Fuzzy Least Squares Twin Support Vector Machines

Least Squares Twin Support Vector Machine (LST-SVM) has been shown to be an efficient and fast algorithm for binary classification. It combines the operating principles of Least Squares SVM (LS-SVM) and Twin SVM (T-SVM); it constructs two non-parallel hyperplanes (as in T-SVM) by solving two systems of linear equations (as in LS-SVM). Despite its efficiency, LST-SVM is still unable to cope with two features of real-world problems. First, in many real-world applications, labels of samples are not deterministic; they come naturally with their associated membership degrees. Second, samples in real-world applications may not be equally important and their importance degrees affect the classification. In this paper, we propose Fuzzy LST-SVM (FLST-SVM) to deal with these two characteristics of real-world data. Two models are introduced for FLST-SVM: the first model builds up crisp hyperplanes using training samples and their corresponding membership degrees. The second model, on the other hand, constructs fuzzy hyperplanes using training samples and their membership degrees. Numerical evaluation of the proposed method with synthetic and real datasets demonstrate significant improvement in the classification accuracy of FLST-SVM when compared to well-known existing versions of SVM

Pruning Error Minimization in Least Squares Support Vector Machines

The support vector machine (SVM) is a method for classification and for function approximation. This method commonly makes use of an /spl epsi/-insensitive cost function, meaning that errors smaller than /spl epsi/ remain unpunished. As an alternative, a least squares support vector machine (LSSVM) uses a quadratic cost function. When the LSSVM method is used for function approximation, a nonsparse solution is obtained. The sparseness is imposed by pruning, i.e., recursively solving the approximation problem and subsequently omitting data that has a small error in the previous pass. However, omitting data with a small approximation error in the previous pass does not reliably predict what the error will be after the sample has been omitted. In this paper, a procedure is introduced that selects from a data set the training sample that will introduce the smallest approximation error when it will be omitted. It is shown that this pruning scheme outperforms the standard one

A duct mapping method using least squares support vector machines

International audienceThis paper introduces a “refractivity from clutter” (RFC) approach with an inversion method based on a pregenerated database. The RFC method exploits the information contained in the radar sea clutter return to estimate the refractive index profile. Whereas initial efforts are based on algorithms giving a good accuracy involving high computational needs, the present method is based on a learning machine algorithm in order to obtain a real-time system. This paper shows the feasibility of a RFC technique based on the least squares support vector machine inversion method by comparing it to a genetic algorithm on simulated and noise-free data, at 1 and 5 GHz. These data are simulated in the presence of ideal trilinear surface-based ducts. The learning machine is based on a pregenerated database computed using Latin hypercube sampling to improve the efficiency of the learning. The results show that little accuracy is lost compared to a genetic algorithm approach. The computational time of a genetic algorithm is very high, whereas the learning machine approach is real time. The advantage of a real-time RFC system is that it could work on several azimuths in near real time

Comparison of partial least squares regression, least squares support vector machines, and Gaussian process regression for a near infrared calibration

This paper investigates the use of least squares support vector machines and Gaussian process regression for multivariate spectroscopic calibration. The performances of these two non-linear regression models are assessed and compared to the traditional linear regression model, partial least squares regression on an agricultural example. The non linear models, least squares support vector machines, and Gaussian process regression, showed enhanced generalization ability, especially in maintaining homogeneous prediction accuracy over the range. The two non-linear models generally have similar prediction performance, but showed different features in some situations, especially when the size of the training set varies. This is due to fundamental differences in fitting criteria between these models

Least squares support vector machines for direction of arrival estimation

Machine learning research has largely been devoted to binary and multiclass problems relating to data mining, text categorization, and pattern/facial recognition. Recently, popular machine learning algorithms, including support vector machines (SVM), have successfully been applied to wireless communication problems. The paper presents a multiclass least squares SVM (LS-SVM) architecture for direction of arrival (DOA) estimation as applied to a CDMA cellular system. Simulation results show a high degree of accuracy, as related to the DOA classes, and prove that the LS-SVM DDAG (decision directed acyclic graph) system has a wide range of performance capabilities. The multilabel capability for multiple DOAs is discussed. Multilabel classification is possible with the LS-SVM DDAG algorithm presented

Iteratively-Reweighted Least-Squares Fitting of Support Vector Machines: A Majorization--Minimization Algorithm Approach

Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an alternative approach to SVM fitting via the majorization--minimization (MM) paradigm. Algorithms that are derived via MM algorithm constructions can be shown to monotonically decrease their objectives at each iteration, as well as be globally convergent to stationary points. We demonstrate the construction of iteratively-reweighted least-squares (IRLS) algorithms, via the MM paradigm, for SVM risk minimization problems involving the hinge, least-square, squared-hinge, and logistic losses, and 1-norm, 2-norm, and elastic net penalizations. Successful implementations of our algorithms are presented via some numerical examples

FORECASTING MODEL OF ENERGY CONSUMPTION USING LEAST SQUARES SUPPORT VECTOR MACHINES

In the oil and gas industry, accurate measurement of gas is a very important aspect for the gas transmission operation. The outgoing gas flow during the transmission operation is monitored and maintained by a metering system. The metering system must be ensured reliable and dependable at all cost to maintain the billing integrity between distributors and customers. The main concern is products sold and returned as money worth product to seller and buyer. An existing system in Transmission Operation Division (TOD), PETRONAS Gas Berhad (PGB), Gurun is held responsible to calculate the energy consumption from the sales gas produced. The system consists of a turbine meter, measuring equipment which are pressure transmitter and temperature transmitter, gas chromatography and flow computer. However, the system is a standalone system that does not have any reference system to verify the integrity of it. Customers are billed according to the amount of energy consumption calculated and any error in calculation will cause loss of profit to the company and affect PETRONAS’s business credibility. As a solution, a Least Squares Support Vector Machines (LS-SVM) prediction model of energy consumption is proposed as a verification system of the outgoing gas flow. The model will predict the energy consumption and compare it with the results of the existing metering system to ensure the reliability and accuracy of the system. The billing integrity between PETRONAS and the customers could be maintained and in the future if the project is expanded, it will have the potential of saving of millions of dollars to Malaysian oil and gas companies