Support Vectors (SV) are a machine learning procedure based on Vapnik’s Statistical Learning Theory, initially defined for bi-classification problems. A lot of work is being made from different research areas to obtain new algorithms for multi-class problems, the more usual task in real-world problems. A promising extension is to treat ‘all data at once’ into one multi-class SVM by modifying th...

—The research presents -hierarchical fuzzy twin support vector regression (-HFTSVR) based on -fuzzy twin support vector regression (-FTSVR) and -twin support vector regression (-TSVR). -FTSVR is achieved by incorporating trapezoidal fuzzy numbers to -TSVR which takes care of uncertainty existing in forecasting problems. -FTSVR determines a pair of -insensitive proximal functions by so...

We explore possible expressions for the conversion between vacuumwavelengths and wavelengths in standard air. We find that the equation proposed in the SDSS website is not appropriate for APOGEE. The differences between the available approximations in the H band are at the level of a fraction of a milliAngstroms, or several meters per second, and a significant contribution is related to the cha...

In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modifications and extensions that have been applied...

Marketing problems often involve binary classification of customers into “buyers” versus “non-buyers” or “prefers brand A” versus “prefers brand B”. These cases require binary classification models such as logistic regression, linear, and quadratic discriminant analysis. A promising recent technique for the binary classification problem is the Support Vector Machine (Vapnik (1995)), which has a...

This paper comments on the recently published work dealing with support vector machine for classification based on fuzzy data [Ji, A.-B., Pang, J.-H., & Qiu, H.-J. (2010). Support vector machine for classification based on fuzzy training data. Expert Systems with Applications 37(4), 3495–3498]. The authors have claimed that their proposed program is a classical convex quadratic program. But, we...

In recent years, support vector machines (SVMs) have become a popular tool for pattern recognition and machine learning. Training a SVM involves solving a constrained quadratic programming problem, which requires large memory and enormous amounts of training time for largescale problems. In contrast, the SVM decision function is fully determined by a small subset of the training data, called su...

The dual formulation of the support vector machine (SVM) objective function is an instance of a nonnegative quadratic programming problem. We reformulate the SVM objective function as a matrix factorization problem which establishes a connection with the regularized nonnegative matrix factorization (NMF) problem. This allows us to derive a novel multiplicative algorithm for solving hard and sof...

Multiple attribute decision making problems with uncertain weights in intuitionistic fuzzy setting are investigated. Some concepts related to the theory of intuitionistic fuzzy set (IFS), including intuitionistic fuzzy weighted averaging (IFWA) operator, score function, and accuracy function, are reviewed. Based on the technology for order preference by similarity to idea solution (TOPSIS) meth...

In the recent years support vector machines (SVMs) have been successfully applied to solve a large number of classification problems. Training an SVM, usually posed as a quadratic programming (QP) problem, often becomes a challenging task for the large data sets due to the high memory requirements and slow convergence. We propose to apply boosting to Platt’s Sequential Minimal Optimization (SMO...