A Weighted Generalized Ls–svm

Neural networks play an important role in system modelling. This is especially true if model building is mainly based on observed data. Among neural models the Support Vector Machine (SVM) solutions are attracting increasing attention, mostly because they automatically answer certain crucial questions involved by neural network construction. They derive an ‘optimal’ network structure and answer the most important question related to the ‘quality’ of the resulted network. The main drawback of standard Support Vector Machines (SVM) is its high computational complexity, therefore recently a new technique, the Least Squares SVM (LS–SVM) has been introduced. This is algorithmically more effective, because the solution can be obtained by solving a linear equation set instead of a computation-intensive quadratic programming problem. Although the gain in efficiency is rather significant, for really large problems the computational burden of LS-SVM is still too high. Moreover, an attractive feature of SVM, its sparseness is lost. This paper proposes a special new generalized formulation and solution technique for the standard LS-SVM. By solving the modified LS–SVM equation set in least squares (LS) sense (LS2–SVM), a pruned solution is achieved, while the computational burden is further reduced (Generalized LS–SVM). In this generalized LS–SVM framework a further modification weighting is also proposed, to reduce the sensitivity of the network construction to outliers while maintaining sparseness.