The census of open clusters in the Milky Way is in a never-before seen state of flux. Recent works have reported hundreds of new open clusters thanks to the incredible astrometric quality of the Gaia satellite, but other works have also reported that many open clusters discovered in the pre Gaia era may be associations. We aim to conduct a comparison of clustering algorithms used to detect open clusters, attempting to statistically quantify their strengths and weaknesses by deriving the sensitivity, specificity, and precision of each as well as their true positive rate against a larger sample. We selected DBSCAN, HDBSCAN, and Gaussian mixture models for further study, owing to their speed and appropriateness for use with Gaia data. We developed a preprocessing pipeline for Gaia data and developed the algorithms further for the specific application to open clusters. We derived detection rates for all 1385 open clusters in the fields in our study as well as more detailed performance statistics for 100 of these open clusters. DBSCAN was sensitive to 50% to 62% of the true positive open clusters in our sample, with generally very good specificity and precision. HDBSCAN traded precision for a higher sensitivity of up to 82%, especially across different distances and scales of open clusters. Gaussian mixture models were slow and only sensitive to 33% of open clusters in our sample, which tended to be larger objects. Additionally, we report on 41 new open cluster candidates detected by HDBSCAN, three of which are closer than 500 pc. When used with additional post-processing to mitigate its false positives, we have found that HDBSCAN is the most sensitive and effective algorithm for recovering open clusters in Gaia data. Our results suggest that many more new and already reported open clusters have yet to be detected in Gaia data.
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