• The Mathematical Education
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• v.51 no.4
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• pp.377-393
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• 2012

The understanding demands the different degree of the understanding according to student's learning situation. In this paper, we investigate what is the foundation for the complete understanding for the generalization in the generalization-process and justification of some concepts or some theories, through a case. We discovered that the completeness of the understanding in the generalization-process and justification requires 'the meaningful-mental object' which can give the meaning about the concept or theory to students. Students can do the generalization-process through the construction of 'the meaningful-mental object' and confirm the validity of generalization through 'the meaningful-mental object' which is constructed by them. And we can judge the whether students construct the completeness of the understanding or not, by 'the meaningful-mental object' of the student. Hence 'the meaningful-mental object' are vital condition for the generalization-process and justification.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.51-69
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• 2012

The cognition of an intrinsic attribute play an important role in the process of theoretical generalization. It is the aim of this paper to study how the theoretical generalization is made. First of all, we suggest the What-if-only-strategy(WIOS) which is the strategy helping the cognition of an intrinsic attribute. And we propose the process of the theoretical generalization that go on the cognitive stage, WIOS stage, conjecture stage, justification stage and insight into an intrinsic attribute in order. We propose the process of generalization adding the concrete process cognizing an intrinsic attribute to the existing process of generalization. And we applied the proposed process of generalization to two mathematical theorem which is being managed in middle school. We got a conclusion that the what-if-only strategy is an useful method of generalization for the proposition. We hope that the what-if-only strategy is helpful for both teaching and learning the mathematical generalization.

• The KIPS Transactions:PartD
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• v.9D no.4
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• pp.543-554
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• 2002

GIS (Geographic Information Systems) need faster access and better visualization. For faster access and better visualization in GIS, map generalization and levels of detail are needed. Existing spatial indexing methods do not support map generalization. Also, a few existing spatial indexing methods supporting map generalization do not support ail map generalization operations. We propose a new index structure, i.e. the LR-tree, supporting ail map generalization operations. This paper presents algorithms for the searching and updating the LR-tree and the results of performance evaluation. Our index structure works better than other spatial indexing methods for map generalization.

• 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 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 Korea Spatial Information System Society
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• v.4 no.1 s.7
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• pp.5-14
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• 2002

The generalization of geospatial data is an important way in deriving a new database from an original one. The generalization of a geospatial object changes not only its geometric and aspatial attributes but also results in propagation to other objects along their relationship. We call it generalization propagation of geospatial databases. Without proper handling of the propagation, it brings about an inconsistent database or loss of semantics. Nevertheless, previous studies in the generalization have focused on the derivation of an object by isolating it from others. And they have proposed a set of generalization operators, which were intended to change the geometric and aspatial attributes of an object. In this paper we extend the definition of generalization operators to cover the propagation from an object to others. In order to capture the propagation, we discover a set of rules or constraints that must be taken into account during generalization procedure. Each generalization operator with constraints is expressed in relational algebra and it can be converted to SQL statements with ease. A prototype system was developed to verify the correctness of extended operators.

• The KIPS Transactions:PartD
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• v.8D no.4
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• pp.367-376
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• 2001

For the electronic map service by wireless, the existing map database cannot be used directly. This is because, the data volume of a map is too big to transfer by wireless and although the map is transferred successfully, the devices to display the map usually don’t have enough resources as the ones for desktop computers. It is also not acceptable to construct map database for the exclusive use of wireless service because of the vast cost. We propose new technique to generate a map for wireless service dynamically, from the existing map database. This technique includes the generalization method to reduce the map data volume and filtering method to guarantee that the data volume don’t exceed the limit of bandwidth. The generalization is performed in 3 steps :ㅁ step of merging the layers, a step of reducing the size of spatial objects, and a step of processing user interface. The filtering is performed by 2 module, counter and selector module. The counter module checks whether the data blume of generated map by generalization, exceeds the bandwidth limit. The selector module eliminates the excess objects and selects the rest, on the basis of distance.

• School Mathematics
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• v.14 no.3
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• pp.357-375
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• 2012

This research intends to examine how 6th graders (age 12) generalize various increasing patterns. In this research, 6 problems corresponding to the ax, x+a, ax+c, ax2, and ax2+c patterns were given to 290 students. Students' generalization methods were analysed by the generalization level suggested by Radford(2006), such as arithmetic and algebraic (factual, contextual, and symbolic) generalization. As the results of the study, we identified that students revealed the most high performance in the ax pattern in the aspect of the algebraic generalization, and lower performance in the ax2, x+a, ax+c, ax2+c in order. Also we identified that students' generalization methods differed in the same increasing patterns. This imply that we need to provide students with the pattern generalization activities in various contexts.

• Journal of information and communication convergence engineering
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• v.6 no.2
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• pp.187-191
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• 2008

In the mobile environments for the vector map services, a map simplification work through the map generalization steps helps improve the readability of the map on a large scale. The generalization operations are various such as selection, aggregation, simplification, displacement, and so on, the formal operation algorithms have not been built yet. Because the algorithms require deep special knowledge and heuristic, which make it hard to automate the processes. This thesis proposes some map generalization algorithms specialized in mobile vector map services, based on previous works. This thesis will show the detail to adapt the approaches on the mobile environment, to display complex spatial objects efficiently on the mobile devices which have restriction on the resources.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2009.04a
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• pp.29-34
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• 2009

Map update is required to provide up-to-date information. In update process, the most adequate generalization is to be applied to all scales of maps simultaneously. Most of existing maps are composed of 2D data and represented in 2D space. However, maps for next generation are to be generated with 3D spatial information including ortho-images and DEMs. Therefore, 3D generalization is necessary for 3D digital map update. This paper proposes methods for 3D generalization and correction for logical errors possibly accompanied with generalization.