• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.941-949
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• 2011

The influence function is used to develop criteria to detect outliers in discriminant analysis. We derive the influence function of observations that estimate the the misclassification probability in discriminant analysis for three groups. The proposed measures are applied to the facial image data to define outliers and redo the discriminant analysis excluding the outliers. The study proves that the derived influence function is more efficient than using the discriminant probability approach.

• Journal of the Korean Society of Clothing and Textiles
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• v.29 no.7 s.144
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• pp.959-967
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• 2005

The color of apparels has the interaction of the face skin colors of the wearers. This study was carried out to classify the face skin colors of Korean males into several similar face skin colors in order to extract favorable colors which flatter to their face skin colors. The criterion that select the new subjects who have the classified face skin colors have to be decided. With color spectrometer, JX-777, face skin colors of subjects were measured quantitatively and classified into three clusters that had similar hue, value and chroma with Munsell Color System. Sample size was 418 Korean males and other 15 of new males subjects. Data were analyzed by K-means cluster analysis, ANOVA, Duncan multiple range test, Stepwise discriminant analysis using SPSS Win. 12. Findings were as follows: 1. 418 subjects who have YR colors were clustered into 3 kinds of face skin color groups. 2. Discriminant variables of face skin colors was 4 variables : L value of forehead, v value of cheek, c value of forehead, and b value of cheek from standardized canonical discriminant function coefficient 1 and c value of forehead, L value of forehead, b value of cheek. and L value of cheek from standardized canonical discriminant function coefficient 2. 3. Hit ratio of type 1 was $92.3\%$, of type 2 was $96.5\%$ and of type 3 was $92.6\%$ by the canonical discriminant function of 4 variables. 4. The canonical discriminant function equation 1 and 2 were calculated with the unstandardized canonical discriminant function coefficient and constant, the cutting score, and range of the score were computed. 5. The criterion that select the new subjects who have the classified face skin colors was decided.

• Journal of the Korean Society of Clothing and Textiles
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• v.29 no.7 s.144
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• pp.978-986
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• 2005

The color of apparel products have a close relationship with the face skin colors of consumers. In order to extract the favorable colors which flatter to consumer's face skin colors, this study was carried our to classify the face skin colors of Korean females. The criteria that select new subjects who have the classified face skin colors have to be decided. With color spectrometer, JX-777, face skin colors of subjects were measured and classified into three clusters that had similar hue, value and chroma with Munsell Color System. Sample size was 324 Korean females and other new 10 college girls. Data were analyzed by K-means cluster analysis, ANOVA, Duncan multiple range test, Stepwise discriminant analysis using SPSS Win. 12. Findings were as follows: 1. 324 subjects who have YR colors were clustered into 3 face skin color groups. 2. Discriminant variables of face skin colors were 5 variables : b value of cheek, V value of forehead, L value of cheek, C value of forehead and H value of cheek by the standardized canonical discriminant function coefficient 1. 3. Hit ratio of type 1 was $96.8\%$, of type 2 was $94.9\%$, of type 3 was $100.0\%$ and mean of hit ratio was $96.9\%$ by canonical discriminant function of 5 variables. 4. With the unstandardized canonical discriminant function coefficient and constant, canonical discriminant function equation 1 and 2 were calculated. And cutting score and range of score of the classified types were computed. The criteria that select the new subjects were decided.

• Proceedings of the Korean Society of Near Infrared Spectroscopy Conference
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• 2001.06a
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• pp.1244-1244
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• 2001

