Research On Algorithm And Application Of Nonlinear Partial Least Squares

With the continuous progress of scientific research,machine learning has been widely used in various fields of people’s production and life.The efficient use of big data information to acquire knowledge through machine learning has gradually become the main driving force for the development of machine learning technology in the current big data environment.How to mine the key data from these big data sets and effectively select the information to infer the future development of things has become a crucial issue.Nonlinear partial least squares is widely used in nonlinear problems such as regression,classification,modeling and fault detection in machine learning because of its simplicity.However,nonlinear partial least squares takes a large cost of calculation and storage in solving problems.In order to improve the learning performance of nonlinear partial least squares,we construct different forms of algorithms based on kernel partial least squares(KPLS)by means of matrix and function approximation,which can deal with nonlinear problems under the condition of sav-ing computing overhead.In addition,the scale of industrial production process is becoming larger and larger,and the production process is becoming more and more complex.The fault detection related to quality is also a topic worth studying.Therefore,this paper focuses on the nonlinear partial least squares algorithm based on large-scale data sets in machine learning and its application.The main work includes the following parts:1.The feature selection algorithm of maximum weight minimum redundancy(MWMR)has fixed evaluation criteria for all data sets,but ignores the problem of different correlation and redundancy among different features of data sets.A kernel partial least squares algorith-m of maximum weight minimum redundancy(KPLS-MWMR)is proposed.The proposed KPLS-MWMR algorithm firstly defines the correlation scores between features,labels and features,and then gives the evaluation criteria of maximum weight and minimum redundan-cy according to the correlation scores.By introducing weight factor,the correlation between maximum weight and minimum redundancy in evaluation criteria is adjusted.Based on K-PLS algorithm,KPLS-MWMR algorithm is proposed.The new algorithm can deal with classification of high dimensional data sets efficiently.The experimental results show that the classification accuracy of the same data set may be different with different weight factors.Compared with the existing algorithm,the new algorithm has higher classification accuracy,and has a remarkable effect on the classification of high-dimensional data sets.2.For KPLS algorithm needs to calculate the whole kernel matrix,due to the number of samples and the calculation of storage problems,it is difficult to deal with the application of large-scale data sets,based on the random Fourier feature and Nystr¨om method,a random kernel partial least squares(RKPLS)algorithm is proposed.The RKPLS algorithm based on random Fourier feature takes advantage of the spectral properties of low-rank kernel matrices,constructs the sum of random feature dot products,and obtains a new variant of the kernel matrix based on random Fourier feature,and then applies the new variant to linear partial least squares(PLS)algorithm.The new algorithm RKPLS can alleviate the calculation and storage cost of linear space approximate KPLS algorithm,and can solve the problem of large-scale data sets.Theoretical analysis shows that the solution of the new algorithm converges to the expected exact kernel matrix.The experimental results show that the classification effect of large scale data sets based on binary and multi-classification is better than that of linear PLS algorithm.3.In order to solve the problem of large computation and high storage cost of KPLS al-gorithm in quality detection,a truncated kernel partial least squares(TKPLS)algorithm is proposed based on truncated singular value decomposition.The algorithm first maps the process variables to the feature space by nonlinear mapping,and then uses truncated sin-gular value decomposition to perform linear PLS algorithm in the feature space to achieve approximate calculation of KPLS algorithm.The new algorithm uses truncated singular value decomposition,has scalability and low computing and storage costs,and can be ex-tended to approximate kernel matrices with limited memory storage.Experimental results show that the new algorithm is effective in nonlinear numerical experiments and penicillin fermentation experiments by using root mean square error(RMSE)and coefficient of deter-mination(~2)as evaluation indicators.The new algorithm can reduce memory and be used to handle real-time and large-scale quality detection problems.4.In order to solve the problem of fault diagnosis in nonlinear process,a locally weighted orthogonal partial least squares(LWOPLS)algorithm based on contribution plots is pro-posed to identify the fault in nonlinear process.Firstly,the process variable space is divided into quality-related subspace and quality-unrelated subspace by orthogonal decomposition.Then,the contribution of corresponding statistics of process variables is calculated separate-ly in each subspace to construct the contribution of process variables.Finally,the fault is detected and diagnosed by comparing the contribution of process variables with the control limits of the contribution plot.Experimental results show that the new algorithm pays more attention to the relationship between process variables and quality variables in the process of detection and diagnosis,and is more suitable for fault diagnosis in nonlinear process.