Nearest Correlation-Based Input Variable Weighting for Soft-Sensor Design

In recent years, soft-sensors have been widely used for estimating product quality or other important variables when online analyzers are not available. In order to construct a highly accurate soft-sensor, appropriate data preprocessing is required. In particular, the selection of input variables or input features is one of the most important techniques for improving estimation performance. Fujiwara et al. proposed a variable selection method, in which variables are clustered into variable groups based on the correlation between variables by nearest correlation spectral clustering (NCSC), and each variable group is examined as to whether or not it should be used as input variables. This method is called NCSC-based variable selection (NCSC-VS). However, these NCSC-based methods have a lot of parameters to be tuned, and their joint optimization is burdensome. The present work proposes an effective input variable weighting method to be used instead of variable selection to conserve labor required for parameter tuning. The proposed method, referred to herein as NC-based variable weighting (NCVW), searches input variables that have the correlation with the output variable by using the NC method and calculates the correlation similarity between the input variables and output variable. The input variables are weighted based on the calculated correlation similarities, and the weighted input variables are used for model construction. There is only one parameter in the proposed NCVW since the NC method has one tuning parameter. Thus, it is easy for NCVW to develop a soft-sensor. The usefulness of the proposed NCVW is demonstrated through an application to calibration model design in a pharmaceutical process.