• Education of Primary School Mathematics
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• v.27 no.2
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• pp.111-137
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• 2024

The purpose of this study is to identify the expected difficulties and necessary support when applying the 2022 revised mathematics curriculum to elementary schools, and to support the establishment of the field. To this end, we explored the major changes in the 2022 revised mathematics curriculum, and based on this, we conducted a survey of elementary school teachers to identify the expected difficulties and necessary support when applying it in the field. In particular, when analyzing the results, we also examined whether there were any differences in the expected difficulties and necessary support depending on the size of the school where it is located and the teaching experience of the teacher. The research results are as follows. First, the proportion of teachers who expect difficulties in applying the 2022 revised mathematics curriculum was mostly below 50%, but the proportion of teachers who demand support was much higher, at around 80%. Second, the difficulty of elementary school teachers in applying the 2022 revised mathematics curriculum was found to be the greatest in evaluation. Third, in relation to the use of edutech, teachers in elementary schools are also expected to have difficulties in teaching and learning methods to foster students' digital literacy, assessment using teaching materials or engineering tools, and assessment in online environments. Fourth, the difficulty of elementary school teachers in applying the 2022 revised mathematics curriculum was also significant in relation to mathematics subject competencies. Fifth, it was found that there is also difficulty in understanding the major changes of the achievement standards, including the addition, deletion, and adjustment of the achievement standards, and the impact on the learning of other achievement standards. Finally, the responses of elementary school teachers to the expected difficulties and necessary support in applying the 2022 revised mathematics curriculum did not differ depending on the size of the school where it is located, but statistically significant differences were found in a number of items depending on the teaching experience of the teacher. Based on these research results, we hope that various support will be provided for the 2022 revised mathematics curriculum, which will be applied annually from 2024.

• Journal of Bio-Environment Control
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• v.5 no.2
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• pp.215-235
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• 1996

The thermal analysis by mathematical model simulation makes it possible to reasonably predict heating and/or cooling requirements of certain greenhouses located under various geographical and climatic environment. It is another advantages of model simulation technique to be able to make it possible to select appropriate heating system, to set up energy utilization strategy, to schedule seasonal crop pattern, as well as to determine new greenhouse ranges. In this study, the control pattern for greenhouse microclimate is categorized as cooling and heating. Dynamic model was adopted to simulate heating requirements and/or energy conservation effectiveness such as energy saving by night-time thermal curtain, estimation of Heating Degree-Hours(HDH), long time prediction of greenhouse thermal behavior, etc. On the other hand, the cooling effects of ventilation, shading, and pad ||||&|||| fan system were partly analyzed by static model. By the experimental work with small size model greenhouse of 1.2m$\times$2.4m, it was found that cooling the greenhouse by spraying cold water directly on greenhouse cover surface or by recirculating cold water through heat exchangers would be effective in greenhouse summer cooling. The mathematical model developed for greenhouse model simulation is highly applicable because it can reflects various climatic factors like temperature, humidity, beam and diffuse solar radiation, wind velocity, etc. This model was closely verified by various weather data obtained through long period greenhouse experiment. Most of the materials relating with greenhouse heating or cooling components were obtained from model greenhouse simulated mathematically by using typical year(1987) data of Jinju Gyeongnam. But some of the materials relating with greenhouse cooling was obtained by performing model experiments which include analyzing cooling effect of water sprayed directly on greenhouse roof surface. The results are summarized as follows : 1. The heating requirements of model greenhouse were highly related with the minimum temperature set for given greenhouse. The setting temperature at night-time is much more influential on heating energy requirement than that at day-time. Therefore It is highly recommended that night- time setting temperature should be carefully determined and controlled. 2. The HDH data obtained by conventional method were estimated on the basis of considerably long term average weather temperature together with the standard base temperature(usually 18.3$^{\circ}C$). This kind of data can merely be used as a relative comparison criteria about heating load, but is not applicable in the calculation of greenhouse heating requirements because of the limited consideration of climatic factors and inappropriate base temperature. By comparing the HDM data with the results of simulation, it is found that the heating system design by HDH data will probably overshoot the actual heating requirement. 3. The energy saving effect of night-time thermal curtain as well as estimated heating requirement is found to be sensitively related with weather condition: Thermal curtain adopted for simulation showed high effectiveness in energy saving which amounts to more than 50% of annual heating requirement. 4. The ventilation performances doting warm seasons are mainly influenced by air exchange rate even though there are some variations depending on greenhouse structural difference, weather and cropping conditions. For air exchanges above 1 volume per minute, the reduction rate of temperature rise on both types of considered greenhouse becomes modest with the additional increase of ventilation capacity. Therefore the desirable ventilation capacity is assumed to be 1 air change per minute, which is the recommended ventilation rate in common greenhouse. 5. In glass covered greenhouse with full production, under clear weather of 50% RH, and continuous 1 air change per minute, the temperature drop in 50% shaded greenhouse and pad ＆ fan systemed greenhouse is 2.6$^{\circ}C$ and.6.1$^{\circ}C$ respectively. The temperature in control greenhouse under continuous air change at this time was 36.6$^{\circ}C$ which was 5.3$^{\circ}C$ above ambient temperature. As a result the greenhouse temperature can be maintained 3$^{\circ}C$ below ambient temperature. But when RH is 80%, it was impossible to drop greenhouse temperature below ambient temperature because possible temperature reduction by pad ||||&|||| fan system at this time is not more than 2.4$^{\circ}C$. 6. During 3 months of hot summer season if the greenhouse is assumed to be cooled only when greenhouse temperature rise above 27$^{\circ}C$, the relationship between RH of ambient air and greenhouse temperature drop($\Delta$T) was formulated as follows : $\Delta$T= -0.077RH＋7.7 7. Time dependent cooling effects performed by operation of each or combination of ventilation, 50% shading, pad ＆ fan of 80% efficiency, were continuously predicted for one typical summer day long. When the greenhouse was cooled only by 1 air change per minute, greenhouse air temperature was 5$^{\circ}C$ above outdoor temperature. Either method alone can not drop greenhouse air temperature below outdoor temperature even under the fully cropped situations. But when both systems were operated together, greenhouse air temperature can be controlled to about 2.0-2.3$^{\circ}C$ below ambient temperature. 8. When the cool water of 6.5-8.5$^{\circ}C$ was sprayed on greenhouse roof surface with the water flow rate of 1.3 liter/min per unit greenhouse floor area, greenhouse air temperature could be dropped down to 16.5-18.$0^{\circ}C$, whlch is about 1$0^{\circ}C$ below the ambient temperature of 26.5-28.$0^{\circ}C$ at that time. The most important thing in cooling greenhouse air effectively with water spray may be obtaining plenty of cool water source like ground water itself or cold water produced by heat-pump. Future work is focused on not only analyzing the feasibility of heat pump operation but also finding the relationships between greenhouse air temperature(T$_{g}$ ), spraying water temperature(T$_{w}$ ), water flow rate(Q), and ambient temperature(T$_{o}$).

