(596a) Event Detection in Multivariate Time-Series Data Using Topology

Topological data analysis (TDA) is a powerful tool for extracting information from complex datasets [1-2]. In recent years, TDA has found remarkable success in diverse applications, spanning neuroscience, materials science, and network analysis [3-6]. The goal of TDA is to use geometric/topological representations of data and to quantify the shape/structure of such representations. For example, TDA represents data as graphs/networks and manifolds and uses topological descriptors to quantify the shape of such objects (e.g., persistent diagrams and the Euler characteristic). TDA also offers robustness, as topological descriptors remain invariant under certain types of data perturbations such as scaling, rotation, and random noise. Moreover, TDA computations are significantly more scalable than competing approaches such as convolutional neural networks [8].

In this work, we show that TDA is a robust, scalable, and interpretable method for detecting events from multivariate time-series data (as that arising in the monitoring of chemical processes). Specifically, we show TDA unravels the complex spatio-temporal connectivity of chemical processes (i.e., across time and across process units). The focus on connectivity is a key defining aspect of TDA over other conventional methods used for event detection such as principal component analysis, convolutional neural networks, autoencoders, support vector machines, and Fisher discriminant analysis [7]. We explore different representations of multivariate time-series data as images/manifolds, graphs/networks, and correlation/functional networks [1] and we use basic topological descriptors and filtration operations of these data representations to identify events and critical variables driving such events. By applying TDA to a couple of real industrial datasets, we show that the proposed approach is capable of identifying “topological signatures” that point towards instability regions of the process and towards diverse types of events. Moreover, we show how the TDA approach can help identify variables that remain strongly connected (or not) during different types of events. We also show how to use TDA information to identify a latent space of the process that helps visualize the onset and dynamics of diverse event types.

References

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