A robust support vector regression with exact predictors and fuzzy responses

Processing experimental data with uncertainty is a huge challenge for robust regression modeling and high-accuracy data forecasting. The objective of the present study is the development of a robust support vector regression model for processing observed data of independent variables containing polyhedral perturbation and achievement of high forecasting precision. Firstly, the conception of the data collection of polyhedral perturbation is given and analyzed. Secondly, a novel robust support vector regression model is constructed by replacing the original independent variables in a linear support vector regression model with the independent variables containing polyhedral perturbation. Thirdly, the novel robust linear support vector regression method is also expanded to the non-linear regression model. Both the two models are validated by the linear and nonlinear numerical regression experiments. Comparison of the experimental results show that the proposed method provide more accurate predictions than the traditional regression method for processing data with polyhedral perturbation.

The characteristic of the fuzzy regression model is to enwrap all the given samples. An interval of fuzzy regression model is created by considering how far a sample is from the central values. That means when samples are widely scattered the size of an interval of the fuzzy model is widened. That is, the fuzziness of the fuzzy regression model is decided by the range of sample distribution. Therefore, many research results on a fuzzy regression model in order to describe the possibility of the target system have been reported. We have proposed two fuzzy robust regression models which remove influences of improper data such as unusual data and outliers. In this paper, we describe the model building of our fuzzy robust regressions by removing influences of improper data.

Fuzzy regression analysis is an important regression analysis method to predict uncertain information in the real world. In this paper, the input data are crisp with randomness; the output data are trapezoid fuzzy number, and three different risk preferences and chaos optimization algorithm are introduced to establish fuzzy regression model. On the basis of the principle of the minimum total spread between the observed and the estimated values, risk-neutral, risk-averse, and risk-seeking fuzzy regression model are developed to obtain the parameters of fuzzy linear regression model. Chaos optimization algorithm is used to determine the digital characteristic of random variables. The mean absolute percentage error and variance of errors are adopted to compare the modeling results. A stock rating case is used to evaluate the fuzzy regression models. The comparisons with five existing methods show that our proposed method has satisfactory performance.

Advances in information technology have led to the proliferation of data in the fields of finance, energy, and economics. Unforeseen elements can cause data to be contaminated by noise and outliers. In this study, a robust online support vector regression algorithm based on a non-convex asymmetric loss function is developed to handle the regression of noisy dynamic data streams. Inspired by pinball loss, a truncated ε-insensitive pinball loss (TIPL) is proposed to solve the problems caused by heavy noise and outliers. A TIPL-based online support vector regression algorithm (TIPOSVR) is constructed under the regularization framework, and the online gradient descent algorithm is implemented to execute it. Experiments are performed using synthetic datasets, UCI datasets, and real datasets. The results of the investigation show that in the majority of cases, the proposed algorithm is comparable, or even superior, to the comparison algorithms in terms of accuracy and robustness on datasets with different types of noise.

Fuzzy regression based on asymmetric support vector machines

<div>An accurate Unmanned Aerial System (UAS) Flight Dynamics Model (FDM) allows us to design its efficient controller in early development phases and to increase safety while reducing costs. Flight tests are normally conducted for a pre-established number of flight conditions, and then mathematical methods are used to obtain the FDM for the entire flight envelope. For our UAS-S4 Ehecatl, 216 local FDMs corresponding to different flight conditions were utilized to create its Local Linear Scheduled Flight Dynamics Model (LLS-FDM). The initial flight envelope data containing 216 local FDMs was further augmented using interpolation and extrapolation methodologies, thus increasing the number of trimmed local FDMs of up to 3,642. Relying on this augmented dataset, the Support Vector Machine (SVM) methodology was used as a benchmarking regression algorithm due to its excellent performance when training samples could not be separated linearly. The trained Support Vector Regression (SVR) predicted the FDM for the entire flight envelope. Although the SVR-FDM showed excellent performance, it remained vulnerable to adversarial attacks. Hence, we modified it using an adversarial retraining defense algorithm by transforming it into a Robust SVR-FDM. For validation studies, the quality of predicted UAS-S4 FDM was evaluated based on the Root Locus diagram. The closeness of predicted eigenvalues to the original eigenvalues confirmed the high accuracy of the UAS-S4 SVR-FDM. The SVR prediction accuracy was evaluated at 216 flight conditions, for different numbers of neighbors, and a variety of kernel functions were also considered. In addition, the regression performance was analyzed based on the step response of state variables in the closed-loop control architecture. The SVR-FDM provided the shortest rise time and settling time, but it failed when adversarial attacks were imposed on the SVR. The Robust-SVR-FDM step response properties showed that it could provide more accurate results than the LLS-FDM approach while protecting the controller from adversarial attacks.</div>

