Fuzzy identification of nonlinear dynamic system based on selection of important input variables

Input variables selection(IVS) is proved to be pivotal in nonlinear dynamic system modeling. In order to optimize the model of the nonlinear dynamic system, a fuzzy modeling method for determining the premise structure by selecting important inputs of the system is studied. Firstly, a simplified two stage fuzzy curves method is proposed, which is employed to sort all possible inputs by their relevance with outputs, select the important input variables of the system and identify the structure.Secondly, in order to reduce the complexity of the model, the standard fuzzy c-means clustering algorithm and the recursive least squares algorithm are used to identify the premise parameters and conclusion parameters, respectively. Then, the effectiveness of IVS is verified by two well-known issues. Finally, the proposed identification method is applied to a realistic variable load pneumatic system. The simulation experiments indi cate that the IVS method in this paper has a positive influence on the approximation performance of the Takagi-Sugeno(T-S) fuzzy modeling.

Incorporating empirical knowledge into data-driven variable selection for quantitative analysis of coal ash content by laser-induced breakdown spectroscopy

Laser-induced breakdown spectroscopy(LIBS)has become a widely used atomic spectroscopic technique for rapid coal analysis.However,the vast amount of spectral information in LIBS contains signal uncertainty,which can affect its quantification performance.In this work,we propose a hybrid variable selection method to improve the performance of LIBS quantification.Important variables are first identified using Pearson's correlation coefficient,mutual information,least absolute shrinkage and selection operator(LASSO)and random forest,and then filtered and combined with empirical variables related to fingerprint elements of coal ash content.Subsequently,these variables are fed into a partial least squares regression(PLSR).Additionally,in some models,certain variables unrelated to ash content are removed manually to study the impact of variable deselection on model performance.The proposed hybrid strategy was tested on three LIBS datasets for quantitative analysis of coal ash content and compared with the corresponding data-driven baseline method.It is significantly better than the variable selection only method based on empirical knowledge and in most cases outperforms the baseline method.The results showed that on all three datasets the hybrid strategy for variable selection combining empirical knowledge and data-driven algorithms achieved the lowest root mean square error of prediction(RMSEP)values of 1.605,3.478 and 1.647,respectively,which were significantly lower than those obtained from multiple linear regression using only 12 empirical variables,which are 1.959,3.718 and 2.181,respectively.The LASSO-PLSR model with empirical support and 20 selected variables exhibited a significantly improved performance after variable deselection,with RMSEP values dropping from 1.635,3.962 and 1.647 to 1.483,3.086 and 1.567,respectively.Such results demonstrate that using empirical knowledge as a support for datadriven variable selection can be a viable approach to improve the accuracy and reliability of LIBS quantification.

Sufficient variable selection of high dimensional nonparametric nonlinear systems based on Fourier spectrum of density-weighted derivative

The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables.For a high dimensional nonparametric nonlinear system,however,identifying whether a variable contributes or not is not easy.Therefore,based on the Fourier spectrum of densityweighted derivative,one novel variable selection approach is developed,which does not suffer from the dimensionality curse and improves the identification accuracy.Furthermore,a necessary and sufficient condition for testing a variable whether it contributes or not is provided.The proposed approach does not require strong assumptions on the distribution,such as elliptical distribution.The simulation study verifies the effectiveness of the novel variable selection algorithm.

Online quantitative analysis of soluble solids content in navel oranges using visible-nearinfrared spectroscopy and variable selection methods

Variable selection is applied widely for visible-near infrared(Vis-NIR)spectroscopy analysis of internal quality in fruits.Different spectral variable selection methods were compared for online quantitative analysis of soluble solids content(SSC)in navel oranges.Moving window partial least squares(MW-PLS),Monte Carlo uninformative variables elimination(MC-UVE)and wavelet transform(WT)combined with the MC-UVE method were used to select the spectral variables and develop the calibration models of online analysis of SSC in navel oranges.The performances of these methods were compared for modeling the Vis NIR data sets of navel orange samples.Results show that the WT-MC-UVE methods gave better calibration models with the higher correlation cofficient(r)of 0.89 and lower root mean square error of prediction(RMSEP)of 0.54 at 5 fruits per second.It concluded that Vis NIR spectroscopy coupled with WT-MC-UVE may be a fast and efective tool for online quantitative analysis of SSC in navel oranges.

