This paper studies an intelligent ultimate technique for health-monitoring and prognostic of common rotary machine components, particularly bearings. During a run-to-failure experiment, rich unsupervised features from vibration sensory data are extracted by a trained sparse auto-encoder. Then, the correlation of the extracted attributes of the initial samples (presumably healthy at the beginning of the test) with the succeeding samples is calculated and passed through a moving-average filter. The normalized output is named auto-encoder correlation-based (AEC) rate which stands for an informative attribute of the system depicting its health status and precisely identifying the degradation starting point. We show that AEC technique well-generalizes in several run-to-failure tests. AEC collects rich unsupervised features form the vibration data fully autonomous. We demonstrate the superiority of the AEC over many other state-of-the-art approaches for the health monitoring and prognostic of machine bearings.