Identification of Stochasticity by Matrix-decomposition: Applied on Black Hole Data

Timeseries classification as non-stochastic (structured) or stochastic (lacking structure) helps understand underlying dynamics, in several domains. One of the novel contributions of this work is to utilize the well-known Principal Component Analysis (PCA) for identifying structured behavior or lack thereof, in a timeseries. For classification, we propose a two-legged matrix decomposition-based algorithm utilizing two complementary techniques (SVD and PCA). SVD-leg performs topological analysis (Betti numbers) on singular vectors containing temporal information, leading to SVD-label. Parallely, temporal-ordering agnostic PCA is performed hierarchically on the timeseries, computing proposed Eigen-ratio based features that quantify structure, on progressively shorter time-windows, to obtain PCA-label. For a given timeseries, if SVD-label and PCA-label concur, then the label is retained; else deemed "Uncertain", requiring further investigation. The proposed methodology is illustrated on publicly available data of black hole GRS 1915+105, obtained from RXTE satellite, with average length of 25000 datapoints, across 12 temporal classes. Comparison of obtained results with those in literature using traditional and deep-learning based methods are presented. Concurrence in labels is shown in 11 temporal classes; the one temporal class deemed "Uncertain" turns out to be differently labelled using yet another deep-learning based approach, warranting further investigation into its characteristics.