Dynamical Pattern Discovery

This technique captures the phase space of high-dimensional non-linear time series data as a specially constructed Markov model, and then analyzes the induced Markov model with a collection of algorithms adapted from system dynamics, ergodic theory, network theory, and graph theory to uncover features of system dynamics not measurable through other means. The representative shift and combination of novel measures yields a unique analysis methodology that can identify and measure tipping points, system control levers, and critical transitions in system processes. Utilizing network flow-based algorithms makes it possible to formally define and measure multiple styles of robustness behavior (maintaining a property, regaining a property, tending to have a property, etc.). Lastly, tracking the pathways through the induced Markov model makes clear multiple types of path sensitivity.

To perform the analysis one needs to follow a special process in building the Markov model representation of data. Then, once created, specific adaptations of the available analysis methods that are tailored to this specific representation are necessary. To scale the system up for large data sets, custom unsupervised learning techniques are used to appropriately set the resolution and scale of analysis. Although novel animated 3D network visualization methods are incorporated to help researchers explore the results of the dynamical property analysis, the high dimensionality and large scale make an artificial intelligence post-processing engine necessary for identifying key features of interest.

Methodology Example

Novel contributions:

-Capture and compare system dynamics and dynamical properties across diverse applications: compare brain activity in different animals in a parsimonious way.
-Identify patterns in both signal and noise; these can be identified by comparing independent trials and looking for similarities in the differences.
-Automated discovery of control parameters (lever points in the system dynamics).
-State/variable sensitivity analysis reveals what additional data will have the greatest impact in improving the dynamical property and pattern results.