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Machine fault diagnosis collects massive amounts of vibration data about complex mechanical systems. Performing feature detection from these data sets has already led to a major challenge. Compressive sensing theory is a new sampling framework that provides an alternative to the well-known Shannon sampling theory. This theory enables the recovery of sparse or compressible signals from a small set of nonadaptive linear measurements. However, it is suboptimal to recover the whole signals from the compressive measurements and then solve feature identification problems through traditional DSP techniques. Thus, a novel mechanical feature identification method is proposed in this paper. Its main advantage is that fault features are extracted directly in the compressive measurement domain without sacrificing accuracy, while a significant reduction in the dimensionality of the measurement data is achieved …