• Education of Primary School Mathematics
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• v.27 no.1
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• pp.91-110
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• 2024

The purpose of this study is to explore visual models for deriving the fractional division algorithm, to see how students understand this integrated model, the rectangular partition model, when taught in elementary school classrooms, and how they structure relationships between fractional division situations. The conclusions obtained through this study are as follows. First, in order to remind the reason for multiplying the reciprocal of the divisor or the meaning of the reciprocal, it is necessary to explain the calculation process by interpreting the fraction division formula as the context of a measurement division or the context of the determination of a unit rate. Second, the rectangular partition model can complement the detour or inappropriate parts that appear in the existing model when interpreting the fraction division formula as the context of a measurement division, and can be said to be an appropriate model for deriving the standard algorithm from the problem of the context of the inverse of a Cartesian product. Third, in the context the inverse of a Cartesian product, the rectangular partition model can naturally reveal the calculation process in the context of a measurement division and the context of the determination of a unit rate, and can show why one division formula can have two interpretations, so it can be used as an integrated model.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 1999.05a
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• pp.109-112
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• 1999

Image segmentation is the critical first step in image information extraction for computer vision systems. Clustering methods have been used extensively in color image segmentation. Most analytic fuzzy clustering approaches are divided from the fuzzy c-means(FCM) algorithm. The FCM algorithm uses fie probabilistic constraint that the memberships of a data point across classes sum to 1. However, the memberships resulting from the FCM do not always correspond to the intuitive concept of degree of belonging or compatibility. Moreover, the FCM algorithm has considerable trouble under noisy environments in the feature space. Recently, a possibilistic approach to clustering(PCM) for solving above problems was proposed. In this paper, we used the PCM for color image segmentation. This approach differs from existing fuzzy clustering methods for color image segmentation in that the resulting partition of the data can be interpreted as a possibilistic partition. So, the problems in the FCM can be solved by the PCM. But, the clustering results by the PCM are not smoothly bounded, and they often have holes. The region growing was used as a postprocessing after smoothing the noise points in the pixel seeds. In our experiments, we illustrate that the PCM us reasonable than the FCM in noisy environments.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2012.10a
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• pp.35-36
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• 2012

The generation of fuzzy rules is inevitable in order to construct fuzzy modeling and in general, has the problem that the number of rules increases exponentially with increasing dimension. To solve this problem, we introduce the system that generate the fuzzy rules and make a inference based on FCM clustering algorithm that partition the input space in the scatter form. The parameters in the premise part of the fuzzy rules is determined as membership matrix by the FCM clustering algorithm and the consequence part of the fuzzy rules is are expressed as a polynomial function. Proposed model evaluated using the numerical data.

• Proceedings of the KIEE Conference
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• 1998.11b
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• pp.657-659
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• 1998

In order to optimize fuzzy modeling of nonlinear system, we proposed a optimal fuzzy model according to the characteristic of I/O relationship, HCM method, the genetic algorithm, and the objective function with weighting factor. A conventional fuzzy model has difficulty in definition of membership function. In order to solve its problem, the premise structure of the proposed fuzzy model is selected by both the partition of input space and the analysis of input-output relationship using the clustering algorithm. The premise parameters of the fuzzy model are optimized respectively by the genetic algorithm and the consequence parameters of the fuzzy model are identified by the standard least square method. Also, the objective function with weighting factor is proposed to achieve a balance between the performance results for the training and testing data.

• The Transactions of the Korea Information Processing Society
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• v.6 no.7
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• pp.1849-1857
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• 1999

We proposed the RPA (Recursive Partition Averaging) method in order to improve the storage requirement and classification rate of the Memory Based Reasoning. This algorithm recursively partitions the pattern space until each hyperrectangle contains only those patterns of the same class, then it computes the average values of patterns in each hyperrectangle to extract a representative. Also we have used the mutual information between the features and classes as weights for features to improve the classification performance. The proposed algorithm used 30~90% of memory space that is needed in the k-NN (k-Nearest Neighbors) classifier, and showed a comparable classification performance to the k-NN. Also, by reducing the number of stored patterns, it showed an excellent result in terms of classification time when we compare it to the k-NN.

