Data uncertainty is common in real-world applications due to various causes, including imprecise measurement, network latency, out-datedsources and sampling errors. These kinds of uncertainty have to be handled cautiously, or else the mining results could be unreliable or even wrong. We propose that when data mining is performed on uncertain data, data uncertainty has to be considered in order to obtain high quality data mining results. In this paper we study how uncertainty can be incorporated in data mining by using data clustering as a motivating example. We also present a Gaussian process model that can be able to handle data uncertainty in data mining.