• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1139-1171
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• 1996

The purpose of our research is to understand geometric and topological aspects of real projective structures on surfaces. A real projective surface is a differentiable surface with an atlas of charts to $RP^2$ such that transition functions are restrictions of projective automorphisms of $RP^2$. Since such an atlas lifts projective geometry on $RP^2$ to the surface locally and consistently, one can study the global projective geometry of surfaces.

• 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.

• Journal of Korea Multimedia Society
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• v.19 no.2
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• pp.146-154
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• 2016

This paper presents methods to analyze the topological structures of the spaces composed of patches extracted from waveform signals, which can be applied to the classification of signals. Commute time embedding is performed to transform the patch sets into the corresponding geometries, which has the properties that the embedding geometries of periodic or quasi-periodic waveforms are represented as closed curves on the low dimensional Euclidean space, while those of aperiodic signals have the shape of open curves. Persistent homology is employed to determine the topological invariants of the simplicial complexes constructed by randomly sampling the commute time embedding of the waveforms, which can be used to discriminate between the groups of waveforms topologically.

• Proceedings of the KIEE Conference
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• 2003.11c
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• pp.1010-1013
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• 2003

This paper describes an algorithm for determining robot location using appearance-based paradigm. This algorithm compress the image set using PCA(principal component analysis) to obtain a low-dimensional subspace, called the eigenspace, and it makes a manifold that represent a continuous-appearance function. To determine robot location, given an unknown input image, the recognition system first projects the image to eigenspace. Neural network use coefficients of the eigenspace to estimate the location of the mobile robot. The algorithm has been implemented and tested on a mobile robot system. In several trials it computes location accurately.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.41 no.6
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• pp.47-53
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• 2004

This paper proposes an algerian for determining robot location using appearance-based paradigm. First, this algorithm compresses the image set using Principal Component Analysis(PCA) to obtain a low-dimensional subspace, called the eigenspace, and it makes a manifold that represent a continuous-appearance function. Neural network is employed to estimate the location of the mobile robot from the coefficients of the eigenspace. Then, Kalman filtering scheme is used for the fine estimation of the robot location. The algorithm has been implemented and tested on a mobile robot system. It is shown that the robot location is estimated accurately in several trials.

• The Korean Journal of Applied Statistics
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• v.22 no.2
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• pp.415-424
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• 2009

As one of the unsupervised learning neural network methods, self-organizing maps(SOM) are applied to various fields. It reduces the dimension of multidimensional data by representing observations on the low dimensional manifold. On the other hand, the minimal spanning tree(MST) of a graph that achieves the most economic subset of edges connecting all components by a single open loop. In this study, we apply the MST technique to SOM with subnodes. We propose SOM's with embedded MST and a distance measure for optimum choice of the size and shape of the map. We demonstrate the method with Fisher's Iris data and a real gene expression data. Simulated data sets are also analyzed to check the validity of the proposed method.