Uncover the path from PCR to PLS via elastic component regression |
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Authors: | Hong-Dong Li Qing-Song Xu |
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Affiliation: | a Research Center of Modernization of Traditional Chinese Medicines, College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR Chinab School of Mathematic Sciences, Central South University, Changsha 410083, PR China |
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Abstract: | 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/.) |
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Keywords: | Elastic component regression Model path Principal component regression Partial least squares |
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