Graph-Based, Time-Warped Embedding for Time Series Analysis and Process Monitoring
Kyle Territo, José A. Romagnoli · Industrial & Engineering Chemistry Research · 2026
High Resolution Image Download MS PowerPoint Slide This work presents an unsupervised approach for visualizing, analyzing, and monitoring large multivariate time series data in lower-dimensional spaces. The method integrates dynamic time warping (DTW) with graph-based layout algorithms to uncover temporal structure and similarity across complex data sets─without requiring labeled data or predefined models. It works by segmenting time series into windows and computing pairwise DTW distances to capture the temporal alignment. These distances are then used to construct a k -nearest neighbor ( k -NN) graph, which is visualized by using a force-directed layout algorithm. The resulting map offers an interpretable representation of the time series structure, where the spatial proximity corresponds to the temporal similarity between data windows. Unlike traditional dimensionality reduction (DR) techniques, this method does not project data into feature space; instead, it visualizes the relational topology of DTW-aligned patterns. This provides a powerful and intuitive tool for revealing the structure in complex temporal data. The framework also supports online monitoring with an adaptive threshold mechanism for real-time anomaly detection.