• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.278-281
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• 2011

The global coordinates generated from Isomap algorithm provide a simple way to analyze and manipulate high dimensional observations in terms of their intrinsic nonlinear degrees of freedom. Thus, Isomap can find globally meaningful coordinates and nonlinear structure of complex data sets, while neither principal component analysis (PCA) nor multidimensional scaling (MDS) are successful in many cases. It is demonstrated that the adapted Isomap algorithm successfully enhances the quality of pattern classification for damage identification in various numerical examples.

• Proceedings of the Korean Information Science Society Conference
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• 2005.07b
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• pp.748-750
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• 2005

Isomap [1] is a manifold learning algorithm, which extends classical multidimensional scaling (MDS) by considering approximate geodesic distance instead of Euclidean distance. The approximate geodesic distance matrix can be interpreted as a kernel matrix, which implies that Isomap can be solved by a kernel eigenvalue problem. However, the geodesic distance kernel matrix is not guaranteed to be positive semidefinite. In this paper we employ a constant-adding method, which leads to the Mercer kernel-based Isomap algorithm. Numerical experimental results with noisy 'Swiss roll' data, confirm the validity and high performance of our kernel Isomap algorithm.

• The Journal of the Korea Contents Association
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• v.7 no.3
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• pp.9-16
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• 2007

This paper describe methodology that is distributed on 2-dimensional plane to much high-dimensional facial motion datas using Isomap algorithm, and user interface techniques to control facial expressions by selecting expressions while user navigates this space in real-time. Isomap algorithm is processed of three steps as follow; first define an adjacency expression of each expression data, and second, calculate manifold distance between each expressions and composing expression spaces. These facial spaces are created by calculating of the shortest distance(manifold distance) between two random expressions. We have taken a Floyd algorithm for it. Third, materialize multi-dimensional expression spaces using Multidimensional Scaling, and project two dimensions plane. The smallest adjacency distance to define adjacency expressions uses Pearson Correlation Coefficient. Users can control facial expressions of 3-dimensional avatar by using user interface while they navigates two dimension spaces by real-time.

• Proceedings of the Korean Information Science Society Conference
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• 2010.06c
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• pp.345-348
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• 2010

본 논문에서는 Isomap을 통해 기상 정보에서 특징을 추출하여, 보다 향상된 오존 경보 예측시스템의 구현을 제안한다. 큰 흐름은 전처리 과정과 특징 추출 과정 및 후처리 과정을 통해 정제한 데이터를, 기계 학습에 널리 사용되고 있는 SVM (Support Vector Machine) 등의 분류기로 오존 경보에 대한 예측을 하여 성능을 측정한다. 또한, 압축된 데이터를 분석하여 원 데이터에서의 중요한 특징들이 무엇이었는지를 분석하였다. 분류기의 실험 결과, 기후 데이터에서의 특징 추출은 제안된 Isomap 방법이 PCA 방법에 비해 성능이 우수한 것을 알 수 있었으며, 원래 데이터를 분류한 결과에 비해서는 15~35%정도가 향상되었다. 그리고 실험에 사용된 72가지의 Feature들 중, Tb, WSa, WSp 의 정보가 오존 경보 예측에 주요한 요인 인 것으로 분석되었다.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.1251-1252
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• 2011

• Journal of the Korea Society of Computer and Information
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• v.23 no.12
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• pp.21-26
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• 2018

As the large amount of data can be efficiently stored, the methods extracting meaningful features from big data has become important. Especially, the techniques of converting high- to low-dimensional data are crucial for the 'Data visualization'. In this study, principal component analysis (PCA; linear dimensionality reduction technique) and Isomap (non-linear dimensionality reduction technique) are introduced and applied to neural big data obtained by the functional magnetic resonance imaging (fMRI). First, we investigate how much the physical properties of stimuli are maintained after the dimensionality reduction processes. We moreover compared the amount of residual variance to quantitatively compare the amount of information that was not explained. As result, the dimensionality reduction using Isomap contains more information than the principal component analysis. Our results demonstrate that it is necessary to consider not only linear but also nonlinear characteristics in the big data analysis.

