• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2010.04a
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• pp.5-6
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• 2010

Needs for the methodology of segmentation of linear feature according to the shape characteristics of line feature are increasing in cartographic linear generalization. In this study, the line segmentation method using expansible moving window is presented. This method analyzes the generalization effect of line simplification algorithms depend on the line characters of linear feature and extracts the sections which show exclusively low positional error due to a specific algorithm. The description measurements of these segments are calculated and the target line data are segmented based on the measurements. For segmenting the linear feature to a homogeneous section, expansible moving window is applied. This segmentation method is expected to be used in the cartographic map generalization considering the shape characteristics of linear feature.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2010.04a
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• pp.19-21
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• 2010

In this study, regarding to the generalization of the map, we analyze how the different tolerances influence on the performances of linear generalization operators. For the analysis, we apply the generalization operators, especially two simplification algorithms provided in the commercial GIS software, to 1:1000 digital topographic map for analyzing the aspect of the changes in positional error depending on the tolerances. And we evaluate the changes in positional error with the quantitative assessments. The results show that the analysis can be used as the criteria for determining proper tolerance in linear generalization.

• Journal of the Korean Geographical Society
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• v.39 no.4
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• pp.633-642
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• 2004

This study tries to generalize the stream network by constructing rule-based modelling. A study on the map generalization tends to be concentrated on development of algorithms for modification of linear features and evaluations to the limited cartographic elements. Rule-based modelling can help to improve previous algorithms by application of generalization process with the results that analyzing mapping principles and spatial distribution patterns of geographical phenomena. Rule-based modelling can be applied to generalize various cartographic elements, and make an effective on multi-scaling mapping in the digital environments. In this research, nile-based modelling for stream network is composed of generalization rule, algorithm for centerline extraction and linear features. Before generalization, drainage pattern was analyzed by the connectivity with lake to minimize logical errors. As a result, 17 streams with centerline are extracted from 108 double-lined streams. Total length of stream networks is reduced as 17% in 1:25,000 scale, and as 29% in 1:50,000. Simoo algorithm, which is developed to generalize linear features, is compared to Douglas-Peucker(D-P) algorithm. D-P made linear features rough due to the increase of data point distance and widening of external angle. But in Simoo, linear features are smoothed with the decrease of scale.

• Journal of the Korean Association of Geographic Information Studies
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• v.7 no.1
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• pp.39-51
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• 2004

This study aims to suggest new algorithm, named as Simoo, in order to improve spatial conflicts and vector displacement between linear features in generalization of the linear features. Main principles of Simoo algorithm is adoption of simplification and smoothening methods. Tolerance conditions used in Simoo are perpendicular length, external angle, and average vertex length. Main characteristics of Simoo are the application of scale, cartographic refinement, minimization of logical errors, and maintenance of geographical properties. The Simoo was applied through comparison to existing Douglas-Peucker algorithm. Resultantly, maintenance ratios of line such as coastal line and stream network were over 97% in both algorithms. The elimination ratio of vertex points may be more effective in Douglas-Peucker than in Simoo. Spatial conflicts between linear features may be more minimized in Simoo. The curvature and smoothening of lines become decreased in scale in application of Simoo. Finally, Simoo algorithm may be more effective than Douglas-Peucker for cartographic generalization.

• Journal of the Korean Geographical Society
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• v.40 no.4 s.109
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• pp.441-453
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• 2005

This study aims to generalize the stream network developing algorithm of the geographic hierarchy Stream networks with hierarchy system should be spatially hierarchized in linear features. The generalization procedure of the stream networks are composed of the hierarchy of stream, selection and elimination, and algorithm. Working of stream networks is composed by the decision of direction on stream networks, ranking of stroke segments, and ordering by the strahler method, using geographic data query for controlling selection and elimination of the linear feature by scale. Improved Simoo algorithm was effective in enhancement and decreasing curvature of linear features. Resultantly, it is expected to improve generalization of features with various spatial hierarchy.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.217-233
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• 2022

Although machine learning shows state-of-the-art performance in a variety of fields, it is short a theoretical understanding of how machine learning works. Recently, theoretical approaches are actively being studied, and there are results for one of them, margin and its distribution. In this paper, especially we focused on the role of margin in the perturbations of inputs and parameters. We show a generalization bound for two cases, a linear model for binary classification and neural networks for multi-classification, when the inputs have normal distributed random noises. The additional generalization term caused by random noises is related to margin and exponentially inversely proportional to the noise level for binary classification. And in neural networks, the additional generalization term depends on (input dimension) × (norms of input and weights). For these results, we used the PAC-Bayesian framework. This paper is considering random noises and margin together, and it will be helpful to a better understanding of model sensitivity and the construction of robust generalization.

• Journal of Intelligence and Information Systems
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• v.28 no.2
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• pp.19-31
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• 2022

In Machine learning, we usually divide the entire data into training data and test data, train the model using training data, and use test data to determine the accuracy and generalization performance of the model. In the case of models with low generalization performance, the prediction accuracy of newly data is significantly reduced, and the model is said to be overfit. This study is about a method of generating training data based on central limit theorem and combining it with existed training data to increase normality and using this data to train models and increase generalization performance. To this, data were generated using sample mean and standard deviation for each feature of the data by utilizing the characteristic of central limit theorem, and new training data was constructed by combining them with existed training data. To determine the degree of increase in normality, the Kolmogorov-Smirnov normality test was conducted, and it was confirmed that the new training data showed increased normality compared to the existed data. Generalization performance was measured through differences in prediction accuracy for training data and test data. As a result of measuring the degree of increase in generalization performance by applying this to K-Nearest Neighbors (KNN), Logistic Regression, and Linear Discriminant Analysis (LDA), it was confirmed that generalization performance was improved for KNN, a non-parametric technique, and LDA, which assumes normality between model building.

• Journal for History of Mathematics
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• v.26 no.4
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• pp.245-257
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• 2013

Hermann Grassmann classified mathematics and extended the dimension of vector spaces by using dialectics of contrasts. In this paper, we investigate his mathematical idea and its background, and the process of the classification of mathematics. He made a synthetic concept of mathematics based on his idea of 'equal' and 'inequal', 'discrete' and 'indiscrete' mathematics. Also, he showed a creation of new mathematics and a process of generalization using a dialectic of contrast of 'special' and 'general', 'real' and 'formal'. In addition, we examine his unique development in using 'real' and 'formal' in a process of generalization of basis and dimension of a vector space. This research on Grassmann will give meaningful suggestion to an effective teaching and learning of linear algebra.

• Proceedings of the KGS Conference
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• 2005.05a
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• pp.37-39
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• 2005