Uncover the path from PCR to PLS via elastic component regression

This contribution introduces Elastic Component Regression (ECR) as an explorative data analysis method that utilizes a tuning parameter α ∈ [0,1] to supervise the X-matrix decomposition. It is demonstrated theoretically that the elastic component resulting from ECR coincides with principal components of PCA when α = 0 and also coincides with PLS components when α = 1. In this context, PCR and PLS occupy the two ends of ECR and α ∈ (0,1) will lead to an infinite number of transitional models which collectively uncover the model path from PCR to PLS. Therefore, the framework of ECR shows a natural progression from PCR to PLS and may help add some insight into their relationships in theory. The performance of ECR is investigated on a series of simulated datasets together with a real world near infrared dataset. (The source codes implementing ECR in MATLAB are freely available at http://code.google.com/p/ecr/.)