Quantitative analysis of the content of nitrogen and sulfur in coal based on laserinduced breakdown spectroscopy: effects of variable selection

Coal is a crucial fossil energy in today’s society,and the detection of sulfir(S) and nitrogen(N)in coal is essential for the evaluation of coal quality.Therefore,an efficient method is needed to quantitatively analyze N and S content in coal,to achieve the purpose of clean utilization of coal.This study applied laser-induced breakdown spectroscopy(LIBS) to test coal quality,and combined two variable selection algorithms,competitive adaptive reweighted sampling(CARS) and the successive projections algorithm(SPA),to establish the corresponding partial least square(PLS) model.The results of the experiment were as follows.The PLS modeled with the full spectrum of 27,620 variables has poor accuracy,the coefficient of determination of the test set(R^2 P) and root mean square error of the test set(RMSEP) of nitrogen were 0.5172 and 0.2263,respectively,and those of sulfur were0.5784 and 0.5811,respectively.The CARS-PLS screened 37 and 25 variables respectively in the detection of N and S elements,but the prediction ability of the model did not improve significantly.SPA-PLS finally screened 14 and 11 variables respectively through successive projections,and obtained the best prediction effect among the three methods.The R^2 P and RMSEP of nitrogen were0.9873 and 0.0208,respectively,and those of sulfur were 0.9451 and 0.2082,respectively.In general,the predictive results of the two elements increased by about 90% for RMSEP and 60% for R2 P compared with PLS.The results show that LIBS combined with SPA-PLS has good potential for detecting N and S content in coal,and is a very promising technology for industrial application.

Estimation of leaf color variances of Cotinus coggygria based on geographic and environmental variables

Capturing leaf color variances over space is important for diagnosing plant nutrient and health status,estimating water availability as well as improving ornamental and tourism values of plants.In this study,leaf color variances of the Eurasian smoke tree,Cotinus coggygria were estimated based on geographic and climate variables in a shrub community using generalized elastic net(GELnet)and support vector machine(SVM)algorithms.Results reveal that leaf color varied over space,and the variances were the result of geography due to its effect on solar radiation,temperature,illumination and moisture of the shrub environment,whereas the influence of climate were not obvious.The SVM and GELnet algorithm models were similar estimating leaf color indices based on geographic variables,and demonstrates that both techniques have the potential to estimate leaf color variances of C.coggygria in a shrubbery with a complex geographical environment in the absence of human activity.

Characteristic wavelength selection of volatile organic compounds infrared spectra based on improved interval partial least squares

As important components of air pollutant,volatile organic compounds(VOCs)can cause great harm to environment and human body.The concentration change of VOCs should be focused on in real-time environment monitoring system.In order to solve the problem of wavelength redundancy in full spectrum partial least squares(PLS)modeling for VOCs concentration analysis,a new method based on improved interval PLS(iPLS)integrated with Monte-Carlo sampling,called iPLS-MC method,was proposed to select optimal characteristic wavelengths of VOCs spectra.This method uses iPLS modeling to preselect the characteristic wavebands of the spectra and generates random wavelength combinations from the selected wavebands by Monte-Carlo sampling.The wavelength combination with the best prediction result in regression model is selected as the characteristic wavelengths of the spectrum.Different wavelength selection methods were built,respectively,on Fourier transform infrared(FTIR)spectra of ethylene and ethanol gas at different concentrations obtained in the laboratory.When the interval number of iPLS model is set to 30 and the Monte-Carlo sampling runs 1000 times,the characteristic wavelengths selected by iPLS-MC method can reduce from 8916 to 10,which occupies only 0.22%of the full spectrum wavelengths.While the RMSECV and correlation coefficient(Rc)for ethylene are 0.2977 and 0.9999 ppm,and those for ethanol gas are 0.2977 ppm and 0.9999.The experimental results show that the iPLS-MC method can select the optimal characteristic wavelengths of VOCs FTIR spectra stably and effectively,and the prediction performance of the regression model can be significantly improved and simplified by using characteristic wavelengths.

