• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1557-1565
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• 2022

In this paper, Glift codes, generalized lifted polynomials, matrices are introduced. The advantage of Glift code is "distance preserving" over the ring R. Then optimal codes can be obtained over the rings by using Glift codes and lifted polynomials. Zero divisors are classified to satisfy "distance preserving" for codes over non-chain rings. Moreover, Glift codes apply on MDS codes and MDS codes are obtained over the ring 𝓡 and the non-chain ring 𝓡_e,s.

• Journal of KIISE:Computing Practices and Letters
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• v.16 no.3
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• pp.356-360
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• 2010

Recently, there have been many research efforts on privacy-preserving data mining. In privacy-preserving data mining, accuracy preservation of mining results is as important as privacy preservation. Random perturbation privacy-preserving data mining technique is known to well preserve privacy. However, it has a problem that it destroys distance orders among time-series. In this paper, we propose a notion of the noise averaging effect of piecewise aggregate approximation(PAA), which can be preserved the clustering accuracy as high as possible in time-series data clustering. Based on the noise averaging effect, we define the PAA distance in computing distance. And, we show that our PAA distance can alleviate the problem of destroying distance orders in random perturbing time series.

• The Pure and Applied Mathematics
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• v.10 no.3
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• pp.193-198
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• 2003

Let X and Y be n-dimensional Euclidean spaces with $n\;{\geq}\;3$. In this paper, we generalize a classical theorem of Bookman and Quarles by proving that if a mapping, from a half space of X into Y, preserves a distance $\rho$, then the restriction of f to a subset of the half space is an isometry.

• The Transactions of the Korea Information Processing Society
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• v.3 no.7
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• pp.1707-1718
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• 1996

Given a signal net N=s, 1,...,n to be the set of nodes, with s the source and the remaining nodes sinks, an MRDPT (minimum-cost rectilinear Steiner distance -preserving tree) has the property that the length of every source to sink path is equal to the rectilinear distance between the source and sink. The minimum- cost rectilinear Steiner distance-preserving tree minimizes the total wore length while maintaining minimal source to sink length. Recently, some heuristic algorithms have been proposed for the problem offending the MRDPT. In this paper, we investigate an optimal structure on the MRDPT and present a theoretical breakthrough which shows that the min-cost flow formulation leads to an efficient O(n2logm)2) time algorithm. A more practical extension is also in vestigated along with interesting open problems.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.771-782
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• 2019

We show that mappings preserving unit distance are close to two-isometries. We also prove that a mapping f is a linear isometry up to translation when f is a two-expansive surjective mapping preserving unit distance. Then we apply these results to consider two-isometries between normed spaces, strictly convex normed spaces and unital $C^*$-algebras. Finally, we propose some remarks and problems about generalized two-isometries on Banach spaces.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.667-680
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• 2004

We generalize a theorem of W. Benz by proving the following result: Let $H_{\theta}$ be a half space of a real Hilbert space with dimension $\geq$ 3 and let Y be a real normed space which is strictly convex. If a distance $\rho$ > 0 is contractive and another distance N$\rho$ (N $\geq$ 2) is extensive by a mapping f : $H_{\theta}$ \longrightarrow Y, then the restriction f│$_{\theta}$ $H_{+}$$\rho$/2// is an isometry, where $H_{\theta}$＋$\rho$/2/ is also a half space which is a proper subset of $H_{\theta}$. Applying the above result, we also generalize a classical theorem of Beckman and Quarles.

• Journal of KIISE:Databases
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• v.35 no.6
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• pp.481-494
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• 2008

In this paper we propose Fourier magnitudes based privacy preserving clustering on time-series data. The previous privacy-preserving method, called DFT coefficient method, has a critical problem in privacy-preservation itself since the original time-series data may be reconstructed from privacy-preserved data. In contrast, the proposed DFT magnitude method has an excellent characteristic that reconstructing the original data is almost impossible since it uses only DFT magnitudes except DFT phases. In this paper, we first explain why the reconstruction is easy in the DFT coefficient method, and why it is difficult in the DFT magnitude method. We then propose a notion of distance-order preservation which can be used both in estimating clustering accuracy and in selecting DFT magnitudes. Degree of distance-order preservation means how many time-series preserve their relative distance orders before and after privacy-preserving. Using this degree of distance-order preservation we present greedy strategies for selecting magnitudes in the DFT magnitude method. That is, those greedy strategies select DFT magnitudes to maximize the degree of distance-order preservation, and eventually we can achieve the relatively high clustering accuracy in the DFT magnitude method. Finally, we empirically show that the degree of distance-order preservation is an excellent measure that well reflects the clustering accuracy. In addition, experimental results show that our greedy strategies of the DFT magnitude method are comparable with the DFT coefficient method in the clustering accuracy. These results indicate that, compared with the DFT coefficient method, our DFT magnitude method provides the excellent degree of privacy-preservation as well as the comparable clustering accuracy.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.9-15
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• 2003

In this paper, we will deal with the Aleksandrov-Rassias problem. More precisely, we prove some theorems concerning the mappings preserving one or two distances.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.643-654
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• 2000

In this paper, we review some class of t-norms on which fuzzy arithmetic operations preserve the shapes of fuzzy numbers and the Hausdorff-distance between fuzzy numbers as the measure of distance between fuzzy numbers. And we suggest the least Hausdorff-distance square method for fuzzy linear regression model using shape preserving fuzzy arithmetic operations.

• Proceedings of the Korea Information Processing Society Conference
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• 2024.05a
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• pp.229-230
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• 2024

최근 드론으로 극한 환경에서 범죄 수배자 및 실종자를 탐색하는 시도가 활발하다. 이때 생체 인증 기술인 얼굴 인증 기술을 사용하면 탐색 효율이 높아지지만, 암호화되지 않은 인증 프로토콜 적용 시 생체 정보 유출의 위험이 있다. 본 논문에서는 드론이 수집한 얼굴 이미지 템플릿을 암호화하여 안전하게 인증할 수 있는 효율적인 생체 인증 프레임워크인 DF-PPHDM(Privacy-Preserving Hamming Distance biometric Matching for Drone-collected Facial images)을 제안한다. 수집된 얼굴 이미지는 암호문 형태로 서버에 전달되며 서버는 기존 등록된 암호화된 템플릿과의 Hamming distance 분석을 통해 검증한다. 제안한 DF-PPHDM을 RaspberryPI 4B 환경에서 직접 실험하여 분석한 결과, 한정된 리소스를 소유한 드론에서 효율적인 구현이 가능하며, 인증 단계에서 7.83~155.03 ㎲ (microseconds)가 소요된다는 것을 입증하였다. 더불어 서버는 드론이 전송한 암호문으로부터 생체 정보를 복구할 수 없으므로 프라이버시 침해 문제를 예방할 수 있다. 향후 DF-PPHDM에 AI(Artificial Intelligence)를 결합하여 자동화 기능을 추가하고 코드 최적화를 통해 성능을 향상시킬 예정이다.