11 papers · 1 filter
Where Do Two Populations of Persistence Diagrams Differ? Calibrated Local Inference at a Fixed Budget
Pramita Bagchi, Edward Bae, Atish Mitra +3
Many two-sample tests for populations of persistence diagrams assess global differences without identifying the regions of the birth-death plane that contribute to them. We study s…
COMPLEX: A Closed-Form Certified Embedding of Multiparameter Persistence Modules
Sushovan Majhi, Atish Mitra, Žiga Virk +1
Every multiparameter persistence vectorization we know of carries a one-sided Lipschitz upper bound and nothing below it: without a lower gauge there is no sense in which the featu…
Statistical Inference for Persistence Diagrams via Landmark Embeddings: Minimax Theory and Finite Approximation
Pramita Bagchi, Sushovan Majhi, Atish Mitra +1
Hilbert-space embeddings enable inference for populations of persistence diagrams, but separation between individual diagrams need not survive population averaging. We develop a fr…
The Intersection Euler Characteristic Profile: Euler Calculus and Stability for Topological Interaction of Ball Unions
Kazuhiro Kawamura, Sushovan Majhi, Atish Mitra
The Intersection Euler Characteristic Profile (Intersection ECP) of colored point clouds is the Euler characteristic $χ(\bigcap_{i=1}^k…
A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classification
Sushovan Majhi, Atish Mitra, Žiga Virk +1
We introduce PLACE (Persistence-Landmark Analytic Classification Engine), a closed-form pipeline for classifying point clouds and graphs through their persistent-homology signature…
A Closed-Form Adaptive-Landmark Kernel for Certified Point-Cloud and Graph Classification
Sushovan Majhi, Atish Mitra, Žiga Virk +1
We introduce PALACE (Persistence Adaptive-Landmark Analytic Classification Engine), the data-adaptive companion to PLACE, paying a small cross-validation tier on three knobs (budge…
Detecting Regime Transitions in Dynamical Systems via the Mixup Euler Characteristic Profile
Sushovan Majhi, Atish Mitra, Santanu Nandi +2
We develop a framework for detecting regime transitions in dynamical systems using the Mixup Euler Characteristic Profile (Mixup ECP) -- the Euler characteristic of the geometric i…
Transfinitely iterated wild sets
Jeremy Brazas, Atish Mitra
In this paper, we study homotopical analogues of the Cantor-Bendixson derivative. For each , the "-wild set" of a topological space is the subsp…
Topological Characterization of Churn Flow and Unsupervised Correction to the Wu Flow-Regime Map in Small-Diameter Vertical Pipes
Brady Koenig, Sushovan Majhi, Atish Mitra +2
Churn flow-the chaotic, oscillatory regime in vertical two-phase flow-has lacked a quantitative mathematical definition for over years. We introduce the first topology-based c…
Interpretable Classification of Time Series Using Euler Characteristic Surfaces
Salam Rabindrajit Luwang, Sushovan Majhi, Vishal Mandal +3
Persistent homology (PH) -- the conventional method in topological data analysis -- is computationally expensive, requires further vectorization of its signatures before machine le…
The Shadow of Vietoris--Rips Complexes in Limits
Kazuhiro Kawamura, Sushovan