• Journal of applied mathematics & informatics
• /
• v.42 no.4
• /
• pp.879-897
• /
• 2024

The emergence of generalized square metrics in Finsler geometry can be attributed to various classification concerning (𝛼, 𝛽)-metrics. They have excellent geometric properties in Finsler geometry. Within the scope of this research paper, we have conducted an investigation into the generalized square metric denoted as $F(x,y)=\frac{[{\alpha}(x,y)+{\beta}(x,y)]^{n+1}}{[{\alpha}(x,y)]^n}$, focusing specifically on its application to the Finslerian hypersurface. Furthermore, the classification and existence of first, second, and third kind of hyperplanes of the Finsler manifold has been established.

• Journal of the Korean Mathematical Society
• /
• v.58 no.1
• /
• pp.109-122
• /
• 2021

In this paper, we consider the problem of finding the hypersurface Mn in the Euclidean (n + 1)-space ℝn+1 that satisfies an equation of mean curvature type, called singular minimal hypersurface equation. Such an equation physically characterizes the surfaces in the upper half-space ℝ+3 (u) with lowest gravity center, for a fixed unit vector u ∈ ℝ3. We first state that a singular minimal cylinder Mn in ℝn+1 is either a hyperplane or a α-catenary cylinder. It is also shown that this result remains true when Mn is a translation hypersurface and u is a horizantal vector. As a further application, we prove that a singular minimal translation graph in ℝ3 of the form z = f(x) + g(y + cx), c ∈ ℝ - {0}, with respect to a certain horizantal vector u is either a plane or a α-catenary cylinder.

• International Journal of Control, Automation, and Systems
• /
• v.6 no.6
• /
• pp.928-938
• /
• 2008

This study presents an approach for approximation an unknown function from a numerical data set based on the synthesis of a neuro-fuzzy model. An adaptive input data space parting method, which is used for building hyperbox-shaped clusters in the input data space, is proposed. Each data cluster is implemented here as a fuzzy set using a membership function MF with a hyperbox core that is constructed from a min vertex and a max vertex. The focus of interest in proposed approach is to increase degree of fit between characteristics of the given numerical data set and the established fuzzy sets used to approximate it. A new cutting procedure, named NCP, is proposed. The NCP is an adaptive cutting procedure using a pure function $\Psi$ and a penalty function $\tau$ for direction the input data space parting process. New algorithms named CSHL, HLM1 and HLM2 are presented. The first new algorithm, CSHL, built based on the cutting procedure NCP, is used to create hyperbox-shaped data clusters. The second and the third algorithm are used to establish adaptive neuro- fuzzy inference systems. A series of numerical experiments are performed to assess the efficiency of the proposed approach.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.16 no.4
• /
• pp.1110-1127
• /
• 2022

To improve the training efficiency and generalization performance of a support vector machine (SVM) in a large-scale set, an optimal SVM learning method based on adaptive sparse sampling and the granularity shift factor is presented. The proposed method combines sampling optimization with learner optimization. First, an adaptive sparse sampling method based on the potential function density clustering is designed to adaptively obtain sparse sampling samples, which can achieve a reduction in the training sample set and effectively approximate the spatial structure distribution of the original sample set. A granularity shift factor method is then constructed to optimize the SVM decision hyperplane, which fully considers the neighborhood information of each granularity region in the sparse sampling set. Experiments on an artificial dataset and three benchmark datasets show that the proposed method can achieve a relatively higher training efficiency, as well as ensure a good generalization performance of the learner. Finally, the effectiveness of the proposed method is verified.

• Information Systems Review
• /
• v.24 no.4
• /
• pp.23-40
• /
• 2022

Although Support Vector Machine(SVM) has been used in various fields such as bankruptcy prediction model, the hyperplane learned by SVM in class imbalance problem can be severely skewed toward minority class and has a negative impact on performance because the area of majority class is expanded while the area of minority class is invaded. This study proposed optimized uneven margin SVM(OPT-UMSVM) combining threshold moving or post scaling method with UMSVM to cope with the limitation of the traditional even margin SVM(EMSVM) in class imbalance problem. OPT-UMSVM readjusted the skewed hyperplane to the majority class and had better generation ability than EMSVM improving the sensitivity of minority class and calculating the optimized performance. To validate OPT-UMSVM, 10-fold cross validations were performed on five sub-datasets with different imbalance ratio values. Empirical results showed two main findings. First, UMSVM had a weak effect on improving the performance of EMSVM in balanced datasets, but it greatly outperformed EMSVM in severely imbalanced datasets. Second, compared to EMSVM and conventional UMSVM, OPT-UMSVM had better performance in both balanced and imbalanced datasets and showed a significant difference performance especially in severely imbalanced datasets.