• Korean Journal of Remote Sensing
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• v.29 no.5
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• pp.509-516
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• 2013

Since traditional linear feature extraction methods are unable to handle nonlinear characteristics often exhibited in hyperspectral imagery, nonlinear feature extraction, also known as manifold learning, is receiving increased attention in hyperspectral remote sensing society as well as other community. A most widely used manifold Isomap is generally promising good results in classification and spectral unmixing tasks, but significantly high computational overhead is problematic, especially for large scale remotely sensed data. A small subset of distinguishing points, referred to as landmarks, is proposed as a solution. This study proposes a new robust and controllable landmark selection method based on the maximum volume of the simplex spanned by landmarks. The experiments are conducted to compare classification accuracies with standard deviation according to sampling methods, the number of landmarks, and processing time. The proposed method could employ both classification accuracy and computational efficiency.

• The Korean Journal of Applied Statistics
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• v.36 no.2
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• pp.167-173
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• 2023

This paper investigates several methods of visualizing high-dimensional data in a low-dimensional space. At first, principal component analysis and multidimensional scaling are briefly introduced as linear approaches, and then kernel principal component analysis, self-organizing map, locally linear embedding, Isomap, Laplacian Eigenmaps, and local multidimensional scaling are introduced as nonlinear approaches. In particular, t-SNE, which is widely used but relatively unfamiliar in the field of statistics, is described in more detail. We also present a simple example for several methods, including t-SNE. Finally, we provide a review of several recent studies pointing out the limitations of t-SNE and discuss the future research problems presented.

• The Journal of the Korea Contents Association
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• v.9 no.9
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• pp.97-104
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• 2009

This paper describes comparison and analysis of methodology which enables us in order to search the projection technique of optimum for projection in the plane. For this methodology, we applies the high-dimensional facial motion capture data respectively in linear and nonlinear projection techniques. The one core element of the methodology is to applies the high-dimensional facial expression data of frame unit in PCA where is a linear projection technique and Isomap, MDS, CCA, Sammon's Mapping and LLE where are a nonlinear projection techniques. And another is to find out the methodology which distributes in this low-dimensional space, and analyze the result last. For this goal, we calculate the distance between the high-dimensional facial expression frame data of existing. And we distribute it in two-dimensional plane space to maintain the distance relationship between the high-dimensional facial expression frame data of existing like that from the condition which applies linear and nonlinear projection techniques. When comparing the facial expression data which distribute in two-dimensional space and the data of existing, we find out the projection technique to maintain the relationship of distance between the frame data like that in condition of optimum. Finally, this paper compare linear and nonlinear projection techniques to projection high-dimensional facial expression data in low-dimensional space and analyze it. And we find out the projection technique of optimum from it.

• Korean Journal of Ecology and Environment
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• v.41 no.spc
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• pp.1-10
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• 2008

We patterned water quality of agricultural reservoirs according to the differences of six physico-chemical environmental factors (TN, TP, DO, BOD, COD, and SS) using four different ordination methods: Principal Components Analysis (PCA), Detrended Correspondence Analysis (DCA), Nonmetric Multidimensional Scaling (NMS), and Isometric Feature Mapping (Isomap). The data set was obtained from the water quality monitoring networks operated by the Ministry of Agriculture and Forestry and the Ministry of Environments. Chlorophyll-${\alpha}$ displayed the highest correlation with COD, followed by TP, BOD, SS, and TN (p<0.01), while negatively correlated with altitude and bank height of the reservoirs (p<0.01). Although four different ordination methods similarly patterned the reservoirs according to the gradient of nutrient concentration, PCA and NMS appeared to be the most efficient methods to pattern water quality of reservoirs based on the explanation power. Considering variable scores in the ordination map, the concentration of nutrients was positively correlated with Chl-${\alpha}$, while negatively correlated with altitude and bank height. These ordination methods may help to pattern agricultural reservoirs according to their water quality characteristics.