tokens: membership probabilities for the 7312 sample stars. Figure 8 shows that the stars with high GMM membership probabilities ( P GMM ≥ 0.8) generally have high RF membership probabilities, and the stars with low GMM membership probabilities ( P GMM 0.2) have low RF membership probabilities in general. However, some stars with near zero GMM probabilities still have a certain probability of being RF memberships, indicating that the color and magnitude parameters play non-negligible roles in the RF-based membership determination. In our previous work, we have confirmed that color and magnitude parameters cannot be ignored in the RF-based membership determination (Gao 2018a ). As a model-dependent clustering technique, the GMM method cannot directly handle the color and magnitude parameters since they do not follow Gaussian distributions. Fortunately, the RF method does not require any mathematical model, only a reliable training set is needed. This allows us to easily identify most likely cluster members of M67 in the 11-dimensional parameter space, even if the color and magnitude parameters are taken into account. The 1502 likely cluster members ( P RF ≥ 0.6) are listed in Table 3 , this table is published in its entirety in the electronic edition. It should be noted that Gaia Collaboration et al. ( 2018a ) have investigated M67 using Gaia -DR2 data and obtained 1520 cluster members, but they did not calculate membership probabilities for these stars. Among the 1520 cluster members in Gaia Collaboration et al. ( 2018a ), 1240 (∼82%) and 1201 (∼79%) stars are determined to be likely ( P RF ≥ 0.6) and high-probability ( P RF ≥ 0.8) cluster members by the RF method, respectively. This once again indicates the high effectiveness of the RF method for identifying likely cluster members in high-dimensional parameter space. Figure 8. A comparison between the GMM and RF membership probabilities of the 7312 sample stars. Table 3 A Catalog of Fundamental Information for 1502 Likely Cluster Members with P RF ≥ 0.6 Note. This table contains Gaia -DR2 identifier, positions and RF membership probabilities for the 1502 likely cluster members (≥0.6). Only a portion of this table is shown here to demonstrate its form and content, a machine-readable version of the full table is available. ID: Gaia -DR2 identifier; R.A., decl.: right ascension and declination; P RF : RF membership probability. (This table is available in its entirety in machine-readable form.) Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available. 3. Distance, Proper Motion, and Radial Velocity We have obtained 1361 high-probability cluster members ( P RF ≥ 0.8), 1260 of which have quite high membership probabilities ( P RF ≥ 0.9). We use the 1260 cluster members to calculate the weighted mean parallax (distance) and proper motion of the cluster, but also taking into account the observational errors. Using 687
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