Reference-related component analysis: A new method inheriting the advantages of PLS and PCA for separating interesting information and reducing data dimension

•Separating information and reducing data dimension are viewed as two processes.•A new method named RRCA is proposed, which inherits the advantages of PLS and PCA.•A general linear regression formula is developed.

Separating information and reducing data dimension are an arousing increasing attention in chemometrics because the data measured on samples often contains complex information and is of high dimension. However these two topics in chemometrics are tangled, which hinders insight into models and obstructs the development of new methods. In this paper, a viewpoint is presented to clarify how to separate information and reduce data dimension as two different processes by showing some geometric properties of principle component analysis (PCA). To overcome the weakness of PCA that it constructs principal components (PCs) without considering the reference information, a new method named reference-related component analysis (RRCA) is developed. RRCA inherits the spirit of partial least squares (PLS) in finding new variables and the way that PCA separates information and reduces data dimension. The advantage inherited from PLS makes RRCA has good performance in practical applications. And the advantage inherited from PCA makes RRCA as a versatile and handy method. In addition to the above results, a general linear regression formula is also developed, which is suitable for ordinary least squares (OLS), principal component regression (PCR), reference-related component regression (RRCR) and any other regression methods that contain the separating information process as suggested in this paper. Here RRCR is a regression method that combines RRCA and multiple linear regression (MLR).