Variable Selection of Partially Linear Single-index Models

In this article, we study the variable selection of partially linear single-index model(PLSIM). Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average variance with adaptive l1 penalty. Implementation algorithm is given. Under some regular conditions, we demonstrate the oracle properties of aLASSO procedure for PLSIM. Simulations are used to investigate the effectiveness of the proposed method for variable selection of PLSIM.

Spectroscopic Multicomponent Analysis Using Multi-objective Optimization for Variable Selection

The multiple determination tasks of chemical properties are a classical problem in analytical chemistry. The major problem is concerned in to find the best subset of variables that better represents the compounds. These variables are obtained by a spectrophotometer device. This device measures hundreds of correlated variables related with physicocbemical properties and that can be used to estimate the component of interest. The problem is the selection of a subset of informative and uncorrelated variables that help the minimization of prediction error. Classical algorithms select a subset of variables for each compound considered. In this work we propose the use of the SPEA-II （strength Pareto evolutionary algorithm II）. We would like to show that the variable selection algorithm can selected just one subset used for multiple determinations using multiple linear regressions. For the case study is used wheat data obtained by NIR （near-infrared spectroscopy） spectrometry where the objective is the determination of a variable subgroup with information about E protein content （%）, test weight （Kg/HI）, WKT （wheat kernel texture） （%） and farinograph water absorption （%）. The results of traditional techniques of multivariate calibration as the SPA （successive projections algorithm）, PLS （partial least square） and mono-objective genetic algorithm are presents for comparisons. For NIR spectral analysis of protein concentration on wheat, the number of variables selected from 775 spectral variables was reduced for just 10 in the SPEA-II algorithm. The prediction error decreased from 0.2 in the classical methods to 0.09 in proposed approach, a reduction of 37%. The model using variables selected by SPEA-II had better prediction performance than classical algorithms and full-spectrum partial least-squares.

Bayesian Variable Selection for Mixture Process Variable Design Experiment

This paper discussed Bayesian variable selection methods for models from split-plot mixture designs using samples from Metropolis-Hastings within the Gibbs sampling algorithm. Bayesian variable selection is easy to implement due to the improvement in computing via MCMC sampling. We described the Bayesian methodology by introducing the Bayesian framework, and explaining Markov Chain Monte Carlo (MCMC) sampling. The Metropolis-Hastings within Gibbs sampling was used to draw dependent samples from the full conditional distributions which were explained. In mixture experiments with process variables, the response depends not only on the proportions of the mixture components but also on the effects of the process variables. In many such mixture-process variable experiments, constraints such as time or cost prohibit the selection of treatments completely at random. In these situations, restrictions on the randomisation force the level combinations of one group of factors to be fixed and the combinations of the other group of factors are run. Then a new level of the first-factor group is set and combinations of the other factors are run. We discussed the computational algorithm for the Stochastic Search Variable Selection (SSVS) in linear mixed models. We extended the computational algorithm of SSVS to fit models from split-plot mixture design by introducing the algorithm of the Stochastic Search Variable Selection for Split-plot Design (SSVS-SPD). The motivation of this extension is that we have two different levels of the experimental units, one for the whole plots and the other for subplots in the split-plot mixture design.

Variable Selection in Randomized Block Design Experiment

In the experimental field, researchers need very often to select the best subset model as well as reach the best model estimation simultaneously. Selecting the best subset of variables will improve the prediction accuracy as noninformative variables will be removed. Having a model with high prediction accuracy allows the researchers to use the model for future forecasting. In this paper, we investigate the differences between various variable selection methods. The aim is to compare the analysis of the frequentist methodology (the backward elimination), penalised shrinkage method (the Adaptive LASSO) and the Least Angle Regression (LARS) for selecting the active variables for data produced by the blocked design experiment. The result of the comparative study supports the utilization of the LARS method for statistical analysis of data from blocked experiments.