• Journal of Intelligence and Information Systems
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• v.23 no.4
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• pp.147-168
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• 2017

There have been many studies on accurate stock market forecasting in academia for a long time, and now there are also various forecasting models using various techniques. Recently, many attempts have been made to predict the stock index using various machine learning methods including Deep Learning. Although the fundamental analysis and the technical analysis method are used for the analysis of the traditional stock investment transaction, the technical analysis method is more useful for the application of the short-term transaction prediction or statistical and mathematical techniques. Most of the studies that have been conducted using these technical indicators have studied the model of predicting stock prices by binary classification - rising or falling - of stock market fluctuations in the future market (usually next trading day). However, it is also true that this binary classification has many unfavorable aspects in predicting trends, identifying trading signals, or signaling portfolio rebalancing. In this study, we try to predict the stock index by expanding the stock index trend (upward trend, boxed, downward trend) to the multiple classification system in the existing binary index method. In order to solve this multi-classification problem, a technique such as Multinomial Logistic Regression Analysis (MLOGIT), Multiple Discriminant Analysis (MDA) or Artificial Neural Networks (ANN) we propose an optimization model using Genetic Algorithm as a wrapper for improving the performance of this model using Multi-classification Support Vector Machines (MSVM), which has proved to be superior in prediction performance. In particular, the proposed model named GA-MSVM is designed to maximize model performance by optimizing not only the kernel function parameters of MSVM, but also the optimal selection of input variables (feature selection) as well as instance selection. In order to verify the performance of the proposed model, we applied the proposed method to the real data. The results show that the proposed method is more effective than the conventional multivariate SVM, which has been known to show the best prediction performance up to now, as well as existing artificial intelligence / data mining techniques such as MDA, MLOGIT, CBR, and it is confirmed that the prediction performance is better than this. Especially, it has been confirmed that the 'instance selection' plays a very important role in predicting the stock index trend, and it is confirmed that the improvement effect of the model is more important than other factors. To verify the usefulness of GA-MSVM, we applied it to Korea's real KOSPI200 stock index trend forecast. Our research is primarily aimed at predicting trend segments to capture signal acquisition or short-term trend transition points. The experimental data set includes technical indicators such as the price and volatility index (2004 ~ 2017) and macroeconomic data (interest rate, exchange rate, S&P 500, etc.) of KOSPI200 stock index in Korea. Using a variety of statistical methods including one-way ANOVA and stepwise MDA, 15 indicators were selected as candidate independent variables. The dependent variable, trend classification, was classified into three states: 1 (upward trend), 0 (boxed), and -1 (downward trend). 70% of the total data for each class was used for training and the remaining 30% was used for verifying. To verify the performance of the proposed model, several comparative model experiments such as MDA, MLOGIT, CBR, ANN and MSVM were conducted. MSVM has adopted the One-Against-One (OAO) approach, which is known as the most accurate approach among the various MSVM approaches. Although there are some limitations, the final experimental results demonstrate that the proposed model, GA-MSVM, performs at a significantly higher level than all comparative models.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.1 no.1
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• pp.53-68
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• 1981

