A robust principal component analysis |
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Authors: | Mohamed Ibazizen Jacques Dauxois |
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Institution: | 1. Département de mathématiques , Université Mouloud Mammeri , 15000, Tizi-Ouzou, Algérie;2. Laboratoire de Statistique et probabilités , Université Paul Sabatier 118 , route de Narbonne, 31062, Toulouse Cedex, France |
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Abstract: | 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. |
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Keywords: | Influence function Principal component analysis Robustness ρ-orthogonality |
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