Bandwidth adjustable Tanimoto kernel: a smooth alternative to the Gaussian kernel

In this paper, we propose M-estimator based robust kernels for support vector machine. The main motivation for our proposed kernels is that the sum of squared difference in the widely used Gaussian radial basis function kernels is not robust to outlier or noise. In addition, inspired by using a robust loss function in support vector machine regression to control training error and the idea of robust template matching with M-estimator, we apply M-estimator techniques to Gaussian radial basis functions and form a new class of robust kernels for support vector machines. We test our proposed kernels in several classification benchmark datasets and experimental results show that SVM with proposed kernels are better than SVM with Gaussian radial basis function kernels.

Active learning based on minimization of the expected path-length of random walks on the learned manifold structure

In this paper, we develop an approach to exploiting kernel methods with manifold-valued data. In many computer vision problems, the data can be naturally represented as points on a Riemannian manifold. Due to the non-Euclidean geometry of Riemannian manifolds, usual Euclidean computer vision and machine learning algorithms yield inferior results on such data. In this paper, we define Gaussian radial basis function (RBF)-based positive definite kernels on manifolds that permit us to embed a given manifold with a corresponding metric in a high dimensional reproducing kernel Hilbert space. These kernels make it possible to utilize algorithms developed for linear spaces on nonlinear manifold-valued data. Since the Gaussian RBF defined with any given metric is not always positive definite, we present a unified framework for analyzing the positive definiteness of the Gaussian RBF on a generic metric space. We then use the proposed framework to identify positive definite kernels on two specific manifolds commonly encountered in computer vision: the Riemannian manifold of symmetric positive definite matrices and the Grassmann manifold, i.e., the Riemannian manifold of linear subspaces of a Euclidean space. We show that many popular algorithms designed for Euclidean spaces, such as support vector machines, discriminant analysis and principal component analysis can be generalized to Riemannian manifolds with the help of such positive definite Gaussian kernels.

Support Vector Machines (SVMs) versus Multilayer Perception (MLP) in data classification

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.

The stability of commodity prices for food is very influential on the economy of a region because stable prices have a direct impact on the level of people's purchasing power. The need to maintain the stability of food commodity prices is the background of this research and this can be anticipated by forecasting the Consumer Price Index (CPI). The CPI is an index number that calculates the average change in prices of goods and services consumed by households and society. The purpose of this study is to predict the CPI of the Foodstuff Group using the Support Vector Regression (SVR) method by utilizing Linear, Polynomial, Gaussian Radial Basis Function (RBF) and SPLine Kernel Functions. Selection of this SVR method, because SVR is able to map input vectors into higher dimensions and can produce a function with a trend of bumpy data following the data path formed, resulting in more accurate predictive values Research is limited to the city of Surabaya, the period of time the study begins January 1, 2016 until December 31, 2018. The data source used is the Surabaya Food Basic Price data as an input variable with 34 input attributes and the CPI data for Surabaya city Foodstuffs group as output variables. The results of this study are expected to be able to predict CPI with an error rate below 5%, which is indicated by MSE (Mean Square Error) < 0.05

In this paper, we evaluate the use of an electronic nose (EN) containing 13 conducting polymer gas sensors to discriminate between patterns of volatile organic compounds (VOCs) emitted by plants. The VOC patterns examined were produced by tomato, cucumber and pepper plants under both healthy and infected or infested conditions. Leaves from the plants were subjected to mechanical damage or pest and disease attacks (i.e. spider mites infested or mildew infected) and others were judged against undamaged healthy leaves. Support vector machines (SVMs) with linear, polynomial and Gaussian radial basis function (RBF) kernels were used to process and classify the raw data collected. The SVM illustrated an ability to discriminate between different VOC patterns and hence was able to classify correctly the infected leaves using the EN data. The results indicate that the array of 13 EN gas sensors can discriminate among VOC patterns from undamaged and artificially damaged leaves of the three plant species. This study demonstrates the potential application of such an EN technology coupled with suitable pattern recognition and signal processing methods to be used as a real time pest and disease detection system in the greenhouse environment.

In this paper, we propose M-estimator based robust kernels for support vector machine. The main motivation for our proposed kernels is that the sum of squared difference in the widely used Gaussian radial basis function kernels is not robust to outlier or noise. In addition, inspired by using a robust loss function in support vector machine regression to control training error and the idea of robust template matching with M-estimator, we apply M-estimator techniques to Gaussian radial basis functions and form a new class of robust kernels for support vector machines. We test our proposed kernels in several classification benchmark datasets and experimental results show that SVM with proposed kernels are better than SVM with Gaussian radial basis function kernels.

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.

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.

An IKPCA-ELM-based intrusion detection method is developed to address the problem of the low accuracy and slow speed of intrusion detection caused by redundancies and high dimensions of data in the network. First, in order to reduce the effects of uneven sample distribution and sample attribute differences on the extraction of KPCA features, the sample attribute mean and mean square error are introduced into the Gaussian radial basis function and polynomial kernel function respectively, and the two improved kernel functions are combined to construct a hybrid kernel function. Second, an improved particle swarm optimization (IPSO) algorithm is proposed to determine the optimal hybrid kernel function for improved kernel principal component analysis (IKPCA). Finally, IKPCA is conducted to complete feature extraction, and an extreme learning machine (ELM) is applied to classify common attack type detection. The experimental results demonstrate the effectiveness of the constructed hybrid kernel function. Compared with other intrusion detection methods, IKPCA-ELM not only ensures high accuracy rates, but also reduces the detection time and false alarm rate, especially reducing the false alarm rate of small sample attacks.

This work describes a Support Vector Machine (SVM) method used to analyze ECG signals for diagnosing cardiac arrhythmias effectively. The proposed method can accurately classify and differentiate normal (Normal) and abnormal heartbeats. Abnormal heartbeats include left bundle branch block (LBBB), right bundle branch block (RBBB), atrial premature contractions (APC) and premature ventricular contractions (PVC). This paper proposes a two stage, feature extraction and classification method for the detection of ECG beat types. Feature extraction module extracts higher order statistics of ECG signals in conjunction with three timing interval features. Then a number of support vector machine (SVM) classifiers with different value parameters are designed. These parameters are: Gaussian radial basis function (GRBF) kernel parameter and C penalty parameter of SVM classifier. We compared the classification ability of five different classes of ECG signals that were achieved over eight files from the MIT/BIH arrhythmia database.

The kernel function plays a basic role in support vector machines (SVM) algorithms. This paper presents an automatic method for selecting the parameters of the Gaussian radial basis function (GRBF) kernel which is one of the commonly used forms in SVM regression algorithms. The proposed method uses the expectation maximization (EM) algorithm for the automatic selection. The SVM regression algorithm is used to solve two major problems in remote sensing image segmentation: the density estimation problem and the Markov random field modeling problem. The density estimation is used for class conditional probabilities in Bayesian setups. The MRF is used for region modeling in boosting the Bayesian image segmentation. The proposed algorithms are integrated in a framework for remote sensing image segmentation. Experimental evaluation of the proposed algorithms using synthetic data set and hyperspectral data set illustrates the outstanding performance of the proposed algorithms.

Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel-based methods for additive models. These learning rates compare favorably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel-based quantile regression using the Gaussian radial basis function kernel, provided the assumption of an additive model is valid. Additionally, a concrete example is presented to show that a Gaussian function depending only on one variable lies in a reproducing kernel Hilbert space generated by an additive Gaussian kernel, but does not belong to the reproducing kernel Hilbert space generated by the multivariate Gaussian kernel of the same variance.

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