On Modified Multi-Output Chebyshev-Polynomial Feed-Forward Neural Network for Pattern Classification of Wine Regions

Abstract

Wine, an alcoholic beverage made from fermented grapes, has become an increasingly popular drink. However, wine regions may directly affect the quality and taste of the wine, and misjudgment of the wine regions leads to confusion for dealers and consumers in choosing wine types. In recent decades, different methods in machine learning have been presented and investigated the pattern classification. In this paper, based on the existing results, a modified multi-output Chebyshev-polynomial feed-forward neural network (MOCPFFNN) is presented, analyzed, and applied to the pattern classification of wines regions. According to the orthogonal polynomial theory, the activation functions of the MOCPFFNN are improved to some Chebyshev polynomials. In addition, to have a lower computational complexity, the presented neural network model is automatically determined by the eight-fold cross validation (8FCV) algorithm and the weight direct determination (WDD) algorithm. Finally, comparisons are made among the presented model and other classical methods, e.g., feed-forward back propagation (FFBP), layer recurrent neural network (LRNN), and nonlinear auto regressive with exogenous inputs (NARX), K-nearest neighbors (KNN), random forest, which confirm that the modified MOCPFFNN has the best approximation and generalization performance in the pattern classification of wine regions, with the accuracy rates of the training set and test set reaching 99.17% and 94.83%, respectively. Moreover, the variance of the accuracy of the presented MOCPFFNN method in the experiments is 0, which illustrates its high robustness in pattern classification. INDEX TERMS Eight fold cross validation (8FCV), multi-output Chebyshev-polynomial feed-forward neural network (MOCPFFNN), weight direct determination (WDD), wine region.

Discrete Perturbation-Immunity Neural Network for Dynamic Constrained Redundant Robot Control

“…In this section, the potential performances of the proposed DPINN model (10) are explored and the corresponding theoretical verifications are established. Firstly, for arranging the proposed DPINN model (10) and simplifying the study process, a remark is introduced as below.…”

“…In the next part of the abovementioned series, the theoretical verifications on the convergence performance of the proposed DPINN model (10) are discussed with various injected perturbations.…”

“…The above theorems consider the convergence characteristics of the proposed DPINN model (10) under the condition of without perturbation and three different perturbations, indicating that the generated trajectory synthesized by the proposed DPINN model (10) invariably approaches the desired one with a tiny residual error that is able to be controlled by adjusting the design parameters or the sampling interval.…”

“…Proof: The analysis is able to be discussed from two perspectives similar to that in Theorem 2, i.e., the bounded random perturbations ψ(t) and O(δ 2 ). Then, taking the similar effect as O(δ 2 ) in formula (12) with ψ k , the ıth subsystem of the proposed DPINN model (10)…”

“…common idea using serial processing solving [6], [7], which is a complicated and long iteration process, brings heavy computational load, and limits the application of such algorithms in large-scale online optimization, especially for the time-critical ones as time-dependent problems or more challenging situations. In contrast, the neural network/dynamic method displays powerful competitiveness with its parallel distribution structure, nonlinear mapping, strong learning ability, and it approximates any function accurately in the control field, including robot motion control [8]- [10] and other aspects [11], [12]. It is worth noting that the realization of robot control is through a quadratic programming (QP) based scheme that can generally be reorganized as a linear equation system with bound constraints neglected or a linear projection one with those involved [13].…”