Most clays under sustained load exhibit time-dependent deformation because of creep movement of soil particles and many investigators have attempted to relate their findings to the creep behavior of natural ground and to the long-term stability of slopes. Since the creep behavior of clays may assume a variety of forms depending on such factors as soil plasticity, activity and water content, it is difficult and complicated to analyse the creep behavior of clays. Rheological models composed of linear springs in combination with linear or nonlinear dashpots and sliders, are generally used for the mathematical description of the time-dependent behavior of soils. Most rheological models, however, have been proposed to simulate the behavior of secondary compression for saturated clays and few definitive data exist that can evaluate the behavior of non-saturated clays under the action of sustained stress. The clays change gradually from a solid state through plastic state to a liquid state with increasing water content, therefore, the rheological models also change. On the other hand, creep is time-dependent, and also the effect of thixotropy is time-function. Consequently, there may be certain correlations between creep behavior and the effects of thixotropy in compacted clays. In addition, the states of clay depend on water content and hence the height of the specimen under drained conditions. Futhermore, based on present and past studies, because immediate elastic deformation occurs instantly after the pressure increment without time-delayed behavior, the factor representing immediate elastic deformations in the rheological model is necessary. The investigation described in this paper, based on rheological model, is designed to identify the immediate elastic deformations and the effects of thixotropy and height of clay specimens with varing water content and stress level on creep deformations. For these purposes, the uniaxial drain-type creep tests were performed. Test results and data for three compacted clays have shown that a linear top spring is needed to account for immediate elastic deformations in the rheological model, and at lower water content below the visco-plastic limit, the effects of thixotropy and height of clay specimens can be represented by the proposed rheological model not considering the effects. Therefore, the rheological model does not necessitate the other factors representing these effects. On the other hand, at water content higher than the visco-plastic limit, although the state behavior of clays is visco-plastic or viscous flow at the beginning of the test, the state behavior, in the case of the lower height sample, does not represent the same behavior during the process of the test, because of rapid drainage. In these cases, the rheological model does not coincide with the model in the case of the higher specimens.

• The Korean Journal of Nuclear Medicine
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• v.31 no.1
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• pp.73-82
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• 1997

Regional myocardial blood flow (rMBF) can be noninvasively quantified using N-13 ammonia and dynamic positron emission tomography (PET). The quantitative accuracy of the rMBF values, however, is affected by the distortion of myocardial PET images caused by finite PET image resolution and cardiac motion. Although different methods have been developed to correct the distortion typically classified as partial volume effect and spillover, the methods are too complex to employ in a routine clinical environment. We have developed a refined method incorporating a geometric model of the volume representation of a region-of-interest (ROI) into the two-compartment N-13 ammonia model. In the refined model, partial volume effect and spillover are conveniently corrected by an additional parameter in the mathematical model. To examine the accuracy of this approach, studies were performed in 9 coronary artery disease patients. Dynamic transaxial images (16 frames) were acquired with a GE $Advance^{TM}$ PET scanner simultaneous with intravenous injection of 20 mCi N-13 ammonia. rMBF was examined at rest and during pharmacologically (dipyridamole) induced coronary hyperemia. Three sectorial myocardium (septum, anterior wall and lateral wall) and blood pool time-activity curves were generated using dynamic images from manually drawn ROIs. The accuracy of rMBF values estimated by the refined method was examined by comparing to the values estimated using the conventional two-compartment model without partial volume effect correction rMBF values obtained by the refined method linearly correlated with rMBF values obtained by the conventional method (108 myocardial segments, correlation coefficient (r)=0.88). Additionally, underestimated rMBF values by the conventional method due to partial volume effect were corrected by theoretically predicted amount in the refined method (slope(m)=1.57). Spillover fraction estimated by the two methods agreed well (r=1.00, m=0.98). In conclusion, accurate rMBF values can be efficiently quantified by the refined method incorporating myocardium geometric information into the two-compartment model using N-13 ammonia and PET.

