Topological Data Analysis for High-Dimensional Dynamic Process Monitoring
For industrial process monitoring, this work offers a novel trajectory-based event detection approach that leverages topological structure, though results are limited to a single dataset and comparisons are not exhaustive.
The paper introduces a process monitoring method that combines topological data analysis with neural ODEs to detect events in high-dimensional time-series data, demonstrating effectiveness on real industrial data against PCA, autoencoders, and Koopman autoencoders.
Real-time process monitoring requires methods that extract actionable information from high-dimensional time-series data. In this work, we present a new approach for process monitoring that combines tools of topological data analysis (TDA) and machine learning. In the proposed approach, we represent multivariate time-series data as manifolds and use topological descriptors to summarize the structure of such data; we then use a neural ordinary differential equation to learn the dynamic evolution of the topological structure of the system. Using real data from an industrial process, we show that this trajectory-based event detection approach is effective at detecting diverse types of events. We contrast this approach against reconstruction-based approaches such as principal component analysis and autoencoders and against a trajectory-based approach that uses Koopman autoencoders.