Machine learning application to detect light echoes around black holes

X-ray reverberation has become a powerful tool to probe the disc-corona geometry near black holes. Here, we develop Machine Learning (ML) models to extract the X-ray reverberation features imprinted in the Power Spectral Density (PSD) of AGN. The machine is trained using simulated PSDs in the form of a simple power-law encoded with the relativistic echo features. Dictionary Learning and sparse coding algorithms are used for the PSD reconstruction, by transforming the noisy PSD to a representative sparse version. Then, the Support Vector Machine is employed to extract the interpretable reverberation features from the reconstructed PSD that holds the information of the source height. The results show that the accuracy of predicting the source height, $h$, is genuinely high and the misclassification is only found when $h$ > 15$r_g$. When the test PSD has a bending power-law shape, which is completely new to the machine, the accuracy is still high. Therefore, the ML model does not require the intrinsic shape of the PSD to be determined in advance. By focusing on the PSD parameter space observed in real AGN data, classification for $h \leq$ 10$r_g$ can be determined with 100% accuracy, even using a PSD in an energy band that contains a reflection flux as low as 10% of the total flux. For $h$ > 10$r_g$, the data, if misclassified, will have small uncertainties of $\Delta h$ ~ 2-4$r_g$. This work shows, as a proof of concept, that the ML technique could shape new methodological directions in the X-ray reverberation analysis.