• KIPS Transactions on Software and Data Engineering
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• v.9 no.3
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• pp.83-90
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• 2020

Prototype selection offers the advantage of ensuring low learning time and storage space by selecting the minimum data representative of in-class partitions from the training data. This paper designs a new training data generation method using hyper-rectangles that can be applied to general classification algorithms. Hyper-rectangular regions do not contain different class data and divide the same class space. The median value of the data within a hyper-rectangle is selected as a prototype to form new training data, and the size of the hyper-rectangle is adjusted to reflect the data distribution in the class area. A set cover optimization algorithm is proposed to select the minimum prototype set that represents the whole training data. The proposed method reduces the time complexity that requires the polynomial time of the set cover optimization algorithm by using the greedy algorithm and the distance equation without multiplication. In experimented comparison with hyper-sphere prototype selections, the proposed method is superior in terms of prototype rate and generalization performance.

• KIPS Transactions on Software and Data Engineering
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• v.5 no.10
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• pp.483-488
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• 2016

In this paper, we propose a prototype-based classification learning by using the nearest-neighbor rule. The nearest-neighbor is applied to segment the class area of all the training data with hyperspheres, and a hypersphere must cover the data from the same class. The radius of a hypersphere is computed by the mid point of the two distances to the farthest same class point and the nearest other class point. And we transform the prototype selection problem into a set covering problem in order to determine the smallest set of prototypes that cover all the training data. The proposed prototype selection method is designed by a greedy algorithm and applicable to process a large-scale training set in parallel. The prediction rule is the nearest-neighbor rule and the new training data is the set of prototypes. In experiments, the generalization performance of the proposed method is superior to existing methods.

• Journal of the Korea Society of Computer and Information
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• v.20 no.2
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• pp.21-28
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• 2015

In this paper, we propose a prototype-based classification learning by using the nearest-neighbor rule. The nearest-neighbor is applied to segment the class area of all the training data into spheres within which the data exist from the same class. Prototypes are the center of spheres and their radii are computed by the mid-point of the two distances to the farthest same class point and the nearest another class point. And we transform the prototype selection problem into a set covering problem in order to determine the smallest set of prototypes that include all the training data. The proposed prototype selection method is based on a greedy algorithm that is applicable to the training data per class. The complexity of the proposed method is not complicated and the possibility of its parallel implementation is high. The prototype-based classification learning takes up the set of prototypes and predicts the class of test data by the nearest neighbor rule. In experiments, the generalization performance of our prototype classifier is superior to those of the nearest neighbor, Bayes classifier, and another prototype classifier.

• Journal of the Korea Convergence Society
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• v.7 no.5
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• pp.213-219
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• 2016

This paper presents a branch-and-bound algorithm for solving the concave minimization problem with upper bounded variables whose single constraint is linear. The algorithm uses simplex as partition element. Because the convex envelope which most tightly underestimates the concave function on the simplex is uniquely determined by solving the related linear equations. Every branching process generates two subsimplices one lower dimensional than the candidate simplex by adding 0 and upper bound constraints. Subsequently the feasible points are partitioned into two sets. During the bounding process, the linear programming problems defined over subsimplices are minimized to calculate the lower bound and to update the incumbent. Consequently the simplices which do certainly not contain the global minimum are excluded from consideration. The major advantage of the algorithm is that the subproblems are defined on the one less dimensinal space. It means that the amount of work required for the subproblem decreases whenever the branching occurs. Our approach can be applied to solving the concave minimization problems under knapsack type constraints.

• Journal of the Korea Institute of Military Science and Technology
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• v.18 no.6
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• pp.797-807
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• 2015

The low-altitude PAC-2 Patriot missile system is the backbone of ROK air defense for intercepting enemy aircraft. Currently there is no missile interceptor which can defend against the relatively high velocity ballistic missile from North Korea which may carry nuclear, biological or chemical warheads. For ballistic missile defense, Korea's air defense systems are being evaluated. In attempting to intercept ballistic missiles at high altitude the most effective means is through a multi-layered missile defense system. The missile defense problem has been studied considering a single interception system or any additional capability. In this study, we seek to establish a mathematical model that's available for multi-layered missile defense and minimize total interception fail probability and proposes a solution based on genetic algorithms. We perform computational tests to evaluate the relative speed and solution of our GA algorithm in comparison with the commercial optimization tool GAMS.