Variable selection for skew-normal mixture of joint location and scale models

Although there are many papers on variable selection methods based on mean model in the nite mixture of regression models,little work has been done on how to select signi cant explanatory variables in the modeling of the variance parameter.In this paper,we propose and study a novel class of models:a skew-normal mixture of joint location and scale models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population.The problem of variable selection for the proposed models is considered.In particular,a modi ed Expectation-Maximization(EM)algorithm for estimating the model parameters is developed.The consistency and the oracle property of the penalized estimators is established.Simulation studies are conducted to investigate the nite sample performance of the proposed methodolo-gies.An example is illustrated by the proposed methodologies.

Comparative Study of Variable Selection Using Genetic Algorithm with Various Types of Chromosomes

In this study,different methods of variable selection using the multilinear step-wise regression（MLR） and support vector regression（SVR） have been compared when the performance of genetic algorithms（GAs） using various types of chromosomes is used.The first method is a GA with binary chromosome（GA-BC） and the other is a GA with a fixed-length character chromosome（GA-FCC）.The overall prediction accuracy for the training set by means of 7-fold cross-validation was tested.All the regression models were evaluated by the test set.The poor prediction for the test set illustrates that the forward stepwise regression（FSR） model is easier to overfit for the training set.The results using SVR methods showed that the over-fitting could be overcome.Further,the over-fitting would be easier for the GA-BC-SVR method because too many variables fleetly induced into the model.The final optimal model was obtained with good predictive ability（R2 = 0.885,S = 0.469,Rcv2 = 0.700,Scv = 0.757,Rex2 = 0.692,Sex = 0.675） using GA-FCC-SVR method.Our investigation indicates the variable selection method using GA-FCC is the most appropriate for MLR and SVR methods.

VARIABLE SELECTION BY PSEUDO WAVELETS IN HETEROSCEDASTIC REGRESSION MODELS INVOLVING TIME SERIES

A simple but efficient method has been proposed to select variables in heteroscedastic regression models. It is shown that the pseudo empirical wavelet coefficients corresponding to the significant explanatory variables in the regression models are clearly larger than those nonsignificant ones, on the basis of which a procedure is developed to select variables in regression models. The coefficients of the models are also estimated. All estimators are proved to be consistent.

Ensemble Variable Selection for Naive Bayes to Improve Customer Behaviour Analysis

Executing customer analysis in a systemic way is one of the possible solutions for each enterprise to understand the behavior of consumer patterns in an efficient and in-depth manner.Further investigation of customer patterns helps thefirm to develop efficient decisions and in turn,helps to optimize the enter-prise’s business and maximizes consumer satisfaction correspondingly.To con-duct an effective assessment about the customers,Naive Bayes(also called Simple Bayes),a machine learning model is utilized.However,the efficacious of the simple Bayes model is utterly relying on the consumer data used,and the existence of uncertain and redundant attributes in the consumer data enables the simple Bayes model to attain the worst prediction in consumer data because of its presumption regarding the attributes applied.However,in practice,the NB pre-mise is not true in consumer data,and the analysis of these redundant attributes enables simple Bayes model to get poor prediction results.In this work,an ensem-ble attribute selection methodology is performed to overcome the problem with consumer data and to pick a steady uncorrelated attribute set to model with the NB classifier.In ensemble variable selection,two different strategies are applied:one is based upon data perturbation(or homogeneous ensemble,same feature selector is applied to a different subsamples derived from the same learning set)and the other one is based upon function perturbation(or heterogeneous ensemble different feature selector is utilized to the same learning set).Further-more,the feature set captured from both ensemble strategies is applied to NB indi-vidually and the outcome obtained is computed.Finally,the experimental outcomes show that the proposed ensemble strategies perform efficiently in choosing a steady attribute set and increasing NB classification performance efficiently.

