• Journal of KIISE:Computing Practices and Letters
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• v.16 no.10
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• pp.949-954
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• 2010

Computing the rotation-invariant distance between image time-series is a time-consuming process that incurs a lot of Euclidean distances for all possible rotations. In this paper we propose an innovative solution that significantly reduces the number of Euclidean distances using the triangular inequality. To this end, we first present the notion of self rotation distance and show that, by using the self rotation distance with the triangular inequality, we can prune many unnecessary distance computations. We next present that only one self-rotation is enough for all self-rotation distances required. Experimental results show that our self rotation distance-based methods outperform the existing methods by up to an order of magnitude.

• Journal of IKEEE
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• v.23 no.2
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• pp.419-424
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• 2019

The FCM algorithm finds the optimal solution through iterative optimization technique. In particular, there is a difference in execution time depending on the initial center of clustering, the location of noise, the location and number of crowded densities. However, this method gradually updates the center point, and the center of the initial cluster is shifted to one side. In this paper, we propose a TI-FCM(Triangular Inequality-Fuzzy C-Means) clustering algorithm that determines the cluster center density by maximizing the distance between clusters using triangular inequality. The proposed method is an effective method to converge to real clusters compared to FCM even in large data sets. Experiments show that execution time is reduced compared to existing FCM.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.747-755
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• 2020

The mathematical proof for establishing some new inequalities involving arithmetic, geometric, harmonic means for the arguments lying on the paths of triangular wave function (linear) and new parabolic function (curved) over the interval (0, 1) are discussed. The results representing an extension as well as strengthening of Ky Fan Type inequalities.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.39-51
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• 2010

In this paper we consider the uniform central limit theorem for a martingale-difference array of a function-indexed stochastic process under the uniformly integrable entropy condition. We prove a maximal inequality for martingale-difference arrays of process indexed by a class of measurable functions by a method as Ziegler [19] did for triangular arrays of row wise independent process. The main tools are the Freedman inequality for the martingale-difference and a sub-Gaussian inequality based on the restricted chaining. The results of present paper generalizes those of Ziegler [19] and other results of independent problems. The results also generalizes those of Bae and Choi [3] to martingale-difference array of a function-indexed stochastic process. Finally, an application to classes of functions changing with n is given.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.294-297
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• 2005

Time series are comprehensively appeared and developed in many applications, ranging from science and technology to business and entertainrilent. Similarity search under time warping has attracted much interest between the time series in the large sequence databases. DTW (Dynamic Time Warping) is a robust distance measure and is superior to Euclidean distance for time series, allowing similarity matching although one of the sequences can elastic shift along the time axis. Nevertheless, it is more unfortunate that DTW has a quadratic time. Simultaneously the false dismissals are come forth since DTW distance does not satisfy the triangular inequality. In this paper, we propose an efficient range query algorithmbased on a new similarity search method under time warping. When our range query applies for this method, it can remove the significant non-qualify time series as early as possible before computing the accuracy DTW distance. Hence, it speeds up the calculation time and reduces the number of scanning the time series. Guaranteeing no false dismissals, the lower bounding function is advised that consistently underestimate the DTW distance and satisfy the triangular inequality. Through the experimental result, our range query algorithm outperforms the existing others.

• Journal of KIISE:Databases
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• v.35 no.5
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• pp.447-458
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• 2008

In this paper, we address an efficient processing scheme for k-nearest neighbor queries to retrieve k static objects in road network databases. Existing methods cannot expect a query processing speed-up by index structures in road network databases, since it is impossible to build an index by the network distance, which cannot meet the triangular inequality requirement, essential for index creation, but only possible in a totally ordered set. Thus, these previous methods suffer from a serious performance degradation in query processing. Another method using pre-computed network distances also suffers from a serious storage overhead to maintain a huge amount of pre-computed network distances. To solve these performance and storage problems at the same time, this paper proposes a novel approach that creates an index for moving objects by approximating their network distances and efficiently processes k-nearest neighbor queries by means of the approximate index. For this approach, we proposed a systematic way of mapping each moving object on a road network into the corresponding absolute position in the m-dimensional space. To meet the triangular inequality this paper proposes a new notion of average network distance, and uses FastMap to map moving objects to their corresponding points in the m-dimensional space. After then, we present an approximate indexing algorithm to build an R*-tree, a multidimensional index, on the m-dimensional points of moving objects. The proposed scheme presents a query processing algorithm capable of efficiently evaluating k-nearest neighbor queries by finding k-nearest points (i.e., k-nearest moving objects) from the m-dimensional index. Finally, a variety of extensive experiments verifies the performance enhancement of the proposed approach by performing especially for the real-life road network databases.

