Approximation stochastique en analyse factorielle multiple

Jean-Marie Monnez (1)

1 IECN - Institut Élie Cartan de Nancy

We study the multiple factorial analysis of a random vector $X$ in $\Bbb R^p$ as a principal component analysis of $X$ with a particular choice of the inner product in $\Bbb R^p$. We use a stochastic approximation process to estimate recursively the principal components of this analysis by means of a sequence of i.i.d. observation of $X$. Stochastic approximations of the symmetrical positive definite matrix $M$ defining the inner product in $\Bbb R^p$ and of the principal components are made simultaneously

Mots clés: stochastic approximation; principal component analysis

Domaines: Probabilités [math.PR]

Jean-Marie Monnez. Approximation stochastique en analyse factorielle multiple. 2006. ⟨hal-00109529⟩