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

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


Smith, A. - Presenter, University of Wisconsin - Madison
Zavala, V. M., University of Wisconsin-Madison
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].

[1] Youqing Wang, Yabin Si, Biao Huang, and Zhijiang Lou. Survey on the theoretical research and engineering applications of multivariate statistics process monitoring algorithms: 2008–2017. The Canadian Journal of Chemical Engineering, 96(10):2073–2085, 2018.

[2] Thuntee Sukchotrat, Seoung Bum Kim, and Fugee Tsung. One-class classification-based control charts for multivariate process monitoring. IIE transactions, 42(2):107–120, 2009.

[3] Jonathan D Power, Alexander L Cohen, Steven M Nelson, Gagan S Wig, Kelly Anne Barnes, Jessica A Church, Alecia C Vogel, Timothy O Laumann, Fran M Miezin, Bradley L Schlaggar, et al. Functional network organization of the human brain. Neuron, 72(4):665–678, 2011.

[4] Nicolas Langer, Andreas Pedroni, Lorena RR Gianotti, Jurgen Hanggi, Daria Knoch, and Lutz J¨ancke. Functional brain network efficiency predicts intelligence. Human brain mapping, 33(6):1393–1406, 2012.

[5] Sophie Achard, Raymond Salvador, Brandon Whitcher, John Suckling, and ED Bullmore. A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. Journal of Neuroscience, 26(1):63–72, 2006.

[6] Salvador Garcıa-Munoz, Theodora Kourti, John F MacGregor, Arthur G Mateos, and Gerald Murphy. Troubleshooting of an industrial batch process using multivariate methods. Industrial & engineering chemistry research, 42(15):3592–3601, 2003.

[7] Moo K Chung, Hyekyoung Lee, Alex DiChristofano, Hernando Ombao, and Victor Solo. Exact topological inference of the resting-state brain networks in twins. Network Neuroscience, 3(3):674–694, 2019.

[8] Marco Congedo, Alexandre Barachant, and Rajendra Bhatia. Riemannian geometry for eeg-based brain-computer interfaces; a primer and a review. Brain-Computer Interfaces, 4(3):155–174, 2017.

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