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Clustered microcalcifications (MC) in mammograms can be an important early sign of breast cancer in women. Their accurate detection is important in computer-aided detection (CADe). In this paper, we propose the use of a recently developed machine-learning technique - relevance vector machine (RVM) - for detection of MCs in digital mammograms. RVM is based on Bayesian estimation theory, of which a distinctive feature is that it can yield a sparse decision function that is defined by only a very small number of so-called relevance vectors. By exploiting this sparse property of the RVM, we develop computerized detection algorithms that are not only accurate but also computationally efficient for MC detection in mammograms. We formulate MC detection as a supervised-learning problem, and apply RVM as a classifier to determine at each location in the mammogram if an MC object is present or not. To increase the computation speed further, we develop a two-stage classification network, in which a computationally much simpler linear RVM classifier is applied first to quickly eliminate the overwhelming majority, non-MC pixels in a mammogram from any further consideration. The proposed method is evaluated using a database of 141 clinical mammograms (all containing MCs), and compared with a well-tested support vector machine (SVM) classifier. The detection performance is evaluated using free-response receiver operating characteristic (FROC) curves. It is demonstrated in our experiments that the RVM classifier could greatly reduce the computational complexity of the SVM while maintaining its best detection accuracy. In particular, the two-stage RVM approach could reduce the detection time from 250 s for SVM to 7.26 s for a mammogram (nearly 35-fold reduction). Thus, the proposed RVM classifier is more advantageous for real-time processing of MC clusters in mammograms.