• The Journal of Korea Robotics Society
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• v.3 no.2
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• pp.117-122
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• 2008

This paper presents a multi-robot localization based on multidimensional scaling (MDS) in spite of the existence of incomplete and noisy data. While the traditional algorithms for MDS work on the full-rank distance matrix, there might be many missing data in the real world due to occlusions. Moreover, it has no considerations to dealing with the uncertainty due to noisy observations. We propose a robust MDS to handle both the incomplete and noisy data, which is applied to solve the multi-robot localization problem. To deal with the incomplete data, we use the Nystr$\ddot{o}$m approximation which approximates the full distance matrix. To deal with the uncertainty, we formulate a Bayesian framework for MDS which finds the posterior of coordinates of objects by means of statistical inference. We not only verify the performance of MDS-based multi-robot localization by computer simulations, but also implement a real world localization of multi-robot team. Using extensive empirical results, we show that the accuracy of the proposed method is almost similar to that of Monte Carlo Localization(MCL).

• Journal of KIISE:Computing Practices and Letters
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• v.16 no.4
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• pp.427-431
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• 2010

Multidimensional scaling (MDS) is a widely used method for dimensionality reduction, of which purpose is to represent high-dimensional data in a low-dimensional space while preserving distances among objects as much as possible. MDS has mainly been applied to data visualization and feature selection. Among various MDS methods, the classical MDS is not readily applicable to data which has large numbers of objects, on normal desktop computers due to its computational complexity. More precisely, it needs to solve eigenpair problems on dissimilarity matrices based on Euclidean distance. Thus, running time and required memory of the classical MDS highly increase as n (the number of objects) grows up, restricting its use in large-scale domains. In this paper, we propose an efficient approximation algorithm for the classical MDS based on divide-and-conquer and CUDA. Through a set of experiments, we show that our approach is highly efficient and effective for analysis and visualization of data consisting of several thousands of objects.

• The Korean Journal of Applied Statistics
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• v.27 no.4
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• pp.619-627
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• 2014

Distances or dissimilarities among units are assumed to be symmetric in most cases of multidimensional scaling(MDS); consequently, it is not an easy task to deal with asymmetric distances. Current asymmetric MDS still face difficulties in the interpretation of results. This study proposes a simpler asymmetric MDS that utilizes the order statistic of an asymmetric matrix. The proposed Web method demonstrates that some influences among objects are visualized by direction, size and shape of arrow to ease the interpretability of users.

• The Korean Journal of Applied Statistics
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• v.25 no.4
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• pp.613-620
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• 2012

In most cases of multidimensional scaling(MDS), the distances or dissimilarities among units are assumed to be symmetric. Thus, it is not an easy task to deal with asymmetric distances. Asymmetric MDS developed so far face difficulties in the interpretation of results. This study proposes a much simpler asymmetric MDS, that utilizes the notion of "altitude". The analogy arises in mountaineering: It is easier (more difficult) to move from the higher (lower) point to the lower (higher). The idea is formulated as a quantification problem, in which the disparity of distances is maximally related to the altitude difference. The proposed method is demonstrated in three examples, in which the altitudes are visualized by rainbow colors to ease the interpretability of users.

• Journal of the Korean Society for Library and Information Science
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• v.41 no.2
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• pp.335-357
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• 2007

There has been many studies representing intellectual structures with multidimensional scaling(MDS) However MDS configuration is limited in representing local details and explicit structures. In this paper, we identified two components of MDS mapping approach; one is MDS algorithm and the other is preparation of data matrix. Various combinations of the two components of MDS mapping are compared through some measures of fit. It is revealed that the conventional approach composed of ALSCAL algorithm and Euclidean distance matrix calculated from Pearson's correlation matrix is the worst of the compared MDS mapping approaches. Otherwise the best approach to make MDS map is composed of PROXSCAL algorithm and z-scored Euclidean distance matrix calculated from Pearson's correlation matrix. These results suggest that we could obtain more detailed and explicit map of a knowledge domain through careful considerations on the process of MDS mapping.

• Journal of the Korean Society for information Management
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• v.29 no.2
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• pp.45-70
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• 2012

There have been many methods and algorithms proposed for multidimensional scaling to mapping the relationships between data objects into low dimensional space. But traditional techniques, such as PROXSCAL or ALSCAL, were found not effective for visualizing the proximities between objects and the structure of clusters of large data sets have more than 50 objects. The CLUSCAL(CLUster-oriented SCALing) technique introduced in this paper differs from them especially in that it uses cluster structure of input data set. The CLUSCAL procedure was tested and evaluated on two data sets, one is 50 authors co-citation data and the other is 85 words co-occurrence data. The results can be regarded as promising the usefulness of CLUSCAL method especially in identifying clusters on MDS maps.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.93-97
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• 2002

In this paper, we propose personalized recommendation techniques based on multidimensional scaling (MDS) method for Business to Consumer Electronic Commerce. The multidimensional scaling method is traditionally used in marketing domain for analyzing customers' perceptional differences about brands and products. In this study, using purchase history data, customers in learning dataset are assigned to specific product categories, and after then using MDS a positioning map is generated to map product categories and alternative advertisements. The positioning map will be used to select personalized advertisement in real time situation. In this paper, we suggest the detail design of personalized recommendation method using MDS and compare with other approaches (random approach, collaborative filtering, and TOP3 approach)

• Journal of Biomedical Engineering Research
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• v.31 no.2
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• pp.134-140
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• 2010

Readily available high resolution brain MRI scans allow detailed visualization of the brain structures. Researchers have focused on developing methods to quantify shape differences specific to diseased scans. We have developed a novel method to quantify shape information for a specific population based on Multidimensional scaling(MDS). MDS is a well known tool in statistics and here we apply this classical tool to quantify shape change. Distance measures are required in MDS which are computed from pair-wise image registrations of the training set. Registration step establishes spatial correspondence among scans so that they can be compared in the same spatial framework. One benefit of our method is that it is quite robust to errors in registrations. Applying our method to 13 brain MRI showed clear separation between normal and diseased (Cushing's syndrome). Intentionally perturbing the image registration results did not significantly affect the separability of two clusters. We have developed a novel method to quantify shape based on MDS, which is robust to image mis-registration.

• Journal of the Korean housing association
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• v.1 no.2
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• pp.1-11
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• 1990

A study of domestic furniture arrangements may reveal the living style relevant to the room as conceived and coded by occupants and the effects of the physical environment on the structure of behavior settings. The purpose of this study was to investigate, through analizing the furniture usage and behavior as a non-reactive and activity oriented behavioral measures, the occupants` domestic habits as a living style using MDS. MDS(multidimensional scaling technique) is a statistical technique for creating a spatial representation of data. It Is a particularly appropriate technique for analizing qualitative data such as the furniture usage and behavior because it takes into account all of the relationships between items. For the MDS analysis, the furniture usage and behavior examined by housing types based on 114 households in Seoul. The result of spatial configuration by MDS has three dimensions : recogn;lion of room function, pattern of room organization, understanding of room meaning. The effect of housing types for dimensions is identical but configuration of furniture items is different.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.34 no.2
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• pp.60-67
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• 2011

Since the non-metric Multidimensional scaling (nMDS), a data visualization technique, provides with insights about engineering, economic, and scientific applications, it is widely used for analyzing large non-metric multidimensional data sets. The nMDS requires a fitness function to measure fit of the proximity data by the distances among n objects. Most commonly used fitness functions are nonlinear and have a difficulty to find a good configuration. In this paper, we propose a new fitness function, an absolute value type, and show its advantages.