• Spatial Information Research
• /
• v.3 no.2
• /
• pp.191-204
• /
• 1995

The data model is a system model which abstracts the spatial and nonspatial fea¬tures of the real world. A system defines through its data model a framework for the inner rep¬resentation of and connections with the outside world. The spatial query language is one of the most efficent framework for defining connection with outside world in the GIS. Existing GIS uses a spatial data model based on relational data model. Therefore, it has some difficulties in data abstraction and representing complex objects through inheritance. In this paper, we pro-pose an object oriented data model-Topological Object Model(TOM). TOM combines object model in ODMG and the planer topological object. Based on this model, we present an object-oriented spatial query language-OQL/Geo. OQL/Geo extends OQL in ODMG and represents TOM effectively. It also provides several operators such as geometric, topological and visible ope-rators. Moreover, it represents with diverse flexivility the request for complex spatial analysis and presentation of query results.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.27 no.4
• /
• pp.324-341
• /
• 2023

Topological data analysis (TDA) is a data analysis technique, recently developed, that investigates the overall shape of a given dataset. The mapper algorithm is a TDA method that considers the connectivity of the given data and converts the data into a mapper graph. Compared to persistent homology, another popular TDA tool, that mainly focuses on the homological structure of the given data, the mapper algorithm is more of a visualization method that represents the given data as a graph in a lower dimension. As it visualizes the overall data connectivity, it could be used as a prediction method that visualizes the new input points on the mapper graph. The existing mapper packages such as Giotto-TDA, Gudhi and Kepler Mapper provide the descriptive mapper algorithm, that is, the final output of those packages is mainly the mapper graph. In this paper, we develop a simple predictive algorithm. That is, the proposed algorithm identifies the node information within the established mapper graph associated with the new emerging data point. By checking the feature of the detected nodes, such as the anomality of the identified nodes, we can determine the feature of the new input data point. As an example, we employ the fraud credit card transaction data and provide an example that shows how the developed algorithm can be used as a node prediction method.

• Korean Journal of Computational Design and Engineering
• /
• v.5 no.4
• /
• pp.293-300
• /
• 2000

The non-manifold geometric modeling technique is to improve design process and to Integrate design, analysis, and manufacturing by handling mixture of wireframe model, surface model, and solid model in a single data structure. For the non-manifold geometric modeling, Euler operators and other high level modeling methods are necessary. Boolean operation is one of the representative modeling method for the non-manifold geometric modeling. This thesis studies Boolean operations of non-manifold model with the data structure of selective storage. The data structure of selective storage is improved non-manifold data structure in that existing non-manifold data structures using ordered topological representation method always store non-manifold information even if edges and vortices are in the manifold situation. To implement Boolean operations for non-manifold model, intersection algorithm for topological cells of three different dimensions, merging and selection algorithm for three dimensional model, and Open Inventor(tm), a 3D toolkit from SGI, are used.

• Journal of Korea Spatial Information System Society
• /
• v.3 no.1 s.5
• /
• pp.49-62
• /
• 2001

Recently, component-based software has become main trends in designing and developing computer software products. This component-based software has advantage of the interoperability on distributed computing environment and the reusability of pre-developed components. Also, GIS is designed and implemented with this component-based methodology, called Open GIS Component. OGC(OpenGIS Consortium) have announced various implementation and design specification and topic in GIS. In GIS, Spatial analysis functions like network analysis, TIN analysis are very important function and basically, estimate system functionality and performance using this analysis methods. The simple feature geometry specification is announced by OGC to increase the full interoperability of various spatial data. This specification includes just geometry spatial data model. However, in GIS which manages spatial data, not only geometric data but also topological data and various analysis functions have been used. The performance of GIS depends on how this geometric and topological data is managed well and how various spatial analyses are executed efficiently. So it requires integrated spatial data model between geometry and topology and extended data model of topology for spatial analysis, in case network analysis and TIN analysis in open GIS component. In this paper, we design analysis component like network analysis component and TIN analysis component. To manage topological information for spatial analysis in open GIS component, we design extended data model of simple feature geometry for spatial analysis. In addition to, we design the overall system architecture of open GIS component contained this topology model for spatial analysis.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2022.05a
• /
• pp.482-482
• /
• 2022

하천의 합류부에서는 수질이 다른 유체가 혼합하여 합류 전과 다른 특성을 보인다. 하천의 합류부에서 수질을 효율적으로 관리하기 위해서는 수질의 공간적인 혼합 특성을 규명하는 것이 중요하다. 합류부에서 수질의 공간적인 혼합 특성을 분석하기 위해 본 연구에서는 토폴로지 데이터 분석(topological data analysis, TDA), 자기 조직화 지도(Self-Organizing Map, SOM), k-평균 알고리즘(K-means clustering algorithm) 세 가지 기법을 이용하였다. 세 가지 기법을 비교하여 어떤 알고리즘이 합류부의 수질 변화 특성을 더 뚜렷하게 나타내는지 분석하였다. 수질 변화 비교 인자들은 pH, chlorophyll, DO, Turbidity 등이 있고, 수질 인자들은 YSI를 활용해 측정하였다. 자료의 측정 지역은 낙동강과 황강이 합류하는 지역이며, 보트에 YSI 장비를 부착하고 횡단하여 측정하였다. 측정한 데이터를 R 프로그램을 통해 세 가지 기법을 적용시켜 수질 변화 비교를 분석한다. 토폴로지 데이터 분석(topological data analysis, TDA)은 거대하고 복잡한 데이터로부터 유의미한 정보를 추출하는 데 사용하고, 자기조직화지도(Self-Organizing Map, SOM) 기법은 차원 축소와 군집화를 동시에 수행한다. k-평균 알고리즘(K-means clustering algorithm) 기법은 주어진 데이터를 k개의 클러스터로 묶는 머신러닝 비지도학습에 속하는 알고리즘이다. 세 가지 방법들의 주목적은 클러스터링이다. 클러스터 분석(Cluster analysis)이란 주어진 데이터들의 특성을 고려해 동일한 성격을 가진 여러 개의 그룹으로 대상을 분류하는 데이터 마이닝의 한 방법이다. 군집화 방법들인 TDA, SOM, K-means를 이용해 합류 지역의 수질 특성들을 클러스터링하여 수질 패턴들을 분석해 하천 수질 오염을 방지할 수 있을 것이다. 본 연구에서는 토폴로지 데이터 분석(topological data analysis, TDA), 자기조직화지도(Self-Organizing Map, SOM), k-평균 알고리즘(K-means clustering algorithm) 세 가지 기법을 이용하여 합류부에서의 수질 특성을 비교하며 어떤 기법이 합류의 특성을 더욱 뚜렷하게 나타내는지 규명했다. 합류의 특성을 군집화 방법을 이용해 알게 된다면, 합류부의 수질 변화 패턴을 다른 합류 지역에서도 적용할 수 있을 것으로 기대된다.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.4
• /
• pp.296-311
• /
• 2021

