$$p_{l-1}(\vec{m}_{measured}|\vec{m})=\mathcal{N}_{\vec{m},\Sigma}(\vec{m}_{measured}),$$

where $\Sigma$ represents the non-diagonal covariance matrix of the variables in representation space. The matrix elements were derived following the usual rules for uncertainty propagation of variables that are linear combinations of the original ones (the colour indices).

We then redefined the membership lists according to these posterior probabilities. We used two heuristic thresholds $p_{in}$ and $p_{out}$, such that members with posterior membership probabilities below $p_{out}$ were removed from the training set of cluster members, while non-members with posterior membership probabilities above $p_{in}$ were included in it. We have tested three values of $p_{in}=\{0.9545, 0.975, 0.9975\}$ (probability values corresponding to the range from 2$\sigma$ to 3$\sigma$ significance), and set $p_{out}=0.5$. This represents criteria that are very restrictive for the admission of sources not previously classified as members in the literature, while somewhat conservative for the rejection of members.

With these updated membership lists we derived new likelihood models $p_l({\cal D}|{\cal C}_i)$ and prior probabilities (the maximisation step), and iterated the EM scheme until the membership lists remained unchanged.

We stress that the implicit extrapolation of the principal curve beyond the range of magnitudes and colours covered by the initial reference set, carried out during the EM iterations, is not 