• Communications for Statistical Applications and Methods
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• v.31 no.3
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• pp.349-363
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• 2024

Compositional data refers to data where the sum of the values of the components is a constant, hence the sample space is defined as a simplex making it impossible to apply statistical methods developed in the usual Euclidean vector space. A natural approach to overcome this restriction is to consider an appropriate transformation which moves the sample space onto the Euclidean space, and log-ratio typed transformations, such as the additive log-ratio (ALR), the centered log-ratio (CLR) and the isometric log-ratio (ILR) transformations, have been mostly conducted. However, in scenarios with sparsity, where certain components take on exact zero values, these log-ratio type transformations may not be effective. In this work, we mainly suggest an alternative transformation, that is the square-root transformation which moves the original sample space onto the directional space. We compare the square-root transformation with the log-ratio typed transformation by the simulation study and the real data example. In the real data example, we applied both types of transformations to the USG% data obtained from NBA, and used a density based clustering method, DBSCAN (density-based spatial clustering of applications with noise), to show the result.

• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.511-527
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• 2015

For time series analysis, power transformation (especially log-transformation) is widely used for variance stabilization or normalization for stationary ARMA(p, q) model. A simple and naive back transformed forecast is obtained by taking the inverse function of expectation. However, this back transformed forecast has a bias. Under the assumption that the log-transformed data is normally distributed. The unbiased back transformed forecast can be obtained by the expectation of log-normal distribution; consequently, the property of this back transformation was studied by Granger and Newbold (1976). We investigate the sensitivity of back transformed forecasts under several different underlying distributions using simulation studies.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.2
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• pp.1-10
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• 2002

This paper presents the new template based human face recognition methods to improve the recognition performance against scale and in-plane rotation variations of face images. To enhance the recognition performance, the templates are generated by linear or nonlinear operation on multiple images including different scales and rotations of faces. As the invariant features to allow for scale and rotation variations of face images, we adopt the affine transformation, the log-polar mapping, and the log-polar image based FFT. The proposed recognition methods are evaluated in terms of the recognition rate and the processing time. Experimental results show that the proposed template based methods lead to higher recognition rate than the single image based one. The affine transformation based face recognition method shows marginally higher recognition rate than those of the log-polar mapping based method and the log-polar image based FFT, while, in the aspect of processing time, the log-polar mapping based method is the fastest one.

• YAKHAK HOEJI
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• v.44 no.4
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• pp.308-314
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• 2000

Logarithmic transformation of pharmacokinetic parameters is routinely used in bioequivalence studies based on pharmacokinetic and statistical grounds by the United States Food and Drug Administration (FDA), European Committee for Proprietary Medicinal Products (CPMP), and Japanese National Institute of Health and Science (NIHS). Although it has not yet been recommended by the Korea Food and Drug Administration (KFDA), its use is becoming increasingly necessary in order to harmonize with international standards. In the present study, statistical procedures for the analysis of a bioequivalence based on the log transformation and a related SAS procedure were demonstrated in order to aid the understanding and application. The AUC parameters used in this demonstration were taken from the previous bioequivalence study for two aceclofenac tablets, which were performed in a single-dose crossover design. Analysis of variance (ANOVA), statistical power to detect 20% difference between the tablets, minimum detectable difference and confidence intervals were all assessed following log-transformation of the data. Bioequivalence of two aceclofenac tablets was then estimated based on the guideline of FDA. Considering the international effort for harmaonization of guidelines for bioequivalence tests, this approach may require a further evaluation for a future adaptation in the Korea Guidelines of Bioequivalence Tests (KGBT).

• Journal of Korean Society for Atmospheric Environment
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• v.22 no.5
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• pp.614-626
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• 2006

Using the data of three environmental monitoring sites in Pohang area(KME112, KME113, and KME114), statistical forecasting models of the daily maximum and mean values of PM10 have been developed. Since the distributions of the daily maximum and mean PM10 values are skewed, which are similar to the Weibull distribution, these values were log-transformed to increase prediction accuracy by approximating the normal distribution. Three statistical forecasting models, which are regression, neural networks(NN) and support vector regression(SVR), were built using the log-transformed response variables, i.e., log(max(PM10)) or log(mean (PM10)). Also, the forecasting models were validated by the measure of RMSE, CORR, and IOA for the model comparison and accuracy. The improvement rate of IOA before and after the log-transformation in the daily maximum PM10 prediction was 12.7% for the regression and 22.5% for NN. In particular, 42.7% was improved for SVR method. In the case of the daily mean PM10 prediction, IOA value was improved by 5.1% for regression, 6.5% for NN, and 6.3% for SVR method. As a conclusion, SVR method was found to be performed better than the other methods in the point of the model accuracy and fitness views.

