• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.533-545
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• 2017

Quantile regression models provide a variety of useful statistical information by estimating the conditional quantile function of the response variable. However, the traditional linear quantile regression model can lead to the distorted and incorrect results when analysing real data having a nonlinear relationship between the explanatory variables and the response variables. Furthermore, as the complexity of the data increases, it is required to analyse multiple response variables simultaneously with more sophisticated interpretations. For such reasons, we propose a multivariate quantile regression tree model. In this paper, a new split variable selection algorithm is suggested for a multivariate regression tree model. This algorithm can select the split variable more accurately than the previous method without significant selection bias. We investigate the performance of our proposed method with both simulation and real data studies.

• Journal of Advanced Marine Engineering and Technology
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• v.40 no.2
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• pp.138-145
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• 2016

This paper proposes an improved tabu search method for subset selection in multiple linear regression models. Variable selection is a vital combinatorial optimization problem in multivariate statistics. The selection of the optimal subset of variables is necessary in order to reliably construct a multiple linear regression model. Its applications widely range from machine learning, timeseries prediction, and multi-class classification to noise detection. Since this problem has NP-complete nature, it becomes more difficult to find the optimal solution as the number of variables increases. Two typical metaheuristic methods have been developed to tackle the problem: the tabu search algorithm and hybrid genetic and simulated annealing algorithm. However, these two methods have shortcomings. The tabu search method requires a large amount of computing time, and the hybrid algorithm produces a less accurate solution. To overcome the shortcomings of these methods, we propose an improved tabu search algorithm to reduce moves of the neighborhood and to adopt an effective move search strategy. To evaluate the performance of the proposed method, comparative studies are performed on small literature data sets and on large simulation data sets. Computational results show that the proposed method outperforms two metaheuristic methods in terms of the computing time and solution quality.

• Geomechanics and Engineering
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• v.33 no.3
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• pp.279-289
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• 2023

Brittleness index (BI) is an important property of rocks because it is a good index to predict rockburst. Due to its importance, several empirical and soft computing (SC) models have been proposed in the literature based on the punch penetration test (PPT) results. These models are very important as there is no clear-cut experimental means for measuring BI asides the PPT which is very costly and time consuming to perform. This study used a novel Multivariate Adaptive regression spline (MARS), M5P, and white-box ANN to predict the BI of rocks using the available data in the literature for an improved BI prediction. The rock density, uniaxial compressive strength (σ_c) and tensile strength (σ_t) were used as the input parameters into the models while the BI was the targeted output. The models were implemented in the MATLAB software. The results of the proposed models were compared with those from existing multilinear regression, linear and nonlinear particle swarm optimization (PSO) and genetic algorithm (GA) based models using similar datasets. The coefficient of determination (R²), adjusted R² (Adj R²), root-mean squared error (RMSE) and mean absolute percentage error (MAPE) were the indices used for the comparison. The outcomes of the comparison revealed that the proposed ANN and MARS models performed better than the other models with R² and Adj R² values above 0.9 and least error values while the M5P gave similar performance to those of the existing models. Weight partitioning method was also used to examine the percentage contribution of model predictors to the predicted BI and tensile strength was found to have the highest influence on the predicted BI.

• Structural Engineering and Mechanics
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• v.60 no.3
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• pp.471-488
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• 2016

This study predicts the strength of rotary brace damper by analyzing a new set of probabilistic models using the usual method of multiple linear regressions (MLR) and advanced machine-learning methods of multivariate adaptive regression splines (MARS), Rotary brace damper can be easily assembled with high energy-dissipation capability. To investigate the behavior of this damper in structures, a steel frame is modeled with this device subjected to monotonic and cyclic loading. Several response parameters are considered, and the performance of damper in reducing each response is evaluated. MLR and MARS methods were used to predict the strength of this damper. Displacement was determined to be the most effective parameter of damper strength, whereas the thickness did not exhibit any effect. Adding thickness parameter as inputs to MARS and MLR models did not increase the accuracies of the models in predicting the strength of this damper. The MARS model with a root mean square error (RMSE) of 0.127 and mean absolute error (MAE) of 0.090 performed better than the MLR model with an RMSE of 0.221 and MAE of 0.181.

• Journal of Environmental Health Sciences
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• v.42 no.4
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• pp.280-292
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• 2016

Objectives: The objective of this study was to build COD regression models for the Han River and evaluate water quality. Methods: Water quality data sets for the dry season (as of January) during a four-year period (2012-2015) were collected from the database of the Han River automatic water quality monitoring stations. Statistical techniques, including combined genetic algorithm-multiple linear regression (GA-MLR) were used to build five-descriptor COD models. Multivariate statistical techniques such as principal component analysis (PCA) and cluster analysis (CA) are useful tools for extracting meaningful information. Results: The $r^2$ of the best COD models provided significant high values (> 0.8) between 2012 and 2015. Total organic carbon (TOC) was a surrogate indicator for COD (as COD/TOC) with high reliability ($r^2=0.63$ in 2012, $r^2=0.75$ for 2013, $r^2=0.79$ for 2014 and $r^2=0.85$ for 2015). The ratios of COD/TOC were calculated as 2.08 in 2012, 1.79 in 2013, 1.52 and 1.45 in 2015, indicating that biodegradability in the water body of the Han River was being sustained, thereby further improving water quality. The BOD/COD ratio supported these findings. The cluster analysis revealed higher annual levels of microorganisms and phosphorous at stations along the Hangang-Seoul and Hantangang areas. Nevertheless, the overall water quality over the last four years showed an observable trend toward continuous improvement. These findings also suggest that non-point pollution control strategies should consider the influence of upstreams and downstreams to protect water quality in the Han River. Conclusion: This data analysis procedure provided an efficient and comprehensive tool to interpret complex water quality data matrices. Results from a trend analysis provided much important information about sources and parameters for Han River water quality management.