• Asia pacific journal of information systems
• /
• v.19 no.2
• /
• pp.139-155
• /
• 2009

For the last few decades, many studies have tried to explore and unveil venture companies' success factors and unique features in order to identify the sources of such companies' competitive advantages over their rivals. Such venture companies have shown tendency to give high returns for investors generally making the best use of information technology. For this reason, many venture companies are keen on attracting avid investors' attention. Investors generally make their investment decisions by carefully examining the evaluation criteria of the alternatives. To them, credit rating information provided by international rating agencies, such as Standard and Poor's, Moody's and Fitch is crucial source as to such pivotal concerns as companies stability, growth, and risk status. But these types of information are generated only for the companies issuing corporate bonds, not venture companies. Therefore, this study proposes a method for evaluating venture businesses by presenting our recent empirical results using financial data of Korean venture companies listed on KOSDAQ in Korea exchange. In addition, this paper used multi-class SVM for the prediction of DEA-based efficiency rating for venture businesses, which was derived from our proposed method. Our approach sheds light on ways to locate efficient companies generating high level of profits. Above all, in determining effective ways to evaluate a venture firm's efficiency, it is important to understand the major contributing factors of such efficiency. Therefore, this paper is constructed on the basis of following two ideas to classify which companies are more efficient venture companies: i) making DEA based multi-class rating for sample companies and ii) developing multi-class SVM-based efficiency prediction model for classifying all companies. First, the Data Envelopment Analysis(DEA) is a non-parametric multiple input-output efficiency technique that measures the relative efficiency of decision making units(DMUs) using a linear programming based model. It is non-parametric because it requires no assumption on the shape or parameters of the underlying production function. DEA has been already widely applied for evaluating the relative efficiency of DMUs. Recently, a number of DEA based studies have evaluated the efficiency of various types of companies, such as internet companies and venture companies. It has been also applied to corporate credit ratings. In this study we utilized DEA for sorting venture companies by efficiency based ratings. The Support Vector Machine(SVM), on the other hand, is a popular technique for solving data classification problems. In this paper, we employed SVM to classify the efficiency ratings in IT venture companies according to the results of DEA. The SVM method was first developed by Vapnik (1995). As one of many machine learning techniques, SVM is based on a statistical theory. Thus far, the method has shown good performances especially in generalizing capacity in classification tasks, resulting in numerous applications in many areas of business, SVM is basically the algorithm that finds the maximum margin hyperplane, which is the maximum separation between classes. According to this method, support vectors are the closest to the maximum margin hyperplane. If it is impossible to classify, we can use the kernel function. In the case of nonlinear class boundaries, we can transform the inputs into a high-dimensional feature space, This is the original input space and is mapped into a high-dimensional dot-product space. Many studies applied SVM to the prediction of bankruptcy, the forecast a financial time series, and the problem of estimating credit rating, In this study we employed SVM for developing data mining-based efficiency prediction model. We used the Gaussian radial function as a kernel function of SVM. In multi-class SVM, we adopted one-against-one approach between binary classification method and two all-together methods, proposed by Weston and Watkins(1999) and Crammer and Singer(2000), respectively. In this research, we used corporate information of 154 companies listed on KOSDAQ market in Korea exchange. We obtained companies' financial information of 2005 from the KIS(Korea Information Service, Inc.). Using this data, we made multi-class rating with DEA efficiency and built multi-class prediction model based data mining. Among three manners of multi-classification, the hit ratio of the Weston and Watkins method is the best in the test data set. In multi classification problems as efficiency ratings of venture business, it is very useful for investors to know the class with errors, one class difference, when it is difficult to find out the accurate class in the actual market. So we presented accuracy results within 1-class errors, and the Weston and Watkins method showed 85.7% accuracy in our test samples. We conclude that the DEA based multi-class approach in venture business generates more information than the binary classification problem, notwithstanding its efficiency level. We believe this model can help investors in decision making as it provides a reliably tool to evaluate venture companies in the financial domain. For the future research, we perceive the need to enhance such areas as the variable selection process, the parameter selection of kernel function, the generalization, and the sample size of multi-class.

• Journal of Korean Society of Transportation
• /
• v.33 no.3
• /
• pp.284-293
• /
• 2015

The objective of this paper is to determine the conditions of road surface by utilizing the images collected from closed-circuit television (CCTV) cameras installed on roadside. First, a technique was examined to detect wet surfaces at nighttime. From the literature reviews, it was revealed that image processing using polarization is one of the preferred options. However, it is hard to use the polarization characteristics of road surface images at nighttime because of irregular or no light situations. In this study, we proposes a new discriminant for detecting wet and dry road surfaces using CCTV image data at night. To detect the road surface conditions with night vision, we applied the wavelet packet transform for analyzing road surface textures. Additionally, to apply the luminance feature of night CCTV images, we set the intensity histogram based on HSI(Hue Saturation Intensity) color model. With a set of 200 images taken from the field, we constructed a detection criteria hyperplane with SVM (Support Vector Machine). We conducted field tests to verify the detection ability of the wet road surfaces and obtained reliable results. The outcome of this study is also expected to be used for monitoring road surfaces to improve safety.

