An efficient bi-parametric hyperbolic kernel function yielding the best known iteration bounds for linear programming

Previous studies mainly used radial basis, sigmoid, polynomial, linear, and hyperbolic functions as the kernel function for computation in the neurons of conventional support vector machine (CSVM) whereas orthogonal wavelet requires less number of iterations to converge than these listed kernel functions. We proposed an orthogonal wavelet support vector machine (OSVM) model for predicting the monthly prices of West Texas Intermediate crude oil prices. For evaluation purposes, we compared the performance of our results with that of the CSVM, and multilayer perceptron neural network (MLPNN). It was found to perform better than the CSVM, and the MLPNN. Moreover, the number of iterations, and time computational complexity of the OSVM model is less than that of CSVM, and MLPNN. Experimental results suggest that the OSVM is effective, robust, and can efficiently be used for crude oil price prediction. Our proposal has the potentials of advancing the prediction accuracy of crude oil prices, which makes it suitable for building intelligent decision support systems.

Stuck pipe incidents are one of the contributors to non-productive time (NPT), where they can result in a higher well cost. This research investigates the feasibility of applying machine learning to predict events of stuck pipes during drilling operations in petroleum fields. The predictive model aims to predict the occurrence of stuck pipes so that relevant drilling operation personnel are warned to enact a mitigation plan to prevent stuck pipes. Two machine learning methodologies were studied in this research, namely, the artificial neural network (ANN) and support vector machine (SVM). A total of 268 data sets were successfully collected through data extraction for the well drilling operation. The data also consist of the parameters with which the stuck pipes occurred during the drilling operations. These drilling parameters include information such as the properties of the drilling fluid, bottom-hole assembly (BHA) specification, state of the bore-hole and operating conditions. The R programming software was used to construct both the ANN and SVM machine learning models. The prediction performance of the machine learning models was evaluated in terms of accuracy, sensitivity and specificity. Sensitivity analysis was conducted on these two machine learning models. For the ANN, two activation functions—namely, the logistic activation function and hyperbolic tangent activation function—were tested. Additionally, all the possible combinations of network structures, from [19, 1, 1, 1, 1] to [19, 10, 10, 10, 1], were tested for each activation function. For the SVM, three kernel functions—namely, linear, Radial Basis Function (RBF) and polynomial—were tested. Apart from that, SVM hyper-parameters such as the regularization factor (C), sigma (σ) and degree (D) were used in sensitivity analysis as well. The results from the sensitivity analysis demonstrate that the best ANN model managed to achieve an 88.89% accuracy, 91.89% sensitivity and 86.36% specificity, whereas the best SVM model managed to achieve an 83.95% accuracy, 86.49% sensitivity and 81.82% specificity. Upon comparison, the ANN model is the better machine learning model in this study because its accuracy, sensitivity and specificity are consistently higher than those of the best SVM model. In conclusion, judging from the promising prediction accurateness as demonstrated in the results of this study, it is suggested that stuck pipe prediction using machine learning is indeed practical.

Estimating the hyperbolic distance function: A directional distance function approach

Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. One approach to optimize a multi-objective mathematical model is to employ utility functions for the objectives. Recent studies on utility-based multi-objective optimization concentrates on considering just one utility function for each objective. But, in reality, it is not reasonable to have a unique utility function corresponding to each objective function. Here, a constrained multi-objective mathematical model is considered in which several utility functions are associated for each objective. All of these utility functions are uncertain and in fuzzy form, so a fuzzy probabilistic approach is incorporated to investigate the uncertainty of the utility functions for each objective. Meanwhile, the total utility function of the problem will be a fuzzy nonlinear mathematical model. Since there are not any conventional approaches to solve such a model, a defuzzification method to change the total utility function to a crisp nonlinear model is employed. Also, a maximum technique is applied to defuzzify the conditional utility functions. This action results in changing the total utility function to a crisp single objective nonlinear model and will simplify the optimization process of the total utility function. The effectiveness of the proposed approach is shown by solving a test problem.

By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the reverses and some particular cases are also considered.

We present a liquid-vapour equilibrium using Smoothed Particle Hydrodynamics (SPH), considering the van der Waals equation of state. A hyperbolic kernel function and variable smoothing length are considered along with the periodic boundary condition to study liquid drop-vapour coexistence for different vapour systems. The effect of the existence of the vapour on the coefficient of surface tension is studied, and noted that the surface tension decreases with increase of the density of vapour surrounding it.

Kernel functions serve the central goal of creating new search directions for the primal-dual interiorpoint algorithm to solve linear optimization problems. A significantly improved primal-dual interior-point algorithm for linear optimization is presented based on a novel kernel function. We show a primal-dual interior-point technique for linear optimization based on a class of kernel functions that are eligible. This research presents a new efficient kernel function-based primal-dual IPM algorithm for semidefinite programming problems based on the Nesterov-Todd (NT) direction. With a new and simple technique, we propose a new kernel function to obtain an optimal solution of the perturbed problem (SDP)µ. We obtain the best-known complexity results,for smalland large-update namely O(pp+1/2p √nlog tr(X0S0)/ε) and O((pn)p+1/2p log trX0S0/ε) large update To prove the effectiveness of our proposed kernel function, we compare our numerical results with some alternatives presented by Touil et al. (2017).

