Identification of Stochasticity by Matrix-decomposition: Applied on
  Black Hole Data
Sai Pradeep Chakka Sunil Kumar Vengalil Neelam Sinha
Timeseries classification as stochastic (noise-like) or non-stochastic
(structured), helps understand the underlying dynamics, in several domains.
Here we propose a two-legged matrix decomposition-based algorithm utilizing two
complementary techniques for classification. In Singular Value Decomposition
(SVD) based analysis leg, we perform topological analysis (Betti numbers) on
singular vectors containing temporal information, leading to SVD-label.
Parallely, temporal-ordering agnostic Principal Component Analysis (PCA) is
performed, and the proposed PCA-derived features are computed. These features,
extracted from synthetic timeseries of the two labels, are observed to map the
timeseries to a linearly separable feature space. Support Vector Machine (SVM)
is used to produce PCA-label. The proposed methods have been applied to
synthetic data, comprising 41 realisations of white-noise, pink-noise
(stochastic), Logistic-map at growth-rate 4 and Lorentz-system
(non-stochastic), as proof-of-concept. Proposed algorithm is applied on
astronomical data: 12 temporal-classes of timeseries of black hole GRS
1915+105, obtained from RXTE satellite with average length 25000. For a given
timeseries, if SVD-label and PCA-label concur, then the label is retained; else
deemed "Uncertain". Comparison of obtained results with those in literature are
presented. It's found that out of 12 temporal classes of GRS 1915+105,
concurrence between SVD-label and PCA-label is obtained on 11 of them.