This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results.

This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results.

This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results.

In this work, we propose a new algorithm to improve existing techniques used in the field of spectroscopic data regression analysis. In particular, it combines the power of nonlinear kernel regressors (kernel ridge regression [KRR], kernel principal component regression [KPCR], and Gaussian process regression [GPR]) with an optimization based on nondominated sorting multi-objective genetic algorithm (NSGAII) to filter the residual outliers in the prediction space and leverage points in the features space. The proposed algorithm, contrary to most existing robust algorithms, simultaneously optimizes many complementary objectives for an automatic adaptation and thus a better outliers detection. It is well known that the elimination of outliers greatly improves the regression model. It is thus the aim of this work to develop a new robust regression algorithm. It has been applied on five different datasets, and the results are compared to both classical nonlinear regression methods and the commonly used robust regression methods robust continuum regression (RCR), partial robust M-regression (PRM), robust principal component regression (RPCR), robust PLSR (RSIMPLS), and locally weighted regression (LWR). They show that the proposed algorithm outperforms the classical nonlinear regression methods and is a promising competitor to the robust methods outperforming most of them. Even though the results obtained are only from five datasets, this algorithm can be considered an interesting contribution for improving data analysis in the field of chemometrics.

In this work, we propose a new algorithm to improve existing techniques used in the field of spectroscopic data regression analysis. In particular, it combines the power of nonlinear kernel regressors (kernel ridge regression [KRR], kernel principal component regression [KPCR], and Gaussian process regression [GPR]) with an optimization based on nondominated sorting multi-objective genetic algorithm (NSGAII) to filter the residual outliers in the prediction space and leverage points in the features space. The proposed algorithm, contrary to most existing robust algorithms, simultaneously optimizes many complementary objectives for an automatic adaptation and thus a better outliers detection. It is well known that the elimination of outliers greatly improves the regression model. It is thus the aim of this work to develop a new robust regression algorithm. It has been applied on five different datasets, and the results are compared to both classical nonlinear regression methods and the commonly used robust regression methods robust continuum regression (RCR), partial robust M-regression (PRM), robust principal component regression (RPCR), robust PLSR (RSIMPLS), and locally weighted regression (LWR). They show that the proposed algorithm outperforms the classical nonlinear regression methods and is a promising competitor to the robust methods outperforming most of them. Even though the results obtained are only from five datasets, this algorithm can be considered an interesting contribution for improving data analysis in the field of chemometrics.

In this work, we propose a new algorithm to improve existing techniques used in the field of spectroscopic data regression analysis. In particular, it combines the power of nonlinear kernel regressors (kernel ridge regression [KRR], kernel principal component regression [KPCR], and Gaussian process regression [GPR]) with an optimization based on nondominated sorting multi-objective genetic algorithm (NSGAII) to filter the residual outliers in the prediction space and leverage points in the features space. The proposed algorithm, contrary to most existing robust algorithms, simultaneously optimizes many complementary objectives for an automatic adaptation and thus a better outliers detection. It is well known that the elimination of outliers greatly improves the regression model. It is thus the aim of this work to develop a new robust regression algorithm. It has been applied on five different datasets, and the results are compared to both classical nonlinear regression methods and the commonly used robust regression methods robust continuum regression (RCR), partial robust M-regression (PRM), robust principal component regression (RPCR), robust PLSR (RSIMPLS), and locally weighted regression (LWR). They show that the proposed algorithm outperforms the classical nonlinear regression methods and is a promising competitor to the robust methods outperforming most of them. Even though the results obtained are only from five datasets, this algorithm can be considered an interesting contribution for improving data analysis in the field of chemometrics.

In this work, we propose a new algorithm to improve existing techniques used in the field of spectroscopic data regression analysis. In particular, it combines the power of nonlinear kernel regressors (kernel ridge regression [KRR], kernel principal component regression [KPCR], and Gaussian process regression [GPR]) with an optimization based on nondominated sorting multi-objective genetic algorithm (NSGAII) to filter the residual outliers in the prediction space and leverage points in the features space. The proposed algorithm, contrary to most existing robust algorithms, simultaneously optimizes many complementary objectives for an automatic adaptation and thus a better outliers detection. It is well known that the elimination of outliers greatly improves the regression model. It is thus the aim of this work to develop a new robust regression algorithm. It has been applied on five different datasets, and the results are compared to both classical nonlinear regression methods and the commonly used robust regression methods robust continuum regression (RCR), partial robust M-regression (PRM), robust principal component regression (RPCR), robust PLSR (RSIMPLS), and locally weighted regression (LWR). They show that the proposed algorithm outperforms the classical nonlinear regression methods and is a promising competitor to the robust methods outperforming most of them. Even though the results obtained are only from five datasets, this algorithm can be considered an interesting contribution for improving data analysis in the field of chemometrics.

In this work, we propose a new algorithm to improve existing techniques used in the field of spectroscopic data regression analysis. In particular, it combines the power of nonlinear kernel regressors (kernel ridge regression [KRR], kernel principal component regression [KPCR], and Gaussian process regression [GPR]) with an optimization based on nondominated sorting multi-objective genetic algorithm (NSGAII) to filter the residual outliers in the prediction space and leverage points in the features space. The proposed algorithm, contrary to most existing robust algorithms, simultaneously optimizes many complementary objectives for an automatic adaptation and thus a better outliers detection. It is well known that the elimination of outliers greatly improves the regression model. It is thus the aim of this work to develop a new robust regression algorithm. It has been applied on five different datasets, and the results are compared to both classical nonlinear regression methods and the commonly used robust regression methods robust continuum regression (RCR), partial robust M-regression (PRM), robust principal component regression (RPCR), robust PLSR (RSIMPLS), and locally weighted regression (LWR). They show that the proposed algorithm outperforms the classical nonlinear regression methods and is a promising competitor to the robust methods outperforming most of them. Even though the results obtained are only from five datasets, this algorithm can be considered an interesting contribution for improving data analysis in the field of chemometrics.

In this work, we propose a new algorithm to improve existing techniques used in the field of spectroscopic data regression analysis. In particular, it combines the power of nonlinear kernel regressors (kernel ridge regression [KRR], kernel principal component regression [KPCR], and Gaussian process regression [GPR]) with an optimization based on nondominated sorting multi-objective genetic algorithm (NSGAII) to filter the residual outliers in the prediction space and leverage points in the features space. The proposed algorithm, contrary to most existing robust algorithms, simultaneously optimizes many complementary objectives for an automatic adaptation and thus a better outliers detection. It is well known that the elimination of outliers greatly improves the regression model. It is thus the aim of this work to develop a new robust regression algorithm. It has been applied on five different datasets, and the results are compared to both classical nonlinear regression methods and the commonly used robust regression methods robust continuum regression (RCR), partial robust M-regression (PRM), robust principal component regression (RPCR), robust PLSR (RSIMPLS), and locally weighted regression (LWR). They show that the proposed algorithm outperforms the classical nonlinear regression methods and is a promising competitor to the robust methods outperforming most of them. Even though the results obtained are only from five datasets, this algorithm can be considered an interesting contribution for improving data analysis in the field of chemometrics.