In the era of a data-driven landscape, the development of an efficient and interpretable method has become a pivotal tool for robustly identifying memberships of clusters. We present a novel cluster finder approach called forest fire clustering (FFC). FFC combines iterative label propagation with parallel Monte Carlo simulation to achieve internal validation of clustering results. We use a Gaia DR3 catalog comprising 322 random objects with distinct heliocentric distances from approximately 0 to 5kpc, along with one ultrafaint dwarf galaxy Bootes I (~63kpc), as our validation sample. We compare the performance of FFC with that of DBSCAN and HDBSCAN on this data set by configuring them into the same processing pipeline for identifying star members. Our results indicate that FFC outperforms the two others in terms of the quality of clusters, particularly for clusters located at distances greater than 2kpc. Additionally, FFC demonstrates robust performance and efficiency. Based on the high-quality clusters derived from FFC, we provide a detailed analysis of cluster properties. We determine various cluster parameters, including age, mass, [Fe/H], distance modulus, reddening, and binary fraction. Furthermore, dynamic properties are reliably estimated through the fitting of radial density profiles and theoretical models. This study suggests that FFC is a suitable tool for identifying reliable memberships of stellar systems, highlighting the discovery of more distant clusters and enabling the identification of high-quality clusters to accurately uncover cluster properties.

Cone search capability for table J/AJ/169/115/param (Structural parameters of 280 clusters and 1 dwarf galaxy (Tables 4 and 5))