• 전기의세계
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• v.30 no.6
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• pp.375-385
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• 1981

New algorithms are derived for nonlinear programming problems which are characterized by their large variables and equality and inequality constraints. The algorithms are based upon the introduction of the Dependent-Variable-Elimination method, Independent-Variable-Reduction method, Optimally-Ordered-Triangular-Factorization method, Equality-Inequality-Sequential-Satisfaction method, etc. For a case study problem relating to the optimal determination of load flow in a 10-bus, 13-line sample power system, several approaches are undertaken, such as SUMT, Lagrange's Multiplier method, sequential applications of linear and quadratic programming method. For applying the linear programming method, the conventional simplex algorithm is modified to the large-system-oriented one by the introduction of the Two-Phase method and Variable-Upper-Bounding method, thus resulting in remarkable savings in memory requirements and computing time. The case study shows the validity and effectivity of the algorithms presented herein.

• Proceedings of the Korean Information Science Society Conference
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• 2011.06c
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• pp.112-114
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• 2011

On multimedia databases, in order to realize the fast access method, indexing methods for the multidimension data space are used. However, since it is a premise to use the Euclid distance as the distance measure, this method lacks in flexibility. On the other hand, there are metric indexing methods which require only to satisfy distance axiom. Since metric indexing methods can also apply for distance measures other than the Euclid distance, these methods have high flexibility. This paper proposes an improved method of VP-tree which is one of the metric indexing methods. VP-tree follows the node which suits the search range from a route node at searching. And distances between a query and all objects linked from the leaf node which finally arrived are computed, and it investigates whether each object is contained in the search range. However, search speed will become slow if the number of distance calculations in a leaf node increases. Therefore, we paid attention to the candidates selection method using the triangular inequality in a leaf node. As the improved methods, we propose a method to use the nearest neighbor object point for the query as the datum point of the triangular inequality. It becomes possible to make the search range smaller and to cut down the number of times of distance calculation by these improved methods. From evaluation experiments using 10,000 image data, it was found that our proposed method could cut 5%~12% of search time of the traditional method.

• Journal of the Korea Computer Industry Society
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• v.5 no.2
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• pp.275-280
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• 2004

In this paper, a very fast block matching scheme was proposed to reduce the computations of Block Sum Pyramid Algorithm for motion estimation in video coding. The proposed algorithm is based on Block Sum Pyramid Algorithm and Efficient Multi-level Successive Elimination Algorithm. The proposed algorithm can reduce the computations of motion estimation greatly with 100% motion estimation accuracy. The efficiency of the proposed algorithm was verified by experimental results.

• Journal of Industrial Technology
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• v.20 no.B
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• pp.219-226
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• 2000

In this paper, we propose a new novel method for similarity search that supports time warping. Our primary goal is to innovate on search performance in large databases without false dismissal. To attain this goal, we devise a new distance function $D_{tw-lb}$ that consistently underestimates the time warping distance and also satisfies the triangular inequality. $D_{tw-lb}$ uses a 4-tuple feature vector extracted from each sequence and is invariant to time warping. For efficient processing, we employ a multidimensional index that uses the 4-tuple feature vector as indexing attributes and $D_{tw-lb}$ as a distance function. We prove that our method does not incur false dismissal. To verify the superiority of our method, we perform extensive experiments. The results reveal that our method achieves significant speedup up to 43 times with real-world S&P 500 stock data.