• Communications for Statistical Applications and Methods
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• v.22 no.4
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• pp.321-331
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• 2015

The K-means clustering algorithm is a popular and widely used method for clustering. For covariance matrices, we consider a geodesic clustering algorithm based on the K-means clustering framework in consideration of symmetric positive definite matrices as a Riemannian (non-Euclidean) manifold. This paper considers a geodesic clustering algorithm for data consisting of symmetric positive definite (SPD) matrices, utilizing the Riemannian geometric structure for SPD matrices and the idea of a K-means clustering algorithm. A K-means clustering algorithm is divided into two main steps for which we need a dissimilarity measure between two matrix data points and a way of computing centroids for observations in clusters. In order to use the Riemannian structure, we adopt the geodesic distance and the intrinsic mean for symmetric positive definite matrices. We demonstrate our proposed method through simulations as well as application to real financial data.

• Journal of KIISE:Software and Applications
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• v.36 no.6
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• pp.479-490
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• 2009

A number of temporal abstraction approaches have been suggested so far to handle the high computational complexity of Markov decision problems (MDPs). Although the structure of temporal abstraction can significantly affect the efficiency of solving the MDP, to our knowledge none of current temporal abstraction approaches explicitly consider the relationship between topology and efficiency. In this paper, we first show that a topological measurement from complex network literature, mean geodesic distance, can reflect the efficiency of solving MDP. Based on this, we build an incremental method to systematically build temporal abstractions using a network model that guarantees a small mean geodesic distance. We test our algorithm on a realistic 3D game environment, and experimental results show that our model has subpolynomial growth of mean geodesic distance according to problem size, which enables efficient solving of resulting MDP.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.17 no.2
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• pp.137-143
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• 1999

The straight spatial distance or geodesic distance on WGS84 ellipsoid measured by GPS should be reduced on geoid to be used in Korean Geodetic System. The factors for this reduction are geoidal height and mean radius of the earth. On this study the effects of these factors on reducing distance were analyzed and the result showed that mean geoidal height should be multiplied by $1.6\times{10}^{-7}$ per unit distance for reducing geodesic distance on reference ellipsoid to that on geoid. Condsidering that the geoidal height on Bessel ellipsoid in Korea is -45 m in northeast and -75 m in middle west. It also showed that the difference of geodesic distance between on reference ellipsoid and on geoid is about 7-12 mm per km.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.45-48
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• 2002

Consider the mean distance of Brownian motion on Riemannian manifolds. We obtain the first three terms of the asymptotic expansion of the mean distance by means of Stochastic Differential Equation(SDE) for Brownian motion on Riemannian manifold. This method proves to be much simpler for further expansion than the methods developed by Liao and Zheng(1995). Our expansion gives the same characterizations as the mean exit time from a small geodesic ball with regard to Euclidean space and the rank 1 symmetric spaces.

• Journal of Korea Society of Industrial Information Systems
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• v.12 no.5
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• pp.39-46
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• 2007

Research on human identification in ubiquitous environment has recently attracted a lot of attention. As one of those research, gait recognition is an efficient method of human identification using physical features of a walking person at a distance. In this paper, we present a human shape extraction and tracking for gait recognition using geodesic active contour models(GACMs) combined with mean shift algorithm The active contour models (ACMs) are very effective to deal with the non-rigid object because of its elastic property. However, they have the limitation that their performance is mainly dependent on the initial curve. To overcome this problem, we combine the mean shift algorithm with the traditional GACMs. The main idea is very simple. Before evolving using level set method, the initial curve in each frame is re-localized near the human region and is resized enough to include the targe region. This mechanism allows for reducing the number of iterations and for handling the large object motion. The proposed system is composed of human region detection and human shape tracking modules. In the human region detection module, the silhouette of a walking person is extracted by background subtraction and morphologic operation. Then human shape are correctly obtained by the GACMs with mean shift algorithm. In experimental results, the proposed method show that it is extracted and tracked efficiently accurate shape for gait recognition.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.9 no.2
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• pp.196-204
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• 2016

World Health Organization reported that heart-related diseases such as coronary artery stenoses show the highest occurrence rate which may cause heart attack. Using Computed Tomography angiography images will allow radiologists to detect and have intervention by creating 3D roadmapping of the vessels. However, it is often complex and difficult do reconstruct 3D vessel which causes very large amount of time and previous researches were studied to segment vessels more accurate automatically. Therefore, in this paper, Region Competition, Geodesic Active Contour (GAC), Multi-atlas based segmentation and Active Shape Model algorithms were applied to segment aortic root from CTA images and the results were analyzed by using mean Hausdorff distance, volume to volume measure, computational time, user-interaction and coronary ostium detection rate. As a result, Extracted 3D aortic model using GAC showed the highest accuracy but also showed highest user-interaction results. Therefore, it is important to improve automatic segmentation algorithm in future