Combining nonlinear programming and least squares method, this paper proposes a two-stage mixed fuzzy linear regression model based on distance criterion. In order to ensure that the error of fuzzy estimated value and fuzzy observation value can be reduced when the explanatory variable is a clear number, the fuzzy regression model has a fuzzy adjustment term in addition to the clear regression coefficient. Firstly, based on the distance criterion, a nonlinear programming model is established to obtain the regression coefficient of the explanatory variables, and the fuzzy adjustment term is obtained based on the distance criterion and the least square method. Compared with the existing methods that cannot determine the sign of the coefficient, the method can accurately determine the sign of the regression coefficient. Finally, it is verified that the model has smaller mean square error and higher reliability than other models through a large number of numerical experiments and practical examples.

This study presents an integrated fuzzy regression and time-series technique to estimate and predict electricity demand. Furthermore, it is difficult to model uncertain behaviour of energy consumption with only conventional time-series and fuzzy regression, which could be an ideal substitute for such cases. After reviewing various fuzzy regression models and studying their advantages and shortcomings, the best model is selected. Also, the impact of data preprocessing and post-processing on the fuzzy regression performance is to study and to show that this method does not contribute to the efficiency of the model. In addition, another unique feature of this study is utilisation of autocorrelation function to define input variables versus trial and error method. At last, the comparison of actual data with fuzzy regression and ARIMA model, using Granger?Newbold test, is achieved. Monthly electricity consumption of Iran from 1995 to 2005 is considered as the case of this study.

A knowledge management (KM) system has a different schema that one of them has been studied in the present study. One of version of KM is based on artificial intelligence (AI) methods. KM based on AI has been investigated in the present work based on natural gas consumption estimation domain. Developing accurate and flexible model to natural gas consumption estimation is a strategic step in policy and decision-making process in energy sector. This paper provides a stage algorithm during that it gains optimal fuzzy regression model for studding natural gas consumption in sixteen countries according to data in years 1989 till 2007. Different countries have selected from Africa, America, Asia, Europe and Middle East based on high, middle and low GDP index and for every one of them nine fuzzy regression models have executed and the results and error of each model have calculated. Preprocess has been done on the initial data to gain better results which the min-max method has been used for this purpose. Two criterions have been used to determining suitable and appropriate fuzzy regression model in each country. Firstly, fuzzy regression models with MAPE value below 10 is deleted from the assessment and remained fuzzy regression models are compared with ANOVA. Upon logic that given algorithm sketches for some countries none of used models are proper while for other countries optimal model is gained in first or second filter of algorithm. To show the applicability and superiority of the proposed flexible Fuzzy regression model the data for oil consumption in Japan, Thailand, Bangladesh from Asia and Norway, Italy, Bulgaria from Europe and Qatar, Iran, Iraq from Middle East and The united state, Mexico, Bolivia from North America and Libya, Tunisia, Nigeria from Africa during 1989 to 2007 are used.