Topological Data Analysis (TDA), a relatively new field of data analysis, has proved very useful in a variety of applications. The main persistence tool from TDA is persistent homology in which data structure is examined at many scales. Representations of persistent homology include persistence barcodes and persistence diagrams, both of which are not straightforward to reconcile with traditional machine learning algorithms as they are sets of intervals or multisets. The problem of faithfully representing barcodes and persistent diagrams has been pursued along two main avenues: kernel methods and vectorizations. One vectorization is the Betti sequence, or Betti curve, derived from the persistence barcode. While the Betti sequence has been used in classification problems in various applications, to our knowledge, the stability of the sequence has never before been discussed. In this paper we show that the Betti sequence is unstable under the 1-Wasserstein metric with regards to small perturbations in the barcode from which it is calculated. In addition, we propose a novel stabilized version of the Betti sequence based on the Gaussian smoothing seen in the Stable Persistence Bag of Words for persistent homology. We then introduce the normalized cumulative Betti sequence and provide numerical examples that support the main statement of the paper.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.30 no.3
• /
• pp.229-240
• /
• 2012

In Korea, u-City has been constructed as IT-based new city with introduction of the ubiquitous concept. However, most currently provided u-services are just monitoring services based on the USN(Ubiquitous Sensor Network) technology, so spatial analysis is insufficient. Especially, buildings have been rapidly constructed and expanded in multi-levels, and people spend a lot of time in indoor space, so indoor spatial analysis is necessary. Therefore, connectivity relationship in indoor space is analyzed using the topological data model. Topological relationships could be redefined due to the dynamic changes of environment in indoor space, and changes could have an effect on analysis results. In this paper, the algorithms of finding isolated zones is developed by analyzing connectivity relationship between space objects in built-environments after changes of environment in indoor space due to specific situation such as fire. And the system that visualizes isolated zones as well as three-dimensional data structure of indoor space is developed to get the analysis result by using the analysis algorithms.

• Journal of Environmental Science International
• /
• v.12 no.9
• /
• pp.949-955
• /
• 2003

The subject basin of the research was the basin of Yeongcheon Dam located in the upper reaches of the Kumho River. The parameters of the model were derived from the results of abstracting topological properties out of rainfall-runoff observation data about heavy rains and Digital Elevation Modeling(DEM) materials. This research aimed at suggesting the applicability of the CELLMOD Model, a distribution-type model, in interpreting runoff based on the topological properties of a river basin, by carrying out runoff interpretation far heavy rains using the model. To examine the applicability of the model, the calculated peaking characteristics in the hydrograph was analyzed in comparison with observed values and interpretation results by the Clark Model. According to the result of analysis using the CELLMOD Model proposed in the present research for interpreting the rainfall-runoff process, the model reduced the physical uncertainty in the rainfall-runoff process, and consequently, generated improved results in forecasting river runoff. Therefore it was concluded that the algorithm is appropriate for interpreting rainfall-runoff in river basins. However, to enhance accuracy in interpreting rainfall-runoff it is necessary to supplement heavy rain patterns in subject basins and to subdivide a basin into minor basins for analysis. In addition, it is necessary to apply the model to basins that have sufficient observation data, and to identify the correlation between model parameters and the basin characteristics(channel characteristics).

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.12 no.6
• /
• pp.241-248
• /
• 2008

The objective of sensitivity analyses is to identify critical variables of structural models and how their variability impacts mechanical response results. The sensitivity analyses have been used as significant basis data for practical applications of measuring and reinforcing fragile building structures. This study presents several sensitivity analysis methods for topological optimum designs of linear elastostatic structural systems. Numerical examples for structural analyses and topological optimum modeling demonstrate the reliability of sensitivities formulated in the present study.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.11 no.1
• /
• pp.43-54
• /
• 2001

In this paper we study the use of polyinstantiation for spatial data, for the purpose of solving cover in topology channel in multilevel secure spatial database systems. Spatial database system with topological structure has a number of spatial analysis function using spatial data and neighbored one\`s each other. But. it has problems that information flow is occurred by topological relationship in spatial database systems. Geographic Information System(CIS) must be needed mandatory access control because there ,are many information flow through positioning information And topological relationship between spatial objects. Moreover, most GIS applications also graphe user interface(GUI). In addressing these problems, we design the MLS/SRDM(Multi Level Security/Spatial Relational Data Model) and propose polyinstantiation for spatial data for solving information flow that occurred by toplogical relationship of spatial data.