Nearest Correlation Louvain Method for Fast and Good Selection of Input Variables of Statistical Model∗

In the present work, a new input variable selection method for building linear regression models is proposed. The proposed method is referred to as nearest correlation Louvain method based variable selection (NCLM-VS). NCLM-VS is a correlation-based group-wise method; it constructs an affinity matrix of input variables by the nearest correlation (NC) method, partitions the affinity matrix by the Louvain method (LM), consequently clusters input variables into multiple variable classes, and finally selects variable classes according to their contribution to estimates. LM is very fast and optimizes the number of classes automatically unlike spectral clustering (SC). The advantage of NCLM-VS over conventional methods including NCSC-VS is demonstrated through their applications to soft-sensor design for an industrial chemical process and calibration modeling based on near-infrared (NIR) spectra. In particular, it is confirmed that NCLM-VS is significantly faster than the recently proposed NCSC-VS while NCLM-VS can achieve as good estimation performance as NCSC-VS.