(138a) Topological Data Analysis for Multivariate Process Monitoring: Inspirations from Neuroscience

Process monitoring is essential in detecting abnormal behavior that might compromise efficiency and safety but is challenging due to the presence of multivariable interdependencies and of time-varying and nonlinear behavior [1,2]. A scientific field that requires monitoring a system with similar characteristics is neuroscience [3]. Specifically, the study of the brain through methods such as functional magnetic resonance imaging (fMRI) requires the analysis of high-dimensional multivariate time series that capture the activity and interdependencies of different areas of the brain in order to understand responses to different stimuli or to detect abnormal behavior or disease [4, 5]. Thus, there is a diverse set of insights and methods from neuroscience that can potentially be applied to process monitoring.

In this talk, we discuss connections found between the areas of neuroscience and multivariate process monitoring and how this leads to the incorporation of new data analysis techniques from topology and algebraic geometry. Prevalent data analysis methods in the process monitoring literature are based upon statistical techniques such as principal component analysis (PCA) and partial least squares (PLS) [6]. These methods are effective at identifying informational features from data (e.g., principal components) but might fail to identify other types of hidden features. For instance, data objects live in domains that can be described using topological and geometrical features; these features are robust to noise, generalize to high dimensions, and do not require statistical assumptions such as isotropy and stationarity. Here, we focus on the application of Riemannian geometry and algebraic topology to characterize datasets arising in multivariate process monitoring [7, 8]. Specifically, our approach analyzes process behavior by characterizing the geometrical structure of correlation matrices. We illustrate the benefits of these techniques using datasets from the Tennessee Eastman chemical process [9].

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[9] Philip R Lyman and Christos Georgakis. Plant-wide control of the tennessee eastman problem. Computers & chemical engineering, 19(3):321–331, 1995.