• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.7 no.1
• /
• pp.63-77
• /
• 2003

Some inequalities for the $Csisz{\acute{a}}r\;{\Phi}-divergence$ and applications for the Kullback-Leibler, $R{\acute{e}}nyi$, Hellinger and Bhattacharyya distances in Information Theory are given.

• Journal of the Korean Data and Information Science Society
• /
• v.16 no.4
• /
• pp.1159-1165
• /
• 2005

Basu et al. (1998) proposed a new density-based estimator, called the minimum density power divergence estimator (MDPDE), which avoid the use of nonparametric density estimation and associated complication such as bandwidth selection. Woodward et al. (1995) examined the minimum Hellinger distance estimator (MHDE), proposed by Beran (1977), in the case of estimation of the mixture proportion in the mixture of two normals. In this article, we introduce the MDPDE for a mixture proportion, and show that both the MDPDE and the MHDE have the same asymptotic distribution at a model. Simulation study identifies some cases where the MHDE is consistently better than the MDPDE in terms of bias.

• Communications for Statistical Applications and Methods
• /
• v.10 no.1
• /
• pp.135-144
• /
• 2003

This work is concerned with comparison of the recently developed disparity measures for the partial association model in three dimensional categorical data. Data are generated by using simulation on each term in the log-linear model equation based on the partial association model, which is a proposed method in this paper. This alternative Monte Carlo methods are explored to study the behavior of disparity measures such as the power divergence statistic I(λ), the Pearson chi-square statistic X$^2$, the likelihood ratio statistic G$^2$, the blended weight chi-square statistic BWCS(λ), the blended weight Hellinger distance statistic BWHD(λ), and the negative exponential disparity statistic NED(λ) for moderate sample sizes. We find that the power divergence statistic I(2/3) and the blended weight Hellinger distance family BWHD(1/9) are the best tests with respect to size and power.

• Communications for Statistical Applications and Methods
• /
• v.16 no.6
• /
• pp.989-995
• /
• 2009

Basu et al. (1998) proposed the minimum divergence estimating method which is free from using the painful kernel density estimator. Their proposed class of density power divergences is indexed by a single parameter $\alpha$ which controls the trade-off between robustness and efficiency. In this article, (1) we introduce a new large class the minimum squared distance which includes from the minimum Hellinger distance to the minimum $L_2$ distance. We also show that under certain conditions both the minimum density power divergence estimator(MDPDE) and the minimum squared distance estimator(MSDE) are asymptotically equivalent and (2) in finite samples the MDPDE performs better than the MSDE in general but there are some cases where the MSDE performs better than the MDPDE when estimating a location parameter or a proportion of mixed distributions.

• The Transactions of the Korea Information Processing Society
• /
• v.4 no.9
• /
• pp.2299-2308
• /
• 1997

While most machine learning research has been primarily concerned with the development of systems that implement one type of learning strategy, we use a multistrategy approach which integrates rule induction learning and instance-based learning, and show how this marriage allows for overall better performance. In the rule induction learning phase, we derive an entropy function, based on Hellinger divergence, which can measure the amount of information each inductive rule contains, and show how well the Hellinger divergence measures the importance of each rule. We also propose some heuristics to reduce the computational complexity by analyzing the characteristics of the Hellinger measure. In the instance-based learning phase, we improve the current instance-based learning method in a number of ways. The system has been implemented and tested on a number of well-known machine learning data sets. The performance of the system has been compared with that of other classification learning technique.

• Journal of the Korean Data and Information Science Society
• /
• v.15 no.4
• /
• pp.743-752
• /
• 2004

In this paper, we develop the Bayesian model selection procedure using the reference prior for comparing two nested model such as the independent and intraclass models using the distance or divergence between the two as the basis of comparison. A suitable criterion for this is the power divergence measure as introduced by Cressie and Read(1984). Such a measure includes the Kullback -Liebler divergence measures and the Hellinger divergence measure as special cases. For this problem, the power divergence measure turns out to be a function solely of $\rho$, the intraclass correlation coefficient. Also, this function is convex, and the minimum is attained at $\rho=0$. We use reference prior for $\rho$. Due to the duality between hypothesis tests and set estimation, the hypothesis testing problem can also be solved by solving a corresponding set estimation problem. The present paper develops Bayesian method based on the Kullback-Liebler and Hellinger divergence measures, rejecting $H_0:\rho=0$ when the specified divergence measure exceeds some number d. This number d is so chosen that the resulting credible interval for the divergence measure has specified coverage probability $1-{\alpha}$. The length of such an interval is compared with the equal two-tailed credible interval and the HPD credible interval for $\rho$ with the same coverage probability which can also be inverted into acceptance regions of $H_0:\rho=0$. Example is considered where the HPD interval based on the one-at- a-time reference prior turns out to be the shortest credible interval having the same coverage probability.

• Journal of the Korean Data and Information Science Society
• /
• v.17 no.2
• /
• pp.543-557
• /
• 2006

This paper is concerned with the applicability of the chi-square approximation to the six disparity statistics: the Pearson chi-square, the generalized likelihood ratio, the power divergence, the blended weight chi-square, the blended weight Hellinger distance, and the negative exponential disparity statistic. Three dimensional contingency tables of small and moderate sample sizes are generated to be fitted to all possible hierarchical log-linear models: the completely independent model, the conditionally independent model, the partial association models, and the model with one variable independent of the other two. For models with direct solutions of expected cell counts, point estimates and confidence intervals of the 90 and 95 percentage points of six statistics are explored. For model without direct solutions, the empirical significant levels and the empirical powers of six statistics to test the significance of the three factor interaction are computed and compared.

• Journal of the Korean Data and Information Science Society
• /
• v.14 no.3
• /
• pp.687-696
• /
• 2003

This article presents a new family of the estimating functions related with minimum distance estimations, and discusses its relationship to the family of the minimum density power divergence estimating equations. Two representative minimum distance estimations; the minimum $L_2$ distance estimation and the minimum Hellinger distance estimation are studied in the light of the theory of estimating equations. Despite of the desirable properties of minimum distance estimations, they are not widely used by general researchers, because theories related with them are complex and are hard to be computationally implemented in real problems. Hopefully, this article would be a help for understanding the minimum distance estimations better.

• Journal of the Korean Data and Information Science Society
• /
• v.27 no.2
• /
• pp.353-362
• /
• 2016

By Wikipedia, data mining is the process of discovering patterns in a big data set involving methods at the intersection of association rule, decision tree, clustering, artificial intelligence, machine learning. and database systems. Association rule is a method for discovering interesting relations between items in large transactions by interestingness measures. Association rule interestingness measures play a major role within a knowledge discovery process in databases, and have been developed by many researchers. Among them, the Hellinger measure is a good association threshold considering the information content and the generality of a rule. But it has the drawback that it can not determine the direction of the association. In this paper we proposed a signed Hellinger measure to be able to interpret operationally, and we checked three conditions of association threshold. Furthermore, we investigated some aspects through a few examples. The results showed that the signed Hellinger measure was better than the Hellinger measure because the signed one was able to estimate the right direction of association.

• KIPS Transactions on Software and Data Engineering
• /
• v.3 no.1
• /
• pp.37-42
• /
• 2014

The abstract should concisely state what was done, how it was done, principal results, and their significance. It should be less than 300 words for all forms of publication. The abstract should be written as one paragraph and should not contain tabular material or numbered references. At the end of abstract, keywords should be given in 3 to 5 words or phrases.