A Comparison of Variable Selection by Tabu Search and Stepwise Regression with Multicollinearity Problem

This paper has compared variable selection method for multiple linear regression models that have both relative and non-relative variables in full model when predictor variables are highly correlated 0.999 . In this study two objective functions used in the Tabu Search are mean square error （MSE） and the mean absolute error （MAE）. The results of Tabu Search are compared with the results obtained by stepwise regression method based on the hit percentage criterion. The simulations cover the both cases, without and with multicollinearity problems. For each situation, 1,000 iterations are examined by applying a different sample size n = 25 and 100 at 0.05 level of significance. Without multicollinearity problem, the hit percentages of the stepwise regression method and Tabu Search using the objective function of MSE are almost the same but slightly higher than the Tabu Search using the objective function of MAE. However with multicollinearity problem the hit percentages of the Tabu Search using both objective functions are higher than the hit percentage of the stepwise regression method.

Clustering of the Values of a Response Variable and Simultaneous Covariate Selection Using a Stepwise Algorithm

In supervised learning the number of values of a response variable can be very high. Grouping these values in a few clusters can be useful to perform accurate supervised classification analyses. On the other hand selecting relevant covariates is a crucial step to build robust and efficient prediction models. We propose in this paper an algorithm that simultaneously groups the values of a response variable into a limited number of clusters and selects stepwise the best covariates that discriminate this clustering. These objectives are achieved by alternate optimization of a user-defined model selection criterion. This process extends a former version of the algorithm to a more general framework. Moreover possible further developments are discussed in detail.

An Adaptive Sequential Replacement Method for Variable Selection in Linear Regression Analysis

With the rapid development of DNA technologies, high throughput genomic data have become a powerful leverage to locate desirable genetic loci associated with traits of importance in various crop species. However, current genetic association mapping analyses are focused on identifying individual QTLs. This study aimed to identify a set of QTLs or genetic markers, which can capture genetic variability for marker-assisted selection. Selecting a set with k loci that can maximize genetic variation out of high throughput genomic data is a challenging issue. In this study, we proposed an adaptive sequential replacement (ASR) method, which is considered a variant of the sequential replacement (SR) method. Through Monte Carlo simulation and comparing with four other selection methods: exhaustive, SR method, forward, and backward methods we found that the ASR method sustains consistent and repeatable results comparable to the exhaustive method with much reduced computational intensity.

Variable Selection Procedures in Linear Regression Models with Screening Consistency Property

There are two fundamental goals in statistical learning： identifying relevant predictors and ensuring high prediction accuracy. The first goal, by means of variable selection, is of particular importance when the true underlying model has a sparse representation. Discovering relevant predictors can enhance the performance of the prediction for the fitted model. Usually an estimate is considered desirable if it is consistent in terms of both coefficient estimate and variable selection. Hence, before we try to estimate the regression coefficients β , it is preferable that we have a set of useful predictors m hand. The emphasis of our task in this paper is to propose a method, in the aim of identifying relevant predictors to ensure screening consistency in variable selection. The primary interest is on Orthogonal Matching Pursuit（OMP）.

Bayesian Variable Selection via Perfect Gibbs Coupler Using Approximate Bounds

Variable selection is one of the most fundamental problems in regression analysis. By sampling from the posterior distributions of candidate models, Bayesian variable selection via MCMC （Markov chain Monte-Carlo） is effective to overcome the computational burden of all-subset variable selection approaches. However, the convergence of the MCMC is often hard to determine and one is often not sure about if obtained samples are unbiased. This complication has limited the application of Bayesian variable selection in practice. Based on the idea of CFTP （coupling from the past）, perfect sampling schemes have been developed to obtain independent samples from the posterior distribution for a variety of problems. Here the authors propose an efficient and effective perfect sampling algorithm for Bayesian variable selection of linear regression models, which independently and identically sample from the posterior distribution of the model space and can efficiently handle thousands of variables. The effectiveness of the authors＇ algorithm is illustrated by three simulation studies, which have up to thousands of variables, the authors＇ method is further illustrated in SNPs （single nucleotide polymorphisms） association study among RA （rheumatoid arthritis） patients.