• Radiation Oncology Journal
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• v.16 no.2
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• pp.99-106
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• 1998

Purpose : We conducted clonogenic assay using human cancer cell lines (MKN-45, PC-14, Y-79, HeLa) to investigate a correlation between the parameters of radiosensitivity. Materials and Methods : Human cancer cell lines were irradiated with single doses of 1, 2, 3, 5, 7 and 10Gy for the study of radiosensitivity and subrethal damage repair capacity was assessed with two fractions of 5Gy separated with a time interval of 0, 1, 2, 3, 4, 6 and 24 hours. Surviving fraction was assessed with clonogenic assay using $Sperman-H\"{a}rbor$ method and mathematical analysis of survival curves was done with linear-quadratic (LQ) , multitarget-single hit(MS) model and mean inactivation dose$(\v{D})$. Results : Surviving fractions at 2Gy(SF2) were variable among the cell lines, ranged from 0.174 to 0.85 The SF2 of Y-79 was lowest and that of PC-14 was highest(p<0.05, t-test). LQ model analysis showed that the values of $\alpha$ for Y-79, MKN-45, HeLa and PC-14 were 0.603, 0.356, 0.275 and 0.102 respectively, and those of $\beta$ were 0.005, 0.016, 0.025 and 0.027 respectively. Fitting to MS model showed that the values of Do for Y-79. MKN-45, HeLa and PC-14 were 1.59. 1.84. 1.88 and 2.52 respectively, and those of n were 0.97, 1.46, 1.52 and 1 69 respectively. The $\v{D}s$ calculated by Gauss-Laguerre method were 1.62, 2.37, 2,01 and 3.95 respectively So the SF2 was significantly correlated with $\alpha$, Do and $\v{D}$. Their Pearson correlation coefficiencics were -0.953 and 0,993. 0.999 respectively(p<0.05). Sublethal damage repair was saturated around 4 hours and recovery ratios (RR) at plateau phase ranged from 2 to 3.79. But RR was not correlated with SF2, ${\alpha}$, ${\beta}$, Do, $\v{D}$. Conclusion : The intrinsic radiosensitivity was very different among the tested human cell lines. Y-79 was the most sensitive and PC-l4 was the least sensitive. SF2 was well correlated with ${\alpha}$, Do, and $\v{D}$. RR was high for MKN-45 and HeLa but had nothing to do with radiosensitivity parameters. These basic parameters can be used as baseline data for various in vitro radiobiological experiments.

• Magazine of the Korean Society of Agricultural Engineers
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• v.19 no.1
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• pp.4296-4311
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• 1977