• KCID journal
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• v.5 no.1
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• pp.20-31
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• 1998

The Power transformation, the modified Power transformation, the logarithmic transformation, the square-root logarithmic transformation, the SMEMAX transformation, the Extreme value type III, the Weibull, the log Pearson type III, the lognormal distributi

• Journal of Environmental Health Sciences
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• v.45 no.2
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• pp.192-202
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• 2019

Objectives: According to the central limit theorem, the samples in population might be considered to follow normal distribution if a large number of samples are available. Once we assume that toxicity dataset follow normal distribution, we can treat and process data statistically to calculate genus or species mean value with standard deviation. However, little is known and only limited studies are conducted to investigate whether toxicity dataset follows normal distribution or not. Therefore, the purpose of study is to evaluate the generally accepted normality hypothesis of aquatic toxicity dataset Methods: We selected the 8 chemicals, which consist of 4 organic and 4 inorganic chemical compounds considering data availability for the development of species sensitivity distribution. Toxicity data were collected at the US EPA ECOTOX Knowledgebase by simple search with target chemicals. Toxicity data were re-arranged to a proper format based on the endpoint and test duration, where we conducted normality test according to the Shapiro-Wilk test. Also we investigated the degree of normality by simple log transformation of toxicity data Results: Despite of the central limit theorem, only one large dataset (n>25) follow normal distribution out of 25 large dataset. By log transforming, more 7 large dataset show normality. As a result of normality test on small dataset (n<25), log transformation of toxicity value generally increases normality. Both organic and inorganic chemicals show normality growth for 26 species and 30 species, respectively. Those 56 species shows normality growth by log transformation in the taxonomic groups such as amphibian (1), crustacean (21), fish (22), insect (5), rotifer (2), and worm (5). In contrast, mollusca shows normality decrease at 1 species out of 23 that originally show normality. Conclusions: The normality of large toxicity dataset was not always satisfactory to the central limit theorem. Normality of those data could be improved through log transformation. Therefore, care should be taken when using toxicity data to induce, for example, mean value for risk assessment.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.322-324
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• 2003

Leaf C:N ratio is a new factor in the field of biochemical inversion with hyperspectral data. Effects of common-used spectral transformations including log(R), log(1/R), 1/R, etc. from 400nm to 2490nm on its inversion are compared. Results show that their effects on statistical modeling are not apparent. Continuum removal is used on original reflectance in the range of 2030nm to 2220nm, in which exists an apparent absorption peak due to cellulose, lignin, protein, etc. The effect is distinctive and tends to improve the precision of C:N ratio inversion. Further, it is a robust and physically based transformation.

• The Transactions of the Korea Information Processing Society
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• v.5 no.8
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• pp.2027-2040
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• 1998

In this paper, we present efficient reconfigurable mesh algorithms for transforming between a binary image and its corresponding boundary code. These algorithms use $n\timesn\timesn$ processors when the size of the binary image is $n\timesn$. Recent published results show that these transformations can be done in O(1) time using $O(n^4)$ processors. The number of processors used by these algorithms is very large compared to the number of pixels in the image. Here, we present fast transformation algorithms which use $n^3 processors only. the transformation from a houndary code to a binary image takes O(1) time, and the converse transformation takes O(log n) time.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.1
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• pp.61-69
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• 2002

Active stereo vision system allows us to localize a target object by passing only the features of small disparities without heavy computation for identifying the target. This simple method, however, is not applicable to the situations where a distracting background is included or the target and other objects are located on the zero disparity area simultaneously To alleviate these problems, we combined filtering with foveation which employs high resolution in the center of the visual field and suppresses the periphery which is usually less interesting. We adopted an image pyramid or log-polar transformation for foveated imaging representation. We also extracted the stereo disparity of the target by using projection to keep the stereo disparity small during tracking. Our experiments show that log-polar transformation is superior to either an image pyramid or traditional method in separating a target from the distracting background and fairly enhances the tracking performance.