  Online financial markets can be represented as complex systems where trading
dynamics can be captured and characterized at different resolutions and time
scales. In this work, we develop a methodology based on non-negative tensor
factorization (NTF) aimed at extracting and revealing the multi-timescale
trading dynamics governing online financial systems. We demonstrate the
advantage of our strategy first using synthetic data, and then on real-world
data capturing all interbank transactions (over a million) occurred in an
Italian online financial market (e-MID) between 2001 and 2015. Our results
demonstrate how NTF can uncover hidden activity patterns that characterize
groups of banks exhibiting different trading strategies (normal vs. early vs.
flash trading, etc.). We further illustrate how our methodology can reveal
"crisis modalities" in trading triggered by endogenous and exogenous system
shocks: as an example, we reveal and characterize trading anomalies in the
midst of the 2008 financial crisis.
