Incompleteness and lack of precision are common problems with geochemical data, limiting the data analysis methods that can be reliably applied and what subsets of data can be used. This study introduces a clustering method that is designed to have high robustness to significant data incompleteness. It can also be used to impute missing values and distributions. A Gaussian mixture model is defined over the combination of all data in a log-ratio-transformed space. The Markov chain Monte Carlo within-expectation maximization algorithm is used to solve it. Laterite data from Southwest Yilgarn are used to validate our approach. We demonstrate good performance, with up to 50% of all data removed, and the ability to recover below-detection-limit distributions with high accuracy.