Application of Linear Programming Techniques for Multidimensional Analysis of Preference--Kernel Principal Component Analysis Model in Wastewater Treatment.

According to the limitation of Principal Components Analysis in dealing with the nonlinear data, connecting with the Linear Programming Techniques for Multidimensional Analysis of Preference, this paper presents the Kernel Principal Components Analysis-Linear Programming Techniques for Multidimensional Analysis of Preference evaluation model. Kernel function maps linear inseparable input data into a high dimensional linear separable feature space via a nonlinear mapping technique. Then it carries on the linear principal components analysis in the high dimensional feature space. In addition, the weight of each index can be obtained in this model, thus it makes up another shortage of Principal Components Analysis. In the wastewater evaluation, the indices are numerous and the degree of correlation is not high, therefore, this model is more appropriate. Finally, this paper applies the model to the wastewater evaluation in Shanghai, and we obtain better evaluation results. [ABSTRACT FROM AUTHOR]