This study was conducted to derive an Instantaneous Unit Hydrograph for the accurate and reliable unitgraph which can be used to the estimation and control of flood for the development of agricultural water resources and rational design of hydraulic structures. Eight small watersheds were selected as studying basins from Han, Geum, Nakdong, Yeongsan and Inchon River systems which may be considered as a main river systems in Korea. The area of small watersheds are within the range of 85 to 470$\textrm{km}^2$. It is to derive an accurate Instantaneous Unit Hydrograph under the condition of having a short duration of heavy rain and uniform rainfall intensity with the basic and reliable data of rainfall records, pluviographs, records of river stages and of the main river systems mentioned above. Investigation was carried out for the relations between measurable unitgraph and watershed characteristics such as watershed area, A, river length L, and centroid distance of the watershed area, Lca. Especially, this study laid emphasis on the derivation and application of Instantaneous Unit Hydrograph (IUH) by applying Nash's conceptual model and by using an electronic computer. I U H by Nash's conceptual model and I U H by flood routing which can be applied to the ungaged small watersheds were derived and compared with each other to the observed unitgraph. 1 U H for each small watersheds can be solved by using an electronic computer. The results summarized for these studies are as follows; 1. Distribution of uniform rainfall intensity appears in the analysis for the temporal rainfall pattern of selected heavy rainfall event. 2. Mean value of recession constants, Kl, is 0.931 in all watersheds observed. 3. Time to peak discharge, Tp, occurs at the position of 0.02 Tb, base length of hlrdrograph with an indication of lower value than that in larger watersheds. 4. Peak discharge, Qp, in relation to the watershed area, A, and effective rainfall, R, is found to be {{{{ { Q}_{ p} = { 0.895} over { { A}^{0.145 } } }}}} AR having high significance of correlation coefficient, 0.927, between peak discharge, Qp, and effective rainfall, R. Design chart for the peak discharge (refer to Fig. 15) with watershed area and effective rainfall was established by the author. 5. The mean slopes of main streams within the range of 1.46 meters per kilometer to 13.6 meter per kilometer. These indicate higher slopes in the small watersheds than those in larger watersheds. Lengths of main streams are within the range of 9.4 kilometer to 41.75 kilometer, which can be regarded as a short distance. It is remarkable thing that the time of flood concentration was more rapid in the small watersheds than that in the other larger watersheds. 6. Length of main stream, L, in relation to the watershed area, A, is found to be L=2.044A0.48 having a high significance of correlation coefficient, 0.968. 7. Watershed lag, Lg, in hrs in relation to the watershed area, A, and length of main stream, L, was derived as Lg=3.228 A0.904 L-1.293 with a high significance. On the other hand, It was found that watershed lag, Lg, could also be expressed as {{{{Lg=0.247 { ( { LLca} over { SQRT { S} } )}^{ 0.604} }}}} in connection with the product of main stream length and the centroid length of the basin of the watershed area, LLca which could be expressed as a measure of the shape and the size of the watershed with the slopes except watershed area, A. But the latter showed a lower correlation than that of the former in the significance test. Therefore, it can be concluded that watershed lag, Lg, is more closely related with the such watersheds characteristics as watershed area and length of main stream in the small watersheds. Empirical formula for the peak discharge per unit area, qp, ㎥/sec/$\textrm{km}^2$, was derived as qp=10-0.389-0.0424Lg with a high significance, r=0.91. This indicates that the peak discharge per unit area of the unitgraph is in inverse proportion to the watershed lag time. 8. The base length of the unitgraph, Tb, in connection with the watershed lag, Lg, was extra.essed as {{{{ { T}_{ b} =1.14+0.564( { Lg} over {24 } )}}}} which has defined with a high significance. 9. For the derivation of IUH by applying linear conceptual model, the storage constant, K, with the length of main stream, L, and slopes, S, was adopted as {{{{K=0.1197( {L } over { SQRT {S } } )}}}} with a highly significant correlation coefficient, 0.90. Gamma function argument, N, derived with such watershed characteristics as watershed area, A, river length, L, centroid distance of the basin of the watershed area, Lca, and slopes, S, was found to be N=49.2 A1.481L-2.202 Lca-1.297 S-0.112 with a high significance having the F value, 4.83, through analysis of variance. 10. According to the linear conceptual model, Formular established in relation to the time distribution, Peak discharge and time to peak discharge for instantaneous Unit Hydrograph when unit effective rainfall of unitgraph and dimension of watershed area are applied as 10mm, and $\textrm{km}^2$ respectively are as follows; Time distribution of IUH {{{{u(0, t)= { 2.78A} over {K GAMMA (N) } { e}^{-t/k } { (t.K)}^{N-1 } }}}} (㎥/sec) Peak discharge of IUH {{{{ {u(0, t) }_{max } = { 2.78A} over {K GAMMA (N) } { e}^{-(N-1) } { (N-1)}^{N-1 } }}}} (㎥/sec) Time to peak discharge of IUH tp=(N-1)K (hrs) 11. Through mathematical analysis in the recession curve of Hydrograph, It was confirmed that empirical formula of Gamma function argument, N, had connection with recession constant, Kl, peak discharge, QP, and time to peak discharge, tp, as {{{{{ K'} over { { t}_{ p} } = { 1} over {N-1 } - { ln { t} over { { t}_{p } } } over {ln { Q} over { { Q}_{p } } } }}}} where {{{{K'= { 1} over { { lnK}_{1 } } }}}} 12. Linking the two, empirical formulars for storage constant, K, and Gamma function argument, N, into closer relations with each other, derivation of unit hydrograph for the ungaged small watersheds can be established by having formulars for the time distribution and peak discharge of IUH as follows. Time distribution of IUH u(0, t)=23.2 A L-1S1/2 F(N, K, t) (㎥/sec) where {{{{F(N, K, t)= { { e}^{-t/k } { (t/K)}^{N-1 } } over { GAMMA (N) } }}}} Peak discharge of IUH) u(0, t)max=23.2 A L-1S1/2 F(N) (㎥/sec) where {{{{F(N)= { { e}^{-(N-1) } { (N-1)}^{N-1 } } over { GAMMA (N) } }}}} 13. The base length of the Time-Area Diagram for the IUH was given by {{{{C=0.778 { ( { LLca} over { SQRT { S} } )}^{0.423 } }}}} with correlation coefficient, 0.85, which has an indication of the relations to the length of main stream, L, centroid distance of the basin of the watershed area, Lca, and slopes, S. 14. Relative errors in the peak discharge of the IUH by using linear conceptual model and IUH by routing showed to be 2.5 and 16.9 percent respectively to the peak of observed unitgraph. Therefore, it confirmed that the accuracy of IUH using linear conceptual model was approaching more closely to the observed unitgraph than that of the flood routing in the small watersheds.

