A hybrid model for exchange rate prediction
Decision Support Systems
Dynamic classification for video stream using support vector machine
Applied Soft Computing
Support vector regression based hybrid rule extraction methods for forecasting
Expert Systems with Applications: An International Journal
Charge state determination of peptide tandem mass spectra using support vector machine (SVM)
IEEE Transactions on Information Technology in Biomedicine - Special section on new and emerging technologies in bioinformatics and bioengineering
SVM approach with a genetic algorithm for network intrusion detection
ISCIS'05 Proceedings of the 20th international conference on Computer and Information Sciences
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Support Vector Machines (SVMs) perform pattern recognition between two point classes by finding a decision surface determined by certain points of the training set, termed Support Vectors (SV). This surface, which in some feature space of possibly infinite dimension can be regarded as a hyperplane, is obtained from the solution of a problem of quadratic programming that depends on a regularization parameter. In this paper we study some mathematical properties of support vectors and show that the decision surface can be written as the sum of two orthogonal terms, the first depending only on the {\em margin vectors} (which are SVs lying on the margin), the second proportional to the regularization parameter. For almost all values of the parameter, this enables us to predict how the decision surface varies for small parameter changes. In the special but important case of feature space of finite dimension m, we also show that there are at most m+1 margin vectors and observe that m+1 SVs are usually sufficient to fully determine the decision surface. For relatively small m this latter result leads to a consistent reduction of the SV number.