Generalised eigendecomposition problem for a symmetric matrix pencil is reinterpreted as an unconstrained minimisation problem with a weighted non-linear criterion. The analytical results show that the proposed criter...
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Generalised eigendecomposition problem for a symmetric matrix pencil is reinterpreted as an unconstrained minimisation problem with a weighted non-linear criterion. The analytical results show that the proposed criterion has a unique global minimum which corresponds to the principal generalised eigenvectors, thus guaranteeing the global convergence via iterative methods to search the minimum. A gradient-based adaptive algorithm and a fixed point iteration-based adaptive algorithm are derived for the generalised eigendecomposition, which both work in parallel and avoid the error propagation effect of sequential-type algorithms. By applying the stochastic approximation theory, the global convergence of the proposed adaptive algorithm is proved. The performance of the proposed method is evaluated by simulations in terms of convergence rate, estimation accuracy as well as tracking capability.
In this paper, a new variant of Twin Support Vector Machines (TSVM) termed as Neo-Twin Support Vector Machines (Neo-TSVM) has been proposed for binary pattern classification. TSVM uses hinge loss to allow optimal sepa...
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ISBN:
(纸本)9781665495011
In this paper, a new variant of Twin Support Vector Machines (TSVM) termed as Neo-Twin Support Vector Machines (Neo-TSVM) has been proposed for binary pattern classification. TSVM uses hinge loss to allow optimal separation from the opposite class, casting it as a constrained optimisation problem. Neo-TSVM presents a simpler model which eliminates the constraints and cast it as an unconstrained minimisation problem (UMP). Further to allow, better separation between the non-parallel hyperplanes, the notion of angle has also been introduced in the optimisation problem. For testing the efficacy of the proposed classifier, experiments have been conducted on benchmark datasets, and it is observed that the proposed classifier achieves results comparable to that of TSVM, and is also time efficient.
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