Asymptotically Optimal Choice of ε-Loss for Support Vector Machines

Property Prediction and Structural Feature Extraction of Polyimide Materials Based on Machine Learning

The construction of material prediction models using machine learning algorithms can aid in the polyimide structural design and screening of materials as well as accelerate the development of new materials. There is a lack of research on predicting the optical properties of polyimide materials and the interpretation of the structural features. Here, we collected 652 polyimide molecular structures and used seven popular machine learning algorithms to predict the glass transition temperature and cut-off wavelength of polyimide materials and extract key feature information of repeating unit structures. The results showed that the root mean square error of the glass transition temperature prediction model was 33.92 °C, and the correlation coefficient was 0.861. The root mean square error of the cut-off wavelength prediction model was 17.18 nm, and the correlation coefficient was 0.837. The elasticity of the molecular structure was also found to be the key factor affecting glass transition temperature, and the presence and location of heterogeneous atoms had a significant effect on the cut-off wavelengths. Finally, eight polyimide materials were synthesized to test the accuracy of the prediction models, and the experimental characterization values agreed with the predicted values. The results would contribute to the development of polyimide structural design and materials preparation for flexible display.

Modelling monthly mean air temperature using artificial neural network, adaptive neuro-fuzzy inference system and support vector regression methods: A case of study for Turkey

The accurate modelling and prediction of air temperature values is an exceptionally important meteorological variable that affects in many areas. The present study is aimed at developing models for the prediction of monthly mean air temperature values in Turkey using ANN, ANFIS and SVM_r methods. In developing the models, the monthly data derived from eight stations of the TSMS for the 1963-2015 period were used, including latitude, longitude, elevation, month, and minimum, maximum and mean air temperatures. The performances of the ANN, ANFIS and SVM_r models were compared using R², MSE, MAPE and RRMSE. In order to verify the differences between the predicted temperature values provided by the ANN, ANFIS and SVM_r models and the observed temperature values derived from the stations, a t-test analysis was conducted, and the best ANN, ANFIS and SVM_r models were determined according to the statistical performance values. These models were then used to make air temperature predictions for the cities. Manova was carried out to determine the effects of the differences temperature predictions and RRMSE values of the models. Generally, the statistical performance values of the ANFIS models were found to be slightly better than those of the ANN and SVM_r models.

Online Learning ARMA Controllers With Guaranteed Closed-Loop Stability

This paper presents a novel online block adaptive learning algorithm for autoregressive moving average (ARMA) controller design based on the real data measured from the plant. The method employs ARMA input-output models both for the plant and the resulting closed-loop system. In a sliding window, the plant model parameters are identified first offline using a supervised learning algorithm minimizing an ε -insensitive and regularized identification error, which is the window average of the distances between the measured plant output and the model output for the input provided by the controller. The optimal controller parameters are then determined again offline for another sliding window as the solution to a constrained optimization problem, where the cost is the ε -insensitive and regularized output tracking error and the constraints that are linear inequalities of the controller parameters are imposed for ensuring the closed-loop system to be Schur stable. Not only the identification phase but also the controller design phase uses the input-output samples measured from the plant during online learning. In the developed online controller design method, the controller parameters can always be kept in a parameter region providing Schur stability for the closed-loop system. The ε -insensitiveness provides robustness against disturbances, so does the regularization better generalization performance in the identification and the control. The method is tested on benchmark plants, including the inverted pendulum and dc motor models. The method is also tested on an emulated and also a real dc motor by online block adaptive learning ARMA controllers, in particular, Proportional-Integral-Derivative controllers.

Hierarchical approach for multiscale support vector regression

Support vector regression (SVR) is based on a linear combination of displaced replicas of the same function, called a kernel. When the function to be approximated is nonstationary, the single kernel approach may be ineffective, as it is not able to follow the variations in the frequency content in the different regions of the input space. The hierarchical support vector regression (HSVR) model presented here aims to provide a good solution also in these cases. HSVR consists of a set of hierarchical layers, each containing a standard SVR with Gaussian kernel at a given scale. Decreasing the scale layer by layer, details are incorporated inside the regression function. HSVR has been widely applied to noisy synthetic and real datasets and it has shown the ability in denoising the original data, obtaining an effective multiscale reconstruction of better quality than that obtained by standard SVR. Results also compare favorably with multikernel approaches. Furthermore, tuning the SVR configuration parameters is strongly simplified in the HSVR model.

A division algebraic framework for multidimensional support vector regression

In this paper, division algebras are proposed as an elegant basis upon which to extend support vector regression (SVR) to multidimensional targets. Using this framework, a multitarget SVR called epsilon(Z)-SVR is proposed based on an epsilon-insensitive loss function that is independent of the coordinate system or basis used. This is developed to dual form in a manner that is analogous to the standard epsilon-SVR. The epsilon(H)-SVR is compared and contrasted with the least-square SVR (LS-SVR), the Clifford SVR (C-SVR), and the multidimensional SVR (M-SVR). Three practical applications are considered: namely, 1) approximation of a complex-valued function; 2) chaotic time-series prediction in 3-D; and 3) communication channel equalization. Results show that the epsilon(H)-SVR performs significantly better than the C-SVR, the LS-SVR, and the M-SVR in terms of mean-squared error, outlier sensitivity, and support vector sparsity.

Experimentally optimal nu in support vector regression for different noise models and parameter settings

In Support Vector (SV) regression, a parameter nu controls the number of Support Vectors and the number of points that come to lie outside of the so-called epsilon-insensitive tube. For various noise models and SV parameter settings, we experimentally determine the values of nu that lead to the lowest generalization error. We find good agreement with the values that had previously been predicted by a theoretical argument based on the asymptotic efficiency of a simplified model of SV regression. As a side effect of the experiments, valuable information about the generalization behavior of the remaining SVM parameters and their dependencies is gained. The experimental findings are valid even for complex 'real-world' data sets. Based on our results on the role of the nu-SVM parameters, we discuss various model selection methods.