Variable screening of multiple response system using nonparametric neighborhood component feature selection

Abstract

As industry develops, system complexity of product and number of design variables increases, and response becomes diverse. Computer aided engineering-based design optimization is required to consider complex design requirements, reduce development cost, and shorten development time. However, as the number of design variables increases, convergence rate of optimization can be decreased, number of function calls and design change cost can be increased. To resolve these problems, variable screening techniques are being studied to analyze a significant influence of design variables on the considered responses, and to reduce the number of design variables used for optimization and design. Analysis of variance which is often used for variable screening is a hypothesis test that statistically analyzes influence of response to changes in design variables using level-specific input data such as orthogonal array. However, if there is no the level-specific input data, additional time could arise to obtain the input data. Also, surrogate model-based design optimization is frequently performed because it is difficult to perform optimization using computationally expensive models. To build the surrogate model, input data is generated via design of experiments considering property of space-filling such as optimal Latin hypercube design and maximin distance design. Although the level-specific input data has advantage of analyzing the significant design variables using a small number of sample points, there is a limit which is not suitable for the surrogate modeling. This study adopts neighborhood component feature selection (NCFS) in feature selection technique among machine learning to perform variable screening regardless of input data’s condition [1]. NCFS is a multi-objective optimization that performs variable screening through deriving optimum weights that minimizes mean loss of neighbor component analysis (NCA) regression model and prevents overfitting by regularization term. The objective function consists of a parameter (λ) which is ratio of the NCA regression model's mean loss and regularization term. The parameter is determined by computationally expensive process such as k-fold cross validation and grid search prior to performing NCFS. Therefore, this study proposes nonparametric NCFS (nNCFS) through removing the parameter determination process and modifying optimization problem of NCFS. In addition, screening measure is needed to perform decision making which design variables need to be selected considering multiple responses and design optimization problem. Accordingly, objective-oriented method and violation-based method are proposed to allocate weight for each response by referring [2]. Proposed methods are compared through mathematical problems [3-4] and an engineering problem [5] based on evaluation criteria which are robustness, computational cost, and improvement/feasibility of optimum designs.