Pipelines are a nonlinear and complex component to transfer fluid or gas from one place to another. From economic and environmental points of view, the safety of transmission lines is incredibly important. Furthermore, condition monitoring and effective data analysis are important to leak detection and localization in pipelines. Thus, an effective technique for leak detection and localization is presented in this study. The proposed scheme has four main steps. First, the learning autoregressive technique is selected to approximate the flow signal under normal conditions and extract the mathematical state-space formulation with uncertainty estimations using a combination of robust autoregressive and support vector regression techniques. In the next step, the intelligence-based learning observer is designed using a combination of the robust learning backstepping method and a fuzzy-based technique. The learning backstepping algorithm is the main part of the algorithm that determines the leak estimation. After estimating the signals, in the third step, their classification is performed by the support vector machine algorithm. Finally, to find the size and position of the leak, the multivariable backstepping algorithm is recommended. The effectiveness of the proposed learning control algorithm is analyzed using both experimental and simulation setups.

This study aims to develop an intelligent algorithm by integrating robust independent component analysis (RobustICA) and support vector machines (SVMs). According to different characteristics of source signals including real or complex, super-Gaussian or sub-Gaussian and pollution of signal noise, a new method for fault detection that uses RobustICA based on kurtosis is put forward in this paper. The basic idea of the approach is to use RobustICA optimized by iterative technique to separate independent components which drive a process after wavelet de-noising of the original data. On this basis, statistics are established for fault detection and the kernel density estimation is used in calculating the confidence limit of statistics. After that, support vector machines (SVMs) is utilized to classify the faults. The simulation results of signal experiment and TE model clearly show the effectiveness and advantages of the proposed method in comparison to FastICA method.

This study aims to provide useful information for the conservation and management of Brachydiplax chalybea flavovittata (Ris, 1911) (Insecta: Odonata), which is a climate-sensitive biological indicator species, and to develop a more accurate and optimal distribution model that aligns with the research objectives. To achieve this, we intend to evaluate two factors that influence the prediction accuracy of the distribution model. In order to compare the prediction accuracy of the models based on biased location data in a specific region and based on the multicollinearity of environmental variables known as bioclimatic variables, the confirmed habitat locations of B. chalybea flavovittata were collected from the GBIF database, and 19 biological climate variables used as environmental variables were collected from the Worldclim database. The bias of the location data was examined using four types of data selected with a certain distance between the location data. The multicollinearity of the environmental variables was assessed using the Variation Inflation Factor (VIF). Preprocessed data were applied to seven species distribution models, and the prediction accuracy of the models was compared and analyzed using three evaluation metrics (Kappa, TSS, AUC). Among machine learning and regression models, seven distribution models were used for comparison. The machine learning models included Boosted Regression Trees (BRT), Random Forest (RF), Support Vector Machine (SVM), Classification and Regression Trees (CART), and MaxEnt, while the regression models included Generalized Linear Models (GLM) and Multivariate Adaptive Regression Splines (MARS). Overall, the prediction accuracy of the models was better explained by the Random Forest (RF) model, which is a machine learning method that better captures the complex relationship between species and environmental variables, compared to other models. The bias of location data, which is more commonly surveyed in easily accessible areas, affected the prediction accuracy in all models, while multicollinearity varied depending on the model. This study is expected to serve as fundamental guidance for developing an optimal species distribution model that aligns with the research objectives of species conservation and it can be utilized as foundational data for effective management of wildlife habitat in national parks.

Robust support vector regression in the primal

Construction of robust regression learning models to fit training data corrupted by noise is an important and challenging research problem in machine learning. It is well-known that loss functions play an important role in reducing the effect of noise present in the input data. With the objective of obtaining a robust regression model, motivated by the link between the pinball loss and quantile regression, a novel squared pinball loss twin support vector machine for regression (SPTSVR) is proposed in this work. Further with the introduction of a regularization term, our proposed model solves a pair of strongly convex minimization problems having unique solutions by simple functional iterative method. Experiments were performed on synthetic datasets with different noise models and on real world datasets and those results were compared with support vector regression (SVR), least squares support vector regression (LS-SVR) and twin support vector regression (TSVR) methods. The comparative results clearly show that our proposed SPTSVR is an effective and a useful addition in the machine learning literature.

A novel hybrid multivariate nonlinear grey model for forecasting the traffic-related emissions