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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. Moreover, Gaussian white noises are significantly alleviated, which dramatically enhances the reliability of machine fault diagnosis. Parameter analysis is also profoundly investigated through a set of numerical experiments. Numerical simulations and experiments are further performed to prove the reliability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]