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Process discovery methods automatically infer process models from event logs. Often, event logs contain so-called noise, e.g., infrequent outliers or recording errors, which obscure the main behavior of the process. Existing methods filter this noise based on the frequency of event labels: infrequent paths and activities are excluded. However, infrequent behavior may reveal important insights into the process. Thus, not all infrequent behavior should be considered as noise. This paper proposes the Data-aware Heuristic Miner (DHM), a process discovery method that uses the data attributes to distinguish infrequent paths from random noise by using classification techniques. Data- and control-flow of the process are discovered together. We show that the DHM is, to some degree, robust against random noise and reveals data-driven decisions, which are filtered by other discovery methods. The DHM has been successfully tested on several real-life event logs, two of which we present in this paper.