In this paper, two two-timescale projection neural networks are proposed based on the majorizationminimizationprinciple for nonconvex optimization and distributed nonconvex optimization. They are proved to be globall...
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In this paper, two two-timescale projection neural networks are proposed based on the majorizationminimizationprinciple for nonconvex optimization and distributed nonconvex optimization. They are proved to be globally convergent to Karush-Kuhn-Tucker points. A collaborative neurodynamic approach leverages multiple two-timescale projection neural networks repeatedly re-initialized using a meta-heuristic rule for global optimization and distributed global optimization. Two numerical examples are elaborated to demonstrate the efficacy of the proposed approaches.
The continuous k-center problem aims at finding k balls with the smallest radius to cover a finite number of given points in R-n. In this paper, we propose and study the following generalized version of the k-center p...
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The continuous k-center problem aims at finding k balls with the smallest radius to cover a finite number of given points in R-n. In this paper, we propose and study the following generalized version of the k-center problem: Given a finite number of nonempty closed convex sets in R-n, find k balls with the smallest radius such that their union intersects all of the sets. Because of its nonsmoothness and nonconvexity, this problem is very challenging. Based on nonsmooth optimization techniques, we first derive some qualitative properties of the problem and then propose new algorithms to solve the problem. Numerical experiments are also provided to show the effectiveness of the proposed algorithms.
Dependence of the linear discriminant analysis on location and scale weakens its performance when predicting class under the presence of homogeneous covariance matrices for the candidate classes. Further, outlying sam...
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Dependence of the linear discriminant analysis on location and scale weakens its performance when predicting class under the presence of homogeneous covariance matrices for the candidate classes. Further, outlying samples render the method to suffer from higher rates of misclassification. In this study, we propose the minimization approximation cost classification (MACC) method that accounts for some specific cost function 23.9. The theoretical derivation is made to find an optimal linear hyperplane theta, which yields maximum separation between the dichotomous groups. Real-life data and simulations were used to validate the method against the standard classifiers. Results show that the proposed method is more efficient and outperforms the standard methods when the data are crowded at the class boundaries.
Distance-weighted discrimination (DWD) is a modern margin-based classifier with an interesting geometric motivation. It was proposed as a competitor to the support vector machine (SVM). Despite many recent references ...
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Distance-weighted discrimination (DWD) is a modern margin-based classifier with an interesting geometric motivation. It was proposed as a competitor to the support vector machine (SVM). Despite many recent references on DWD, DWD is far less popular than the SVM, mainly because of computational and theoretical reasons. We greatly advance the current DWD methodology and its learning theory. We propose a novel thrifty algorithm for solving standard DWD and generalized DWD, and our algorithm can be several hundred times faster than the existing state of the art algorithm based on second-order cone programming. In addition, we exploit the new algorithm to design an efficient scheme to tune generalized DWD. Furthermore, we formulate a natural kernel DWD approach in a reproducing kernel Hilbert space and then establish the Bayes risk consistency of the kernel DWD by using a universal kernel such as the Gaussian kernel. This result solves an open theoretical problem in the DWD literature. A comparison study on 16 benchmark data sets shows that data-driven generalized DWD consistently delivers higher classification accuracy with less computation time than the SVM.
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