Support vector machines (SVMs), introduced by Vapnik in the early 1990’s, are powerful techniques for machine learning and data mining. Recent breakthroughs have led to advancements in the theory and applications. SVMs were developed to solve the classification problem at first, but they have been extended to the domain of regression, clustering problems. Such standard SVMs require the solution of either a quadratic or a linear programming. In this chapter, we introduced the basic concepts of SVMs: method of maximum margin, dual problem, soft margin, kernel functions, and then presented the standard algorithm C-support vector classification (C-SVC). Especially, considering the classification problem of which the training set with nominal attributes, we built a new SVM which can learn the distance of the nominal attribute values, to improve most popular approaches assuming that all attribute values are of equal distance from each other.

In this paper, by constructing a new non-homogeneous kernel of mixed hyperbolic functions, we establish a new Hilbert-type integral inequality with the best constant factor.We also consider the equivalent form of the obtained inequality.Moreover, by using the rational fraction expansion of cotangent function and cosecant function, some special Hilbert's type inequalities with the constant factors related to the higher derivatives of cotangent function and cosecant function are presented.

Modeling data relation as a hierarchical structure has proven beneficial for many learning scenarios, and the hyperbolic space, with negative curvature, can encode such data hierarchy without distortion. Several recent studies also show that the representation power of the hyperbolic space can be further improved by endowing the kernel methods. Unfortunately, the known kernel methods, developed in hyperbolic space, are limited by the adaptation capacity or distortion issues. This paper addresses the issues through a novel embedding function. To this end, we propose a curvature-aware isometric embedding, which establishes an isometry from the Poincar\'e model to a special reproducing kernel Hilbert space (RKHS). Then we can further define a series of kernels on this RKHS, including several positive definite kernels and an indefinite kernel. Thorough experiments are conducted to demonstrate the superiority of our proposals over existing-known hyperbolic and Euclidean kernels in various learning tasks, e.g., graph learning and zero-shot learning.

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming, which is an extension of the work of Roos (SIAM J. Optim. 16(4):1110–1136, 2006). The main iteration of the algorithm consists of a feasibility step and several centrality steps. We introduce a kernel function in the algorithm to induce the feasibility step. For parameter p∈[0,1], the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods, that is, O(nlog n/e).

Presenting a sentence in less number of words compared to its original one without changing the meaning is known as sentence compression. Most recent works on sentence compression models define the problem as an integer linear programming problem and solve it using an external ILP-solver which suffers from slow running time. In this paper, we have presented a machine learning approach to single-sentence compression. The sentence compression task is modeled as a two-class classification problem and used support vector machine to solve the problem. Different learning models are created using different types of kernel functions. Finally, it has been observed that RBF kernel gives good result compared to other kernel functions for this compression task of single sentence.

To learn a new visual category from few examples, prior knowledge from unlabeled data as well as previous related categories may be useful. We develop a new method for transfer learning which exploits available unlabeled data and an arbitrary kernel function; we form a representation based on kernel distances to a large set of unlabeled data points. To transfer knowledge from previous related problems we observe that a category might be learnable using only a small subset of reference prototypes. Related problems may share a significant number of relevant prototypes; we find such a concise representation by performing a joint loss minimization over the training sets of related problems with a shared regularization penalty that minimizes the total number of prototypes involved in the approximation. This optimization problem can be formulated as a linear program that can be solved efficiently. We conduct experiments on a news-topic prediction task where the goal is to predict whether an image belongs to a particular news topic. Our results show that when only few examples are available for training a target topic, leveraging knowledge learnt from other topics can significantly improve performance.

In this work, by the introduction of a new kernel function composed of exponent functions with several parameters, and using the method of weight coefficient, Hermite-Hadamard’s inequality, and some other techniques of real analysis, a more accurate half-discrete Hilbert-type inequality including both the homogeneous and non-homogeneous cases is established. Furthermore, by introducing the Bernoulli number and the rational fraction expansion of tangent function, some special and interesting Hilbert-type inequalities and their equivalent hardy-type inequalities are presented at the end of the paper.

Given the increasing amounts of data and high feature dimensionalities in forecasting problems, it is challenging to build regression models that are both computationally efficient and highly accurate. Moreover, regression models commonly suffer from low interpretability when using a single kernel function or a composite of multi-kernel functions to address nonlinear fitting problems. In this paper, we propose a bi-sparse optimization-based regression (BSOR) model and corresponding algorithm with reconstructed row and column kernel matrices in the framework of support vector regression (SVR). The BSOR model can predict continuous output values for given input points while using the zero-norm regularization method to achieve sparse instance and feature sets. Experiments were run on 16 datasets to compare BSOR to SVR, linear programming SVR (LPSVR), least squares SVR (LSSVR), multi-kernel learning SVR (MKLSVR), least absolute shrinkage and selection operator regression (LASSOR), and relevance vector regression (RVR). BSOR significantly outperformed the other six regression models in predictive accuracy, identification of the fewest representative instances, selection of the fewest important features, and interpretability of results, apart from its slightly high runtime.