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Support vector machines (SVMs), with their roots in Statistical Learning Theory (SLT) and optimization methods, have become powerful tools for problem solution in machine learning. SVMs reduce most machine learning problems to optimization problems and optimization lies at the heart of SVMs. Lots of SVM algorithms involve solving not only convex problems, such as linear programming, quadratic programming, second order cone programming, semi-definite programming, but also non-convex and more general optimization problems, such as integer programming, semi-infinite programming, bi-level programming and so on. The purpose of this paper is to understand SVM from the optimization point of view, review several representative optimization models in SVMs, their applications in economics, in order to promote the research interests in both optimization-based SVMs theory and economics applications. This paper starts with summarizing and explaining the nature of SVMs. It then proceeds to discuss optimization models for SVM following three major themes. First, least squares SVM, twin SVM, AUC Maximizing SVM, and fuzzy SVM are discussed for standard problems. Second, support vector ordinal machine, semisupervised SVM, Universum SVM, robust SVM, knowledge based SVM and multi-instance SVM are then presented for nonstandard problems. Third, we explore other important issues such as lp-norm SVM for feature selection, LOOSVM based on minimizing LOO error bound, probabilistic outputs for SVM, and rule extraction from SVM. At last, several applications of SVMs to financial forecasting, bankruptcy prediction, credit risk analysis are introduced. [ABSTRACT FROM AUTHOR]

Simulated Annealing (SA) has been adopted by many Ensemble Clustering methods to achieve global combinational optimisation. However the performance of SA is sensitive to the settings of its parameters. Much work has been done for optimising the settings of these parameters over the last two decades, but few of them analysed the behaviour of different cooling functions for Ensemble Clustering. Our work has demonstrated that the clustering results could be invalid if we use SA for Ensemble Clustering without a good understanding of the behaviour of cooling functions. Therefore this paper aims to present the findings of how different cooling functions may affect the performance of Ensemble Clustering methods that use SA. We analyse the effect of cooling functions from three aspects: the convergence rate, the final value of the objective function, and the accuracy of results. Ten different cooling functions are tested on two Ensemble Clustering methods, and thirteen different datasets have been used for the experiments. The findings are particularly helpful for those who are interested in Ensemble Clustering methods as well as those who want to obtain a deep understanding of the behaviour of the cooling functions. [ABSTRACT FROM AUTHOR]