Low complexity adaptive algorithms for Principal and Minor Component Analysis

Messaoud Thameri (1) , Karim Abed-Meraim (2) , Adel Belouchrani (3)

1 Télécom ParisTech
2 PRISME - Laboratoire Pluridisciplinaire de Recherche en Ingénierie des Systèmes, Mécanique et Energétique
3 INFRES - Département Informatique et Réseaux

This article introduces new low cost algorithms for the adaptive estimation and tracking of principal and minor components. The proposed algorithms are based on the well-known OPAST method which is adapted and extended in order to achieve the desired MCA or PCA (Minor or Principal Component Analysis). For the PCA case, we propose efficient solutions using Givens rotations to estimate the principal components out of the weight matrix given by OPAST method. These solutions are then extended to the MCA case by using a transformed data covariance matrix in such away the desired minor components are obtained from the PCA of the new (transformed) matrix. Finally, as a byproduct of our PCA algorithm, we propose a fast adaptive algorithm for data whitening that is shown to overcome the recently proposed RLS-based whitening method.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Messaoud Thameri, Karim Abed-Meraim, Adel Belouchrani. Low complexity adaptive algorithms for Principal and Minor Component Analysis. Digital Signal Processing, 2013, 23 (1), pp.19-29. ⟨hal-01002063⟩