Cumulative topology for time-series classification and regime detection.
The Euler characteristic is the modest invariant: an alternating sum of simplex counts that, written down, fits on a postcard. Computed across a filtration, however, it encodes considerably more structure than the postcard would suggest. Recent work uses Euler characteristic profiles and Euler characteristic surfaces as fast, interpretable descriptors for time-series classification, regime detection in chaotic dynamical systems, and unsupervised classification of two-phase flow regimes.
The advantage of these descriptors over their persistence-based cousins is computational: the Euler characteristic is linear in simplex count and can be tracked through a filtration in a single pass. The cost is that the descriptor is not, in general, complete—different topologies can share an Euler characteristic surface. The work navigates that trade-off honestly.
Active threads
- Interpretable Classification of Time Series Using Euler Characteristic Surfaces—a fully interpretable pipeline for time-series classification, with Atish Mitra and the NIT Sikkim group; under review at Nature Scientific Reports.
- Detecting Regime Transitions in Dynamical Systems via the Mixup Euler Characteristic Profile—a mixup-style ECP for regime change in chaotic systems, submitted to Chaos.
- Topological Characterization of Churn Flow and Unsupervised Correction to the Wu Flow-Regime Map—ECS for two-phase flow classification in vertical pipes, submitted to International Journal of Multiphase Flow.
Collaborators
- Atish Mitra, Montana Technological University
- Md. Nurujjaman, NIT Sikkim
- Buddha Nath Sharma, Salam Rabindrajit Luwang—NIT Sikkim
- Brady Koenig, Abigail Stein, Burt Todd—Montana Tech
- Vishal Mandal, Santanu Nandi