We present a new straightforward principal component analysis (PCA) method
based on the diagonalization of the weighted variance-covariance matrix through
two spectral decomposition methods: power iteration and Rayleigh quotient
iteration. This method allows one to retrieve a given number of orthogonal
principal components amongst the most meaningful ones for the case of problems
with weighted and/or missing data. Principal coefficients are then retrieved by
fitting principal components to the data while providing the final
decomposition. Tests performed on real and simulated cases show that our method
is optimal in the identification of the most significant patterns within data
sets. We illustrate the usefulness of this method by assessing its quality on
the extrapolation of Sloan Digital Sky Survey quasar spectra from measured
wavelengths to shorter and longer wavelengths. Our new algorithm also benefits
from a fast and flexible implementation.

提出一种新的基于加权方差协方差矩阵的双谱分解方法，旨在在具有加权和 / 或缺失数据问题的情况下，检索给定数量的正交主成分，该方法通过将主成分拟合到数据并进行分解，从而检索主系数。通过在实际情况和模拟情况下进行测试，结果表明该方法能够在数据集中识别最显著的模式，并且可以使用此方法将 Sloan Digital Sky Survey 类星体光谱从测量波长外推至更短和更长波长。同时该算法的实现速度快且灵活。