function for KNWFE. From the experiment results on PAVIA data set, the classification performance of KNWFE still outperforms those of GDA [10] and SVM [10]. The most important of this research, the kernel parameters of GDA and KNWFE based on RBF kernel can be “automatically” determined and the researcher can implement them directly without tuning the kernel parameter.

Data streaming applications such as the Internet of Things (IoT) require processing or predicting from sequential data from various sensors. However, most of the data are unlabeled, making applying fully supervised learning algorithms impossible. The online manifold regularization approach allows sequential learning from partially labeled data, which is useful for sequential learning in environments with scarcely labeled data. Unfortunately, the manifold regularization technique does not work out of the box as it requires determining the radial basis function (RBF) kernel width parameter. The RBF kernel width parameter directly impacts the performance as it is used to inform the model to which class each piece of data most likely belongs. The width parameter is often determined off-line via hyperparameter search, where a vast amount of labeled data is required. Therefore, it limits its utility in applications where it is difficult to collect a great deal of labeled data, such as data stream mining. To address this issue, we proposed eliminating the RBF kernel from the manifold regularization technique altogether by combining the manifold regularization technique with a prototype learning method, which uses a finite set of prototypes to approximate the entire data set. Compared to other manifold regularization approaches, this approach instead queries the prototype-based learner to find the most similar samples for each sample instead of relying on the RBF kernel. Thus, it no longer necessitates the RBF kernel, which improves its practicality. The proposed approach can learn faster and achieve a higher classification performance than other manifold regularization techniques based on experiments on benchmark data sets. Results showed that the proposed approach can perform well even without using the RBF kernel, which improves the practicality of manifold regularization techniques for semi-supervised learning.

Disease prediction is an important aspect of modern medicine, which aims to diagnose disease early and provide appropriate treatment to patients. This research uses a hybrid approach that combines the RBF (Radial Basis Function) kernel algorithm with logistic regression to predict various diseases in medical datasets. This method is intended to improve prediction performance by exploiting the advantages of each algorithm. This research uses a dataset containing medical information about several diseases collected from the Kaggle dataset. First, the RBF kernel is applied to transform the data features into a more informative, non-linear representation. Then, the logistic regression model is used to make predictions based on the features that have been processed by the RBF kernel. In this research, the hybrid RBF (Radial Basis Function) method was proven to be superior in predicting multiple diseases. This method shows the highest accuracy of 0.9460, as well as excellent precision, recall, and F1-score values of 0.8680, 0.8097, and 0.8294, respectively. The advantage of the hybrid RBF method lies in its ability to capture complex patterns in data that other methods often cannot identify, as well as its ability to handle non-linear decision boundaries, which are a common characteristic in medical datasets. Keywords: Disease prediction, Hybrid approach, RBF kernel algorithm, Logistic regression, medical datasets

In this paper, adaptive meshfree methods using local nodes and radial basis functions (RBFs) which based on strong-form formulation is presented. In this present formulation, radial basis functions are used in the function approximation for the discretization of the governing system equations. Regularization techniques are suggested and examined to stabilize the solutions in order to obtain stable and accurate results. Different schemes for constructing regularization matrix are compared and discussed. As stability is restored, meshfree strong-form method using local nodes and RBFs can facilitate an easier implementation for adaptive analysis to achieve desired accuracy. Residual based error indicator is devised in the adaptive scheme. A simple and practical node refinement procedure is presented for node insertion at each adaptive step.

In the evolving field of cybersecurity, detecting malicious activity in high-dimensional network data remains a persistent challenge for traditional machine learning (ML) techniques. This study investigates the use of convolutional variational autoencoders (VAEs) to generate latent features that enhance the performance of various ML classifiers on the 2015 NSL-KDD dataset. Classifiers, including Gaussian Naïve Bayes (GNB), support vector machines (SVMs) with Radial Basis Function (RBF) kernel, decision trees, and dense neural networks, were evaluated using metrics such as accuracy, precision, recall, F1 score, and the Matthews Correlation Coefficient (MCC). To assess the effectiveness of VAEs, Principal Component Analysis (PCA) was used as a baseline dimensionality reduction method, and performance comparisons were made. The best-performing model was an SVM with an RBF kernel, a PCA (threshold = 0.92), and a VAE with six latent features, achieving an accuracy of 82.8%, an F1 score of 0.830, and an MCC of 0.682. The results indicate that VAEs can significantly enhance classifier performance, particularly in GNB and SVM models, suggesting their value in developing more effective intrusion detection systems. Received: 23 August 2024 | Revised: 3 June 2025 | Accepted: 15 July 2025 Conflicts of Interest The authors declare that they have no conflicts of interest to this work. Data Availability Statement The data that support the findings of this study are openly available in NSL-KDD Dataset at https://github.com/t-taylor/cvaes-research/tree/main/results. Author Contribution Statement Thomas Taylor: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing – original draft, Writing – review & editing, Visualization. Amna Eleyan: Conceptualization, Methodology, Writing – original draft, Writing – review & editing, Supervision, Project administration. Mohammed Al-Khalidi: Validation, Resources, Writing – original draft, Writing – review & editing, Visualization, Supervision.

