• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.669-674
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• 2022

In this paper, we shall consider some properties of the metric projection as a set valued mapping. For a set G in a metric space E, the mapping 𝜋_G; x → 𝜋_G(x) of E into 2^G is called set valued metric projection of E onto G. We investigated the properties related to the projection P_S(·)(·) and 𝜋_S(·)(·) as one-sided best simultaneous approximations.

• Journal of information and communication convergence engineering
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• v.5 no.3
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• pp.233-238
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• 2007

An approach to identify Chinese event types is proposed in this paper which combines a good feature selection policy and a Maximum Entropy (ME) model. The approach not only effectively alleviates the problem that classifier performs poorly on the small and difficult types, but improve overall performance. Experiments on the ACE2005 corpus show that performance is satisfying with the 83.5% macro - average F measure. The main characters and ideas of the approach are: (1) Optimal feature set is built for each type according to local feature selection, which fully ensures the performance of each type. (2) Positive and negative features are explicitly discriminated and combined by using one - sided metrics, which makes use of both features' advantages. (3) Wrapper methods are used to search new features and evaluate the various feature subsets to obtain the optimal feature subset.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.743-753
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• 2000

In the space $C_1(X)$ of real-valued continuous functions with $L_1-norm$, every bounded set has a relative Chebyshev center in a finite-dimensional subspace S. Moreover, the set function $F\rightarrowZ_S(F)$ corresponding to F the set of its relative Chebyshev centers, in continuous on the space B[$C_1(X)$(X)] of nonempty bounded subsets of $C_1(X)$ (X) with the Hausdorff metric. In particular, every bounded set has a relative Chebyshev center in the closed convex set S(F) of S and the set function $F\rightarrowZ_S(F)$(F) is continuous on B[$C_1(X)$ (X)] with a condition that the sets S(.) are equal.