• Korean Journal of Mathematics
• /
• v.14 no.1
• /
• pp.65-70
• /
• 2006

In this article, we mention some subsequent developments of the theory of cluster sets, and present a new boundary cluster set for a simply connected domain in the complex plane and its applications.

• Communications of the Korean Mathematical Society
• /
• v.26 no.1
• /
• pp.135-149
• /
• 2011

Using (r, s)-preopen sets [14] and pre-${\omega}_t$-closures [6], a new kind of covering property $P^t_{({\omega}_r,s)}$-closedness is introduced in a bitopological space and several characterizations via filter bases, nets and grills [30] along with various properties of such concept are investigated. Two new types of cluster sets, namely pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets and (r, s)t-${\theta}_f$-precluster sets of functions and multifunctions between two bitopological spaces are introduced. Several properties of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets are investigated and using the degeneracy of such cluster sets, some new characterizations of some separation axioms in topological spaces or in bitopological spaces are obtained. A sufficient condition for $P^t_{({\omega}_r,s)}$-closedness has also been established in terms of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets.

• The Journal of Information Technology and Database
• /
• v.8 no.2
• /
• pp.91-101
• /
• 2001

Previous research efforts on performance evaluation of multidimensional indexes typically have used synthetic data sets distributed uniformly or normally over multidimensional space. However, recent research research result has shown that these hinds of data sets hardly reflect the characteristics of multimedia database applications. In this paper, we discuss issues on generating high dimensional data and query sets for resolving the problem. We first identify the features of the data and query sets that are appropriate for fairly evaluating performances of multidimensional indexes, and then propose HDDQ_Gen(High-Dimensional Data and Query Generator) that satisfies such features. HDDQ_Gen supports the following features : (1) clustered distributions, (2) various object distributions in each cluster, (3) various cluster distributions, (4) various correlations among different dimensions, (5) query distributions depending on data distributions. Using these features, users are able to control tile distribution characteristics of data and query sets. Our contribution is fairly important in that HDDQ_Gen provides the benchmark environment evaluating multidimensional indexes correctly.

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

• Journal of the Korean Institute of Intelligent Systems
• /
• v.10 no.6
• /
• pp.557-563
• /
• 2000

We introduce r-fuzzy $\delta$-cluster ($\theta$-cluster) points and r-fuzzy $\delta$-closure ($\theta$-closure) sets in smooth fuzzy topological spaces in a view of the definition of A.P. Sostak [13]. We study some properties of them.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.3
• /
• pp.363-379
• /
• 2014

In this paper, introducing various separation axioms on a bi-GTS, it has been observed that such separation axioms actually unify the well-known separation axioms on topological spaces. Several characterizations of such separation properties of a bi-GTS are established in terms of ${\gamma}_{{\mu}_i,{\mu}_j}$-closure operator, generalized cluster sets of functions and graph of functions.

• Kyungpook Mathematical Journal
• /
• v.17 no.1
• /
• pp.85-89
• /
• 1977

• Journal of the Korean Statistical Society
• /
• v.15 no.1
• /
• pp.1-8
• /
• 1986

The k-medians clustering method is considered to partition observations into k clusters. Consistency and advantage of bootstrap confidence sets of k optimal cluster centers are discussed. The k-medians and k-means clustering methods are compared by using actual data sets.

• Journal of Integrative Natural Science
• /
• v.7 no.1
• /
• pp.57-61
• /
• 2014

This study measured the stream data from the several sensors, and stores the database in MapReduce framework environment, and it aims to design system with the small performance and cluster analysis error rate through the KMSVM algorithm. Through the KM-SVM algorithm, the cluster analysis effective data was used for U-health system. In the results of experiment by using 2003 data sets obtained from 52 test subjects, the k-NN algorithm showed 79.29% cluster analysis accuracy, K-means algorithm showed 87.15 cluster analysis accuracy, and SVM algorithm showed 83.72%, KM-SVM showed 90.72%. As a result, the process speed and cluster analysis effective ratio of KM-SVM algorithm was better.

• Kyungpook Mathematical Journal
• /
• v.34 no.1
• /
• pp.117-126
• /
• 1994