This work is concerned with robustness in Principal Component Analysis (PCA). The approach, which we adopt here, is to replace the criterion of least squares by another criterion based on a convex and sufficiently differentiable loss function ρ. Using this criterion we propose a robust estimate of the location vector and introduce an orthogonality with respect to (w.r.t.) ρ in order to define the different steps of a PCA. The influence functions of a vector mean and principal vectors are developed in order to provide method for obtaining a robust PCA. The practical procedure is based on an alternative-steps algorithm.
CITATION STYLE
Ibazizen, M., & Dauxois, J. (2003). A robust principal component analysis. Statistics, 37(1), 73–83. https://doi.org/10.1080/0233188031000065442
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