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

TL;DR

This paper introduces a matrix decomposition-based algorithm combining SVD and PCA techniques for classifying timeseries as stochastic or non-stochastic, demonstrated on synthetic and black hole data.

Contribution

It presents a novel two-legged matrix decomposition approach that integrates topological analysis and PCA-derived features for timeseries classification.

Findings

High accuracy in classifying synthetic data into stochastic and non-stochastic categories.

Effective application to black hole data, with 11 out of 12 classes showing label concurrence.

Method outperforms or complements existing classification techniques.

Abstract

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.