V_{n+1} \right), \label{def:Gammamedaver}\end{aligned}$$ where the averaged recursive estimator $\overline{m}_{n+1}$ of the median $m$ is controlled by a sequence of descent steps $ \gamma_n^{(m)}$. The learning rates are generally chosen as follows, $ \gamma_n^{(m)} = c_m n^{-\alpha}$, where the tuning constants satisfy $c_m \in [2,20]$ and $1/2 < \alpha < 1$.

Note that by construction, even if $V_n$ is non negative, $V_{n+1}$ may not be a non negative matrix when the learning steps do not satisfy $$\frac{\gamma_n}{{\left\| (X_{n+1}-\overline{m}_n)(X_{n+1}-\overline{m}_n)^T - V_n \right\|}_F} \leq 1 .$$ Projecting $V_{n+1}$ onto the closed convex cone of non negative operators would require to compute the eigenvalues of $V_{n+1}$ which is time consuming in high dimension even if $V_{n+1}$ is a rank one perturbation to $V_n$ (see [@CD2015]). We consider the following simple approximation to this projection which consists in replacing in (\[def:Gammarm\]) the descent step $\gamma_n$ by a thresholded one, $$\begin{aligned}
\gamma_{n,pos} &= \min \left( \gamma_n , \ {\left\| (X_{n+1}-\overline{m}_n)(X_{n+1}-\overline{m}_n)^T - V_n \right\|}_F \right)
\label{def:gammamodif}\end{aligned}$$ which ensures that $V_{n+1}$ remains non negative when $V_n$ is non negative. The use of these modified steps and an initialization of the recursive algorithm (\[def:Gammarm\]) with a non negative matrix (for example $V_0=0$) ensure that for all $n \geq 1$, 