of the data that are too restrictive in our framework. In Section 4, a comparison with some classic robust PCA techniques is made on simulated data. The interest of considering the MCM is also highlighted on the analysis of individual TV audiences, a large sample of high dimensional data which, because of its dimension, can not be analyzed in a reasonable time with classical robust PCA approaches. The main parts of the proofs are described in Section 5. Perspectives for future research are discussed in Section 6. Some technical parts of the proofs as well as a description of Weiszfeld’s algorithm in our context are gathered in an Appendix.

Population point of view and recursive estimators
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Let $H$ be a separable Hilbert space (for example $H = {\mathbb{R}}^d$ or $H = L^2(I)$, for some closed interval $I \subset \mathbb{R}$). We denote by $\langle .,.\rangle$ its inner product and by ${\left\| \cdot \right\|}$ the associated norm.

We consider a random variable $X$ that takes values in $H$ and define its center $m \in H$ as follows: $$\begin{aligned}
m  & {\mathrel{:=}}\arg \min_{u \in H} {{\mathbb{E}}\left[{\left\| X - u \right\|} - {\left\| X \right\|}\right]} .
\label{defmed}\end{aligned}$$ The solution $m \in H$ is 