• Proceedings of the Korean Information Science Society Conference
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• 2006.06b
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• pp.232-234
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• 2006

본 논문에서는 마르코프 결정 문제 (Markov decision problem)의 풀이 효율을 잴 수 있는 척도를 알아보기 위해 복잡계 네트워크 (complex network) 의 관점에서 MDP를 하나의 그래프로 나타내고, 그 그래프의 위상학적 성질들을 여러 네트워크 척도 (network measurements)들을 이용하여 측정하고 그 MDP의 풀이 효율과의 관계를 분석하였다. 실세계의 여러 문제들이 MDP로 표현될 수 있고, 모델이 알려진 경우에는 평가치 반복(value iteration)이나 모델이 알려지지 않은 경우에도 강화 학습(reinforcement learning) 알고리즘등을 사용하여 풀 수 있으나, 이들 알고리즘들은 시간 복잡도가 높아 크기가 큰 실세계 문제에 적용하기 쉽지 않다. 이 문제를 해결하기 위해 제안된 것이 MDP를 계층적으로 분할하거나, 여러 단계를 묶어서 수행하는 등의 시간적 추상화(temporal abstraction) 방법들이다. 시간적 추상화를 도입할 경우 MDP가 보다 효율적으로 풀리는 꼴로 바뀐다는 사실에 착안하여, MDP의 풀이 효율을 네트워크 척도를 이용하여 측정할 수 있는 여러 위상학적 성질들을 기반으로 분석하였다. 다양한 구조와 파라미터를 가진 MDP들을 사용해 네트워크 척도들과 MDP의 풀이 효율간의 관계를 분석해 본 결과, 네트워크 척도들 중 평균 측지 거리 (mean geodesic distance) 가 그 MDP의 풀이 효율을 결정하는 가장 중요한 기준이라는 사실을 알 수 있었다.

• Journal of Intelligence and Information Systems
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• v.22 no.2
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• pp.57-79
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• 2016

It is a rising trend that the number of users using one of the social media channels, the Social Network Service, so called the SNS, is getting increased. As per to this social trend, more companies have interest in this networking platform and start to invest their funds in it. It has received much attention as a tool spreading and expanding the message that a company wants to deliver to its customers and has been recognized as an important channel in terms of the relationship marketing with them. The environment of media that is radically changing these days makes possible for companies to approach their customers in various ways. Particularly, the social network service, which has been developed rapidly, provides the environment that customers can freely talk about products. For companies, it also works as a channel that gives customized information to customers. To succeed in the online environment, companies need to not only build the relationship between companies and customers but focus on the relationship between customers as well. In response to the online environment with the continuous development of technology, companies have tirelessly made the novel marketing strategy. Especially, as the one-to-one marketing to customers become available, it is more important for companies to maintain the relationship marketing with their customers. Among many SNS, Facebook, which many companies use as a communication channel, provides a fan page service for each company that supports its business. Facebook fan page is the platform that the event, information and announcement can be shared with customers using texts, videos, and pictures. Companies open their own fan pages in order to inform their companies and businesses. Such page functions as the websites of companies and has a characteristic of their brand communities such as blogs as well. As Facebook has become the major communication medium with customers, companies recognize its importance as the effective marketing channel, but they still need to investigate their business performances by using Facebook. Although there are infinite potentials in Facebook fan page that even has a function as a community between users, which other platforms do not, it is incomplete to regard companies' Facebook fan pages as communities and analyze them. In this study, it explores the relationship among customers through the network of the Facebook fan page users. The previous studies on a company's Facebook fan page were focused on finding out the effective operational direction by analyzing the use state of the company. However, in this study, it draws out the structural variable of the network, which customer committment can be measured by applying the social network analysis methodology and investigates the influence of the structural characteristics of network on the business performance of companies in an empirical way. Through each company's Facebook fan page, the network of users who engaged in the communication with each company is exploited and it is the one-mode undirected binary network that respectively regards users and the relationship of them in terms of their marketing activities as the node and link. In this network, it draws out the structural variable of network that can explain the customer commitment, who pressed "like," made comments and shared the Facebook marketing message, of each company by calculating density, global clustering coefficient, mean geodesic distance, diameter. By exploiting companies' historical performance such as net income and Tobin's Q indicator as the result variables, this study investigates influence on companies' business performances. For this purpose, it collects the network data on the subjects of 54 companies among KOSPI-listed companies, which have posted more than 100 articles on their Facebook fan pages during the data collection period. Then it draws out the network indicator of each company. The indicator related to companies' performances is calculated, based on the posted value on DART website of the Financial Supervisory Service. From the academic perspective, this study suggests a new approach through the social network analysis methodology to researchers who attempt to study the business-purpose utilization of the social media channel. From the practical perspective, this study proposes the more substantive marketing performance measurements to companies performing marketing activities through the social media and it is expected that it will bring a foundation of establishing smart business strategies by using the network indicators.