A clustering model sorted 15,502 stars around the Pleiades by how they move and how far away they are. Their colour and brightness were held back, so they can be used to check its result.
The Gaia space telescope catalogued 15,502 well-measured stars in a patch of sky around the Pleiades star cluster. A clustering algorithm sorted them into groups using three numbers per star: its motion across the sky in two directions (proper motion) and its parallax, a measure of distance. It was never told any star's colour or brightness. Did it find a real cluster, or just a convenient blob?
A real one, and the evidence is the part it never saw. The group it picks out holds 528 stars, 3.4% of the field, yet contains 16 of the field's 20 brightest stars. Plotted by colour and brightness, these stars fall on one narrow band, a stellar sequence 0.40 magnitudes wide (magnitude is astronomers' brightness scale). The biggest group is 94.8% of the same catalogue, spreads over 1.56 magnitudes and holds 0 of the 20. Stars born together at one distance look like the first; an unrelated stack of foreground and background stars looks like the second.
How to read this figure. The buttons HDBSCAN, DBSCAN and Gaussian mixture switch between three clustering algorithms' saved results. The buttons below them pick which stars to highlight: all stars, the biggest group the algorithm found, or the Pleiades candidate (the group whose motion and parallax lie closest to published Pleiades values). All three panels highlight the same stars. The panels under “given to the model” show the only data the algorithm used: motion across the sky, and parallax, a measure of distance. “Colour against brightness” shows data it never saw. If the highlighted stars form one narrow band there, they behave like stars born together at one distance. The three numbers under the panels count the highlighted stars, give the width of their band and count how many of the 20 brightest stars they include.
given to the model the only three numbers it ever saw
never shown to it colour and brightness — the check
stars highlighted
magnitudes widesequence width: spread in brightness of the middle half, at one colour
of the 20 brighteststars in the whole field, ringed above
Three clustering algorithms were given the same three numbers per star and nothing else. Each card shows the same measurements for one algorithm's saved result; the highlighted card is the one shown in the figure above. The narrow sequence appears under all three, so it is not a product of one algorithm. “Biggest group, for contrast” gives that group's sequence width and its count of the 20 brightest stars. “Overlap with HDBSCAN” is the number of stars in both candidate groups divided by the number in either (100% means identical).