The Intelligent Fault Diagnosis of rotating machinery currently proposes some captivating challenges. Although results achieved by artificial intelligence and deep learning constantly improve, this field is characterized by several open issues. Models' interpretation is still buried under the foundations of data driven science, thus requiring attention to the development of new opportunities also for machine learning theories. This study proposes a machine learning diagnosis model, based on intelligent spectrogram recognition, via image processing. The approach is characterized by the employment of the eigen-spectrograms and randomized linear algebra in fault diagnosis. Randomized algebra and eigen-spectrograms enable the construction of a significant feature space, which nonetheless emerges as a viable device to explore models' interpretations. The computational efficiency of randomized approaches provides reading keys of well-established statistical learning theories such as the Support Vector Machine (SVM). Machine learning applied to spectrogram recognition shows to be extremely accurate and efficient as compared to state of the art results.