• Journal of KIISE:Software and Applications
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• v.34 no.1
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• pp.11-17
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• 2007

One of the popular methods used for pattern classification is the MBR (Memory-Based Reasoning) algorithm. Since it simply computes distances between a test pattern and training patterns or hyperplanes stored in memory, and then assigns the class of the nearest training pattern, it cannot explain how the classification result is obtained. In order to overcome this problem, we propose an incremental teaming algorithm based on RPA (Recursive Partition Averaging) to extract IF-THEN rules that describe regularities inherent in training patterns. But rules generated by RPA eventually show an overfitting phenomenon, because they depend too strongly on the details of given training patterns. Also RPA produces more number of rules than necessary, due to over-partitioning of the pattern space. Consequently, we present the IREA (Incremental Rule Extraction Algorithm) that overcomes overfitting problem by removing useless conditions from rules and reduces the number of rules at the same time. We verify the performance of proposed algorithm using benchmark data sets from UCI Machine Learning Repository.

• Journal of the Korea Society of Computer and Information
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• v.16 no.8
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• pp.57-66
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• 2011

In this paper, it is proposed for algorithm to detect human efficiently using a edge symmetry and gradient directional characteristics in realtime by the feature extraction in a single input image. Proposed algorithm is composed of three stages, preprocessing, region partition of human candidates, verification of candidate regions. Here, preprocessing stage is strong the image regardless of the intensity and brightness of surrounding environment, also detects a contour with characteristics of human as considering the shape features size and the condition of human for characteristic of human. And stage for region partition of human candidates has separated the region with edge symmetry for human and size in the detected contour, also divided 1st candidates region with applying the adaboost algorithm. Finally, the candidate region verification stage makes excellent the performance for the false detection by verifying the candidate region using feature vector of a gradient for divided local area and classifier. The results of the simulations, which is applying the proposed algorithm, the processing speed of the proposed algorithms is improved approximately 1.7 times, also, the FNR(False Negative Rate) is confirmed to be better 3% than the conventional algorithm which is a single structure algorithm.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.3
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• pp.368-374
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• 2010

Image segmentation is the basic step in the field of the image processing for pattern recognition, environment recognition, and context analysis. The Otsu's automatic threshold selection, which determines the optimal threshold value to maximize the between class scatter using the distribution information of the normalized histogram of a image, is the famous method among the various image segmentation methods. For the automatic threshold selection proposed by Otsu, it is difficult to determine the optimal threshold value by considering the sub-region characteristic of the image because the Otsu's algorithm analyzes the global histogram of a image. In this paper, to alleviate this difficulty of Otsu's image segmentation algorithm and to improve image segmentation capability, the original image is divided into several sub-images by using context fuzzy c-means algorithm. The proposed fuzzy Otsu threshold algorithm is applied to the divided sub-images and the several threshold values are obtained.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.6
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• pp.2761-2781
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• 2018

With the continuous growth of data size and the use of compression technology, data reduction has great research value and practical significance. Aiming at the shortcomings of the existing semantic compression algorithm, this paper is based on the analysis of ItCompress algorithm, and designs a method of bidirectional order selection based on interval partitioning, which named An Optimized Iterative Semantic Compression Algorithm (Optimized ItCompress Algorithm). In order to further improve the speed of the algorithm, we propose a parallel optimization iterative semantic compression algorithm using GPU (POICAG) and an optimized iterative semantic compression algorithm using Spark (DOICAS). A lot of valid experiments are carried out on four kinds of datasets, which fully verified the efficiency of the proposed algorithm.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.11
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• pp.2158-2165
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• 2007

In this paper, a Modified Fuzzy C-Means algorithm with Gaussian Weights(MFCM_GW) is presented for nonlinear blind channel equalization. The proposed algorithm searches the optimal channel output states of a nonlinear channel from the received symbols, based on the Bayesian likelihood fitness function and Gaussian weighted partition matrix instead of a conventional Euclidean distance measure. Next, the desired channel states of a nonlinear channel are constructed with the elements of estimated channel output states, and placed at the center of a Radial Basis Function(RBF) equalizer to reconstruct transmitted symbols. In the simulations, binary signals are generated at random with Gaussian noise. The performance of the proposed method is compared with those of a simplex genetic algorithm(GA), a hybrid genetic algorithm(GA merged with simulated annealing(SA): GASA), and a previously developed version of MFCM. It is shown that a relatively high accuracy and fast search speed has been achieved.