A movie review can be considered as an essential data source for both movie producers and potential consumers. The reviews are usually used as a benchmark for knowing the movie’s quality and are utilized as references to whether the film is worth watching. The study of sentiment analysis has received more attention from researchers. This current study aims to classify the sentiment analysis of movie reviews obtained from the IMDb site. The support vector machine (SVM) method was employed to classify the movie review’s sentiments. Meanwhile, the radial basis function (RBF) kernel and information gain (IG) were used to enhance classification. Feature selection was conducted by removing irrelevant features and selecting features with a strong correlation to classification. The IG algorithm was used for feature selection. The current study revealed that the classification accuracy of movie review sentiment analysis using the SVM algorithm, SVM + RBF kernel, and SVM+RBF Kernel+IG are 81.50%, 82.25%, and 87.25%, respectively.

Epilepsy is a neurological disorder that affects people of any age, which can be detected by Electroencephalogram (EEG) signals. This paper proposes a novel method called Volume of Phase Space Representation (VOPSR) to classify seizure and seizure-free EEG signals automatically. Primarily, the recorded EEG signal is disintegrated into several Intrinsic Mode Functions (IMFs) using the Empirical Mode Decomposition (EMD) method and the three-dimensional phase space have been reconstructed for the obtained IMFs. The volume is measured for the obtained 3D-PSR for different IMFs called VOPSR, which is used as a feature set for the classification of Epileptic seizure EEG signals. Support vector machine (SVM) is used as a classifier for the classification of epileptic and epileptic-free EEG signals. The classification performance of the proposed method is evaluated under different kernels such as Linear, Polynomial and Radial Basis Function (RBF) kernels. Finally, the proposed method outperforms noteworthy state-of-the-art classification methods in the context of epileptic EEG signals, achieving 99.13% accuracy (average) with the Linear, Polynomial, and RBF kernels. The proposed technique can be used to detect epilepsy from the EEG signals automatically without human intervention.

The Kovats retention index is the most robust retention parameter used to identify analytes in gas chromatography. The Kovats retention index’s value in similar compounds tends to have a similar pattern. This pattern allows a close relationship between chemical structure and the retention index value. The Fuzzy Support Vector Regression (FSVR) method is a robust algorithm that has been used to solve various regression problems. This study aimed to evaluate the FSVR algorithm performance to predict the Kovats retention index of flavor and fragrance compounds. The model was built using the Python programming language. The retention index value calculation begins with inputting the molecular descriptor data into the sigmoid fuzzy membership function. The dataset consists of 51 compounds then partitioned into two sets, namely 80% in the training set and 20% in the testing set. The best parameters to build the model were obtained using hyperparameter tuning. The kernels used are linear kernel and Radial Basis Function (RBF) kernel. The model with a linear kernel with parameter values of C = 1000 and epsilon = 10 managed to get the best results compared to the model with an RBF kernel, with R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.977 and Root Mean Square Error (RMSE) = 37.21 on the testing set. This model also can predict the Kovats retention index on the testing set with an average difference of 2.8%. These results showed that the linear kernel is better than the RBF kernel in predicting the value of the Kovats retention index. It can be concluded that the FSVR method can be used to predict the retention index of flavor and fragrance compounds.

This work proposes a methodology for content-based image retrieval of glioblastoma multiforme (GBM) and non-GBM tumors. Regions containing GBM lesions from 40 patients and non-GBM lesions from 20 patients were manually segmented from MR imaging studies (T1 post-contrast and T2 weighted channels) to form the training set. In addition to the two acquired channels, a composite image was formed by an image fusion method. Data reduction techniques, principal component analysis (PCA) and linear discriminant analysis (LDA), were applied on the training sets (T1 post, T2, composite, and multi-channel combining the PCA features from T1 post and T2). The retrieval accuracy was evaluated using a 'leave-one-out' strategy with query images belonging to 'normal', 'GBM' and 'non-GBM' classes. Several combinations of the similarity metric and classifier were used: Euclidean similarity measures with k-means classifier for the PCA and LDA features and support vector machine (SVM) nonlinear classifier (radial basis function kernel) with the PCA derived features. The SVM classifier served as a comparison of nonlinear techniques vs. linear ones. Multi-channel PCA was 100% accurate in classifying a query image as either 'normal' or 'abnormal'. The highest accuracy in classification of tumor grade (GBM or other Grade 3) was 77% and was achieved by SVM coupled with the PCA features. The proposed algorithm intent is to be integrated into an automated decision support system for MR brain tumor studies.

The shape feature of an object represents the geometrical information which plays an important role in the image understanding and image retrieval. How to get an excellent shape feature that has rotation, scaling and translation (RST) invariance is a problem in this field. This paper proposed a novel local extreme learning machine (LELM) classification algorithm to extract the shape features. LELM finds nearest neighbors of the testing set from the original training set and trains a local classification model. The shape feature is represented by an analytic decision function with a radial basis function (RBF) kernel obtained by LELM. Our method has the following advantages: (1) LELM not only keeps the local structure of the samples, but also solves the imbalance problem between variance and bias. (2) Features obtained by the RBF kernel are RST invariant. (3) LELM is more robust against the noise and fragmentation compared to other methods. We also demonstrate the performance of the proposed method in image retrieval.