• Journal of the Korean Data and Information Science Society
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• v.20 no.3
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• pp.577-585
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• 2009

So far in a nonparametric regression model one of the interesting problems is estimating the error variance. In this paper we propose an estimator of the mean of the squared functions which is the numerator of SNR (Signal to Noise Ratio). To estimate SNR, the mean of the squared function should be firstly estimated. Our focus is on estimating the amplitude, that is the mean of the squared functions, in a nonparametric regression using a simple linear regression model with the quadratic form of observations as the dependent variable and the function of a lag as the regressor. Our method can be extended to nonparametric regression models with multivariate functions on unequally spaced design points or clustered designed points.

• Korean Journal of Agricultural Science
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• v.38 no.4
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• pp.761-767
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• 2011

The objective of this study was to predict total bacteria count of pork meats by using the portable electronic nose systems developed throughout two stages of the prototypes. Total bacteria counts were measured for pork meats stored at $4^{\circ}C$ for 21days and compared with the signals of the electronic nose systems. PLS(Partial least square), PCR (Principal component regression), MLR (Multiple linear regression) models were developed for the prediction of total bacteria count of pork meats. The coefficient of determination ($R_p{^2}$) and root mean square error of prediction (RMSEP) for the models were 0.789 and 0.784 log CFU/g with the 1st system for the pork loin, 0.796 and 0.597 log CFU/g with the 2nd system for the pork belly, and 0.661 and 0.576 log CFU/g with the 2nd system for the pork loin respectively. The results show that the developed electronic system has potential to predict total bacteria count of pork meats.

• Geomechanics and Engineering
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• v.30 no.3
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• pp.259-272
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• 2022

Rockburst is a dynamic, multivariate, and non-linear phenomenon that occurs in underground mining and civil engineering structures. Predicting rockburst is challenging since conventional models are not standardized. Hence, machine learning techniques would improve the prediction accuracies. This study describes decision based uncertainty models to predict rockburst in underground engineering structures using gradient boosting algorithms (GBM). The model input variables were uniaxial compressive strength (UCS), uniaxial tensile strength (UTS), maximum tangential stress (MTS), excavation depth (D), stress ratio (SR), and brittleness coefficient (BC). Several models were trained using different combinations of the input variables and a 3-fold cross-validation resampling procedure. The hyperparameters comprising learning rate, number of boosting iterations, tree depth, and number of minimum observations were tuned to attain the optimum models. The performance of the models was tested using classification accuracy, Cohen's kappa coefficient (k), sensitivity and specificity. The best-performing model showed a classification accuracy, k, sensitivity and specificity values of 98%, 93%, 1.00 and 0.957 respectively by optimizing model ROC metrics. The most and least influential input variables were MTS and BC, respectively. The partial dependence plots revealed the relationship between the changes in the input variables and model predictions. The findings reveal that GBM can be used to anticipate rockburst and guide decisions about support requirements before mining development.

• The Korean Journal of Applied Statistics
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• v.21 no.6
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• pp.923-932
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• 2008

We are likely to face complex multivariate data which can be characterized by having a non-trivial correlation structure. For instance, omitted covariates may simultaneously affect more than one count in clustered data; hence, the modeling of the correlation structure is important for the efficiency of the estimator and the computation of correct standard errors, i.e., valid inference. A standard way to insert dependence among counts is to assume that they share some common unobservable variables. For this assumption, we fitted correlated random effect models considering multilevel model. Estimation was carried out by adopting the semiparametric approach through a finite mixture EM algorithm without parametric assumptions upon the random coefficients distribution.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.1
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• pp.216-238
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• 2023

In intelligent transportation systems, traffic management is an important task. The accurate forecasting of traffic characteristics like flow, congestion, and density is still active research because of the non-linear nature and uncertainty of the spatiotemporal data. Inclement weather, such as rain and snow, and other special events such as holidays, accidents, and road closures have a significant impact on driving and the average speed of vehicles on the road, which lowers traffic capacity and causes congestion in a widespread manner. This work designs a model for multivariate short-term traffic congestion prediction using SLSTM_AE-BiLSTM. The proposed design consists of a Bidirectional Long Short Term Memory(BiLSTM) network to predict traffic flow value and a Convolutional Neural network (CNN) model for detecting the congestion status. This model uses spatial static temporal dynamic data. The stacked Long Short Term Memory Autoencoder (SLSTM AE) is used to encode the weather features into a reduced and more informative feature space. BiLSTM model is used to capture the features from the past and present traffic data simultaneously and also to identify the long-term dependencies. It uses the traffic data and encoded weather data to perform the traffic flow prediction. The CNN model is used to predict the recurring congestion status based on the predicted traffic flow value at a particular urban traffic network. In this work, a publicly available Caltrans PEMS dataset with traffic parameters is used. The proposed model generates the congestion prediction with an accuracy rate of 92.74% which is slightly better when compared with other deep learning models for congestion prediction.