• Journal of Intelligence and Information Systems
• /
• v.18 no.2
• /
• pp.29-45
• /
• 2012

Bond rating is regarded as an important event for measuring financial risk of companies and for determining the investment returns of investors. As a result, it has been a popular research topic for researchers to predict companies' credit ratings by applying statistical and machine learning techniques. The statistical techniques, including multiple regression, multiple discriminant analysis (MDA), logistic models (LOGIT), and probit analysis, have been traditionally used in bond rating. However, one major drawback is that it should be based on strict assumptions. Such strict assumptions include linearity, normality, independence among predictor variables and pre-existing functional forms relating the criterion variablesand the predictor variables. Those strict assumptions of traditional statistics have limited their application to the real world. Machine learning techniques also used in bond rating prediction models include decision trees (DT), neural networks (NN), and Support Vector Machine (SVM). Especially, SVM is recognized as a new and promising classification and regression analysis method. SVM learns a separating hyperplane that can maximize the margin between two categories. SVM is simple enough to be analyzed mathematical, and leads to high performance in practical applications. SVM implements the structuralrisk minimization principle and searches to minimize an upper bound of the generalization error. In addition, the solution of SVM may be a global optimum and thus, overfitting is unlikely to occur with SVM. In addition, SVM does not require too many data sample for training since it builds prediction models by only using some representative sample near the boundaries called support vectors. A number of experimental researches have indicated that SVM has been successfully applied in a variety of pattern recognition fields. However, there are three major drawbacks that can be potential causes for degrading SVM's performance. First, SVM is originally proposed for solving binary-class classification problems. Methods for combining SVMs for multi-class classification such as One-Against-One, One-Against-All have been proposed, but they do not improve the performance in multi-class classification problem as much as SVM for binary-class classification. Second, approximation algorithms (e.g. decomposition methods, sequential minimal optimization algorithm) could be used for effective multi-class computation to reduce computation time, but it could deteriorate classification performance. Third, the difficulty in multi-class prediction problems is in data imbalance problem that can occur when the number of instances in one class greatly outnumbers the number of instances in the other class. Such data sets often cause a default classifier to be built due to skewed boundary and thus the reduction in the classification accuracy of such a classifier. SVM ensemble learning is one of machine learning methods to cope with the above drawbacks. Ensemble learning is a method for improving the performance of classification and prediction algorithms. AdaBoost is one of the widely used ensemble learning techniques. It constructs a composite classifier by sequentially training classifiers while increasing weight on the misclassified observations through iterations. The observations that are incorrectly predicted by previous classifiers are chosen more often than examples that are correctly predicted. Thus Boosting attempts to produce new classifiers that are better able to predict examples for which the current ensemble's performance is poor. In this way, it can reinforce the training of the misclassified observations of the minority class. This paper proposes a multiclass Geometric Mean-based Boosting (MGM-Boost) to resolve multiclass prediction problem. Since MGM-Boost introduces the notion of geometric mean into AdaBoost, it can perform learning process considering the geometric mean-based accuracy and errors of multiclass. This study applies MGM-Boost to the real-world bond rating case for Korean companies to examine the feasibility of MGM-Boost. 10-fold cross validations for threetimes with different random seeds are performed in order to ensure that the comparison among three different classifiers does not happen by chance. For each of 10-fold cross validation, the entire data set is first partitioned into tenequal-sized sets, and then each set is in turn used as the test set while the classifier trains on the other nine sets. That is, cross-validated folds have been tested independently of each algorithm. Through these steps, we have obtained the results for classifiers on each of the 30 experiments. In the comparison of arithmetic mean-based prediction accuracy between individual classifiers, MGM-Boost (52.95%) shows higher prediction accuracy than both AdaBoost (51.69%) and SVM (49.47%). MGM-Boost (28.12%) also shows the higher prediction accuracy than AdaBoost (24.65%) and SVM (15.42%)in terms of geometric mean-based prediction accuracy. T-test is used to examine whether the performance of each classifiers for 30 folds is significantly different. The results indicate that performance of MGM-Boost is significantly different from AdaBoost and SVM classifiers at 1% level. These results mean that MGM-Boost can provide robust and stable solutions to multi-classproblems such as bond rating.