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

• Journal of Intelligence and Information Systems
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• v.25 no.2
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• pp.39-55
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• 2019

Recently banks and large financial institutions have introduced lots of Robo-Advisor products. Robo-Advisor is a Robot to produce the optimal asset allocation portfolio for investors by using the financial engineering algorithms without any human intervention. Since the first introduction in Wall Street in 2008, the market size has grown to 60 billion dollars and is expected to expand to 2,000 billion dollars by 2020. Since Robo-Advisor algorithms suggest asset allocation output to investors, mathematical or statistical asset allocation strategies are applied. Mean variance optimization model developed by Markowitz is the typical asset allocation model. The model is a simple but quite intuitive portfolio strategy. For example, assets are allocated in order to minimize the risk on the portfolio while maximizing the expected return on the portfolio using optimization techniques. Despite its theoretical background, both academics and practitioners find that the standard mean variance optimization portfolio is very sensitive to the expected returns calculated by past price data. Corner solutions are often found to be allocated only to a few assets. The Black-Litterman Optimization model overcomes these problems by choosing a neutral Capital Asset Pricing Model equilibrium point. Implied equilibrium returns of each asset are derived from equilibrium market portfolio through reverse optimization. The Black-Litterman model uses a Bayesian approach to combine the subjective views on the price forecast of one or more assets with implied equilibrium returns, resulting a new estimates of risk and expected returns. These new estimates can produce optimal portfolio by the well-known Markowitz mean-variance optimization algorithm. If the investor does not have any views on his asset classes, the Black-Litterman optimization model produce the same portfolio as the market portfolio. What if the subjective views are incorrect? A survey on reports of stocks performance recommended by securities analysts show very poor results. Therefore the incorrect views combined with implied equilibrium returns may produce very poor portfolio output to the Black-Litterman model users. This paper suggests an objective investor views model based on Support Vector Machines(SVM), which have showed good performance results in stock price forecasting. SVM is a discriminative classifier defined by a separating hyper plane. The linear, radial basis and polynomial kernel functions are used to learn the hyper planes. Input variables for the SVM are returns, standard deviations, Stochastics %K and price parity degree for each asset class. SVM output returns expected stock price movements and their probabilities, which are used as input variables in the intelligent views model. The stock price movements are categorized by three phases; down, neutral and up. The expected stock returns make P matrix and their probability results are used in Q matrix. Implied equilibrium returns vector is combined with the intelligent views matrix, resulting the Black-Litterman optimal portfolio. For comparisons, Markowitz mean-variance optimization model and risk parity model are used. The value weighted market portfolio and equal weighted market portfolio are used as benchmark indexes. We collect the 8 KOSPI 200 sector indexes from January 2008 to December 2018 including 132 monthly index values. Training period is from 2008 to 2015 and testing period is from 2016 to 2018. Our suggested intelligent view model combined with implied equilibrium returns produced the optimal Black-Litterman portfolio. The out of sample period portfolio showed better performance compared with the well-known Markowitz mean-variance optimization portfolio, risk parity portfolio and market portfolio. The total return from 3 year-period Black-Litterman portfolio records 6.4%, which is the highest value. The maximum draw down is -20.8%, which is also the lowest value. Sharpe Ratio shows the highest value, 0.17. It measures the return to risk ratio. Overall, our suggested view model shows the possibility of replacing subjective analysts's views with objective view model for practitioners to apply the Robo-Advisor asset allocation algorithms in the real trading fields.