In linear discriminant analysis there are two important properties concerning the effectiveness of discriminant function modeling. The first is the separability of the discriminant function for different classes. The separability reaches its optimum by maximizing the ratio of between-class to within-class variance. The second is the stability of the discriminant function against noises present in the measurement variables. One can optimize the stability by exploring the discriminant variates in a principal variation subspace, i. e., the directions that account for a majority of the total variation of the data. An unstable discriminant function will exhibit inflated variance in the prediction of future unclassified objects, exposed to a significantly increased risk of erroneous prediction. Therefore, an ideal discriminant function should not only separate different classes with a minimum misclassification rate for the training set, but also possess a good stability such that the prediction variance for unclassified objects can be as small as possible. In other words, an optimal classifier should find a balance between the separability and the stability. This is of special significance for multivariate spectroscopy-based classification where multicollinearity always leads to discriminant directions located in low-spread subspaces. A new regularized discriminant analysis technique, the principal discriminant variate (PDV) method, has been developed for handling effectively multicollinear data commonly encountered in multivariate spectroscopy-based classification. The motivation behind this method is to seek a sequence of discriminant directions that not only optimize the separability between different classes, but also account for a maximized variation present in the data. Three different formulations for the PDV methods are suggested, and an effective computing procedure is proposed for a PDV method. Near-infrared (NIR) spectra of blood plasma samples from mastitic and healthy cows have been used to evaluate the behavior of the PDV method in comparison with principal component analysis (PCA), discriminant partial least squares (DPLS), soft independent modeling of class analogies (SIMCA) and Fisher linear discriminant analysis (FLDA). Results obtained demonstrate that the PDV method exhibits improved stability in prediction without significant loss of separability. The NIR spectra of blood plasma samples from mastitic and healthy cows are clearly discriminated between by the PDV method. Moreover, the proposed method provides superior performance to PCA, DPLS, SIMCA and FLDA, indicating that PDV is a promising tool in discriminant analysis of spectra-characterized samples with only small compositional difference, thereby providing a useful means for spectroscopy-based clinic applications.

• Proceedings of the Korean Society of Near Infrared Spectroscopy Conference
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• 2001.06a
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• pp.1042-1042
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• 2001

In linear discriminant analysis there are two important properties concerning the effectiveness of discriminant function modeling. The first is the separability of the discriminant function for different classes. The separability reaches its optimum by maximizing the ratio of between-class to within-class variance. The second is the stability of the discriminant function against noises present in the measurement variables. One can optimize the stability by exploring the discriminant variates in a principal variation subspace, i. e., the directions that account for a majority of the total variation of the data. An unstable discriminant function will exhibit inflated variance in the prediction of future unclassified objects, exposed to a significantly increased risk of erroneous prediction. Therefore, an ideal discriminant function should not only separate different classes with a minimum misclassification rate for the training set, but also possess a good stability such that the prediction variance for unclassified objects can be as small as possible. In other words, an optimal classifier should find a balance between the separability and the stability. This is of special significance for multivariate spectroscopy-based classification where multicollinearity always leads to discriminant directions located in low-spread subspaces. A new regularized discriminant analysis technique, the principal discriminant variate (PDV) method, has been developed for handling effectively multicollinear data commonly encountered in multivariate spectroscopy-based classification. The motivation behind this method is to seek a sequence of discriminant directions that not only optimize the separability between different classes, but also account for a maximized variation present in the data. Three different formulations for the PDV methods are suggested, and an effective computing procedure is proposed for a PDV method. Near-infrared (NIR) spectra of blood plasma samples from daily monitoring of two Japanese cows have been used to evaluate the behavior of the PDV method in comparison with principal component analysis (PCA), discriminant partial least squares (DPLS), soft independent modeling of class analogies (SIMCA) and Fisher linear discriminant analysis (FLDA). Results obtained demonstrate that the PDV method exhibits improved stability in prediction without significant loss of separability. The NIR spectra of blood plasma samples from two cows are clearly discriminated between by the PDV method. Moreover, the proposed method provides superior performance to PCA, DPLS, SIMCA md FLDA, indicating that PDV is a promising tool in discriminant analysis of spectra-characterized samples with only small compositional difference.

• Food Science of Animal Resources
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• v.29 no.1
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• pp.132-139
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• 2009

The objective of this study was to investigate the most effective analysis methods for palatability grading of Hanwoo beef by comparing the results of discriminant analysis with sensory data. The sensory data were obtained from sensory testing by 1,300 consumers evaluated tenderness, juiciness, flavor-likeness and overall acceptability of Hanwoo beef samples prepared by boiling, roasting and grilling cooking methods. For the discriminant analysis with one factor, overall acceptability, the linear discriminant functions and the non-parametric discriminant function with the Gaussian kernel were estimated. The linear discriminant functions were simple and easy to understand while the non-parametric discriminant functions were not explicit and had the problem of selection of kernel function and bandwidth. With the three palatability factors such as tenderness, juiciness and flavor-likeness, the canonical discriminant analysis was used and the ability of classification was calculated with the accurate classification rate and the error rate. The canonical discriminant analysis did not need the specific distributional assumptions and only used the principal component and canonical correlation. Also, it contained the function of 3 factors (tenderness, juiciness and flavor-likeness) and accurate classification rate was similar with the other discriminant methods. Therefore, the canonical discriminant analysis was the most proper method to analyze the palatability grading of Hanwoo beef.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.325-337
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• 1993

This paper propose two test statistics which enable us to proceed the variable selection in Fisher's linear discriminant function for the case of heterogeneous discrimination with equal training sample size. Simultaneous confidence intervals associated with the test are also given. These are exact and approximate results. The latter is based upon an approximation of a linear sum of Wishart distributions with unequal scale matrices. Using simulated sampling experiments, powers of the two tests have been tabulated, and power comparisons have been made between them.

• Journal of Biosystems Engineering
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• v.24 no.4
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• pp.325-334
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• 1999

The aim of this study was to present a groundwork for development of a sorting system of peeled garlics using machine vision. Images of various garlic samples such as sound, partially defective, discolored, rotten and un-peeled were obtained with a B/W machine vision system. Sorting factors which were based on normalized histogram and statistical analysis(STEPDISC Method) had good separability for various garlic samples. Bayes discriminant function and neural network sorting algorithms were developed with the sample images and were experimented on various garlic samples. It was showed that garlic samples could be classified by sorting algorithm with average sorting accuracies of 88.4% by Bayes discriminant function and 93.2% by neural network.

• Journal of Korea Technology Innovation Society
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• v.10 no.2
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• pp.183-205
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• 2007

An investigation was undertaken of the optimal discriminant model for predicting the likelihood of insolvency in advance for medium-sized firms based on the technology evaluation. The explanatory variables included in the discriminant model were selected by both factor analysis and discriminant analysis using stepwise selection method. Five explanatory variables were selected in factor analysis in terms of explanatory ratio and communality. Six explanatory variables were selected in stepwise discriminant analysis. The effectiveness of linear discriminant model and logistic discriminant model were assessed by the criteria of the critical probability and correct classification rate. Result showed that both model had similar correct classification rate and the linear discriminant model was preferred to the logistic discriminant model in terms of criteria of the critical probability In case of the linear discriminant model with critical probability of 0.5, the total-group correct classification rate was 70.4% and correct classification rates of insolvent and solvent groups were 73.4% and 69.5% respectively. Correct classification rate is an estimate of the probability that the estimated discriminant function will correctly classify the present sample. However, the actual correct classification rate is an estimate of the probability that the estimated discriminant function will correctly classify a future observation. Unfortunately, the correct classification rate underestimates the actual correct classification rate because the data set used to estimate the discriminant function is also used to evaluate them. The cross-validation method were used to estimate the bias of the correct classification rate. According to the results the estimated bias were 2.9% and the predicted actual correct classification rate was 67.5%. And a threshold value is set to establish an in-doubt category. Results of linear discriminant model can be applied for the technology financing banks to evaluate the possibility of insolvency and give the ranking of the firms applied.

• Journal of the Korean Statistical Society
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• v.27 no.4
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• pp.471-483
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• 1998

The influence of observations on the misclassification probability in multiple discriminant analysis under the equal covariance assumption is investigated by the local influence method. Under an appropriate perturbation we can get information about influential observations and outliers by studying the curvatures and the associated direction vectors of the perturbation-formed surface of the misclassification probability. We show that the influence function method gives essentially the same information as the direction vector of the maximum slope. An illustrative example is given for the effectiveness of the local influence method.