1. LDA via L1-PCA of Whitened Data
- Author
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Martín-Clemente, Rubén, Zarzoso, Vicente, Departamento de Teoría de la Señal y Comunicaciones, Universidad de Sevilla, Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SIGNAL, Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
- Subjects
[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing ,[INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG] - Abstract
International audience; Principal component analysis (PCA) and Fisher's linear discriminant analysis (LDA) are widespread techniques in data analysis and pattern recognition. Recently, the L1-norm has been proposed as an alternative criterion to classical L2-norm in PCA, drawing considerable research interest on account of its increased robustness to outliers. The present work proves that, combined with a whitening preprocessing step, L1-PCA can perform LDA in an unsupervised manner, i.e., sparing the need for labelled data. Rigorous proof is given in the case of data drawn from a mixture of Gaussians. A number of numerical experiments on synthetic as well as real data confirm the theoretical findings.
- Published
- 2020