Projection Matrices for Partial Least Squares Regression and Principal Component Regression

• 발행기관: 한국자료분석학회
• 저자명: Jong-Duk Kim
• 간행물 정보: 『Journal of The Korean Data Analysis Society (JKDAS)』Vol.5 No.4, 787~800쪽, 전체 14쪽
• 주제분류: 자연과학 > 통계학
• 파일형태: PDF
• 발행일자: 2003.12.30

영문 초록

In this paper projection matrices for partial least squares regression(PLSR) and principal component regression(PCR) are considered with no assumption on the shape and rank of the predictor variable matrix X. It is shown how the original X matrices are transformed to new matrices and how several different forms of projection matrices are obtained for each of the methods. An interpretation is given to the procedure of the regressions using the transformed X matrices and projection matrices. This gives not only solutions for PLSR and PCR in the case of general X but some insight into the properties of the procedures.

목차

1. Introduction

2. Some Background for Orthogonal Projections

3. Projection matrices for PCR and PLSR

4. Summary

References

키워드

Projection matrix Partial least squares regression Principal component regression Moore-Penrose generalized inverse