Mixed kernel function support vector regression for global sensitivity analysis

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

Rotating machinery vibration signals are nonstationary and nonlinear under complicated operating conditions. It is meaningful to extract optimal features from raw signal and provide accurate fault diagnosis results. In order to resolve the nonlinear problem, an enhancement deep feature extraction method based on Gaussian radial basis kernel function and autoencoder (AE) is proposed. Firstly, kernel function is employed to enhance the feature learning capability, and a new AE is designed termed kernel AE (KAE). Subsequently, a deep neural network is constructed with one KAE and multiple AEs to extract inherent features layer by layer. Finally, softmax is adopted as the classifier to accurately identify different bearing faults, and error backpropagation algorithm is used to fine‐tune the model parameters. Aircraft engine intershaft bearing vibration data are used to verify the method. The results confirm that the proposed method has a better feature extraction capability, requires fewer iterations, and has a higher accuracy than standard methods using a stacked AE.

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.

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.

Transmission line protection is an important issue in power system engineering because 85-87% of power system faults are occurring in transmission lines. This paper presents a technique to detect and classify the different shunt faults on a transmission lines for quick and reliable operation of protection schemes. Discrimination among different types of faults on the transmission lines is achieved by application of evolutionary programming tools. PSCAD/EMTDC software is used to simulate different operating and fault conditions on high voltage transmission line, namely single phase to ground fault, line to line fault, double line to ground and three phase short circuit. The discrete wavelet transform (DWT) is applied for decomposition of fault transients, because of its ability to extract information from the transient signal, simultaneously both in time and frequency domain. The data sets which are obtained from the DWT are used for training and testing the SVM architecture. After extracting useful features from the measured signals, a decision of fault or no fault on any phase or multiple phases of a transmission line is carried out using three SVM classifiers. The ground detection task is carried out by a proposed ground index. Gaussian radial basis kernel function (RBF) has been used, and performances of classifiers have been evaluated based on fault classification accuracy. In order to determine the optimal parametric settings of an SVM classifier (such as the type of kernel function, its associated parameter, and the regularization parameter c), fivefold cross-validation has been applied to the training set. It is observed that an SVM with an RBF kernel provides better fault classification accuracy than that of an SVM with polynomial kernel. It has been found that the proposed scheme is very fast and accurate and it proved to be a robust classifier for digital distance protection.

Modelling heating and cooling energy demand for building stock using a hybrid approach

Copula-based methods for global sensitivity analysis with correlated random variables and stochastic processes under incomplete probability information

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.

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.

ABSTRACTPROSAIL is a combination of the leaf optical properties spectra (PROSPECT) model and the scattering by arbitrarily inclined leaves (SAIL) canopy bidirectional reflectance model. When modelling forest canopy reflectance using the PROSAIL radiative transfer model, the sensitivities of parameters can affect the modelling accuracy. Traditionally, sensitivities have been assessed using local sensitivity analysis (LSA); however, drawbacks to this approach include a lack of consideration for coupled effects between different parameters. In this study, parameter sensitivities in the PROSAIL model were calculated using two global sensitivity analysis (GSA) methods (the Extended Fourier Amplitude Sensitivity Test (EFAST) method and the Morris method), field measurements, and Landsat 5 Thematic Mapper (TM) data for a Moso bamboo forest. The results of GSA were compared with those of LSA in order to identify the key parameters impacting the Moso bamboo forest canopy reflectance, and to provide a reference for model optimization and vegetation canopy inversion improvement. The results showed that: (1) the sensitivities of six major input parameters of the PROSAIL model were generally consistent with the sorting orders of the two GSA methods, but were not in accordance with those from the LSA method, especially in the mid-infrared band; (2) coupled effects among parameters acting on reflectance simulation in visible light bands were greater than those in infrared bands; (3) the simulated canopy reflectance was evaluated using Landsat 5 TM data, and the results simulated based on LSA analysis showed higher error than those based on GSA analysis, because the LSA method ignored the influence of some parameters on canopy reflectance, e.g. leaf mesophyll structure (N), average leaf angle (ALA), leaf water content (Cw), and leaf dry matter content (Cm). However, GSA was able to fully consider the coupled effects among parameters, and thus identified the sensitive parameters impacting on reflectance more accurately.

Adaptive sparse polynomial chaos expansions for global sensitivity analysis based on support vector regression

Global sensitivity analysis (GSA) of distribution system with respect to stochastic PV variations plays an important role in designing optimal voltage control schemes. This paper proposes a Kriging, i.e., Gaussian process modeling enabled data-driven GSA method. The key idea is to develop a surrogate model that captures the hidden global relationship between voltage and real and reactive power injections from the historical data. With the surrogate model, the Sobol index can be conveniently calculated to assess the global sensitivity of voltage to various power injection variations. Comparison results with other model-based GSA methods on the IEEE 37-bus feeder, such as the polynomial chaos expansion and the Monte Carlo approaches demonstrate that the proposed method can achieve accurate GSA outcomes while maintaining high computational efficiency.

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

Kernel methods have long played a central role in machine learning by enabling nonlinear modeling in high dimensional feature spaces. Among them, the Gaussian Radial Basis Function (RBF) kernel is widely used due to its smoothness, universality, and excellent performance in supervised learning. In contrast, the Jaccard/Tanimoto coefficient, originally defined over sets and binary vectors, has achieved notable success in chemoinformatics and information retrieval. Recent studies have shown that the Jaccard/Tanimoto coefficient can be extended to real-valued vectors and interpreted as a valid kernel. In this paper, we propose a natural generalization of the Tanimoto kernel by introducing a bandwidth-like parameter, leading to the Bandwidth-Adjustable Tanimoto (BAT) kernel. We focus on the shared structure of the BAT and the Gaussian RBF kernels in terms of their infinite polynomial expansions and investigate the universality of the BAT kernels, clarifying their relationship to the universal Taylor kernels. In particular, we show that by incorporating a bias term, the BAT kernel attains the universal approximation property comparable to that of the Gaussian kernel. Through experiments on classification, regression, and clustering tasks using benchmark datasets, we demonstrate that the BAT kernel performs comparably to the Gaussian kernel, while even the original Tanimoto kernel achieves competitive results. In particular, the BAT kernel attains performance on par with the Gaussian kernel in classification tasks, and it slightly surpasses the Gaussian kernel in regression and clustering tasks. A comparison of their functional forms, together with experiments on both regression and classification tasks involving nonlinear structures, further shows that the BAT kernel yields smoother predictive surfaces than the RBF kernel. Overall, our results indicate that the BAT kernel offers universality and practical performance, making it an alternative to the Gaussian kernel.

Sensing, 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.