Ghost hunting in the nonlinear dynamic machine.

Ascher K. Munion,Ning Cai,Alexander Wong,Jonathan E. Butner,Brian R. W. Baucom

doi:10.1371/journal.pone.0226572

Ascher K. Munion, Ning Cai + Show 3 more

Open Access

https://doi.org/10.1371/journal.pone.0226572

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Journal: PloS one	Publication Date: Dec 19, 2019
Citations: 3	License type: CC BY 4.0

Affiliation: University of Utah, California State University, Chico

Abstract

Integrating dynamic systems modeling and machine learning generates an exploratory nonlinear solution for analyzing dynamical systems-based data. Applying dynamical systems theory to the machine learning solution further provides a pathway to interpret the results. Using random forest models as an illustrative example, these models were able to recover the temporal dynamics of time series data simulated using a modified Cusp Catastrophe Monte Carlo. By extracting the points of no change (set points) and the predicted changes surrounding the set points, it is possible to characterize the topology of the system, both for systems governed by global equation forms and complex adaptive systems. RESULTS: The model for the simulation was able to recover the cusp catastrophe (i.e. the qualitative changes in the dynamics of the system) even when applied to data that have a significant amount of error variance. To further illustrate the approach, a real-world accelerometer example was examined, where the model differentiated between movement dynamics patterns by identifying set points related to cyclic motion during walking and attraction during stair climbing. These example findings suggest that integrating machine learning with dynamical systems modeling provides a viable means for classifying distinct temporal patterns, even when there is no governing equation for the nonlinear dynamics. Results of these integrated models yield solutions with both a prediction of where the system is going next and a decomposition of the topological features implied by the temporal dynamics.

Highlights

Advancements in machine learning are frequently utilized for an extensive array of applications, from pattern identification and robotics to classification [1, 2] and are even harnessed for traditional statistical analyses [3]
When machine learning approaches are applied within the context of inferential dynamical systems analyses, the results provide a rich set of information about both prediction and decomposition of the different temporal patterns reflected in the data set
This paper explores how seeking set points and the stability around those set points can decompose complex dynamical systems-based machine learning solutions

Summary

Introduction

Advancements in machine learning are frequently utilized for an extensive array of applications, from pattern identification and robotics to classification [1, 2] and are even harnessed for traditional statistical analyses [3]. Statistical learning generally serves two purposes: 1) prediction of a response variable (i.e., classification), and 2) to address inferential questions– identifying the relationships between sets of variables [4]. Machines generate a prediction algorithm but do not generally provide the decomposition of the linear, or nonlinear, relationship between various predictors within the analysis–even those that focus on inference. When the goal is categorization or outcome prediction, the decomposition of relationships building the prediction is of minimal importance.

Results

Discussion

Conclusion