but conservative value that only removes clear outliers). We then recomputed the principal curve with the filtered data set.

Figure \[firstPC\] shows these two consecutive fits to the initial reference data. The blue line corresponds to the first principal component fit to the initial reference set (with outliers removed), while the green line represents the second fit to the subset represented as red circles.

![\[firstPC\] Principal curve fits to the initial reference set (blue line) and to the subset of sources with all magnitudes fainter than its closest point in the first principal curve (green line). This subset of points is represented in red.](figs/pcfit)

As mentioned above, we maintain the mixture-of-Gaussians model, and the model complexity selection based on the BIC for the subspace of proper motions of cluster members.

Iterative refinement of the initial reference set
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In the previous paragraphs we have described the derivation of the likelihood models from the initial reference set defined by the membership list in [@2007ApJS..172..663S]. Close examination of the membership probabilities derived from Eq. \[bayes.th\] and these likelihood models reveals the presence of sources in the initial reference set with low membership probabilities and [*vice versa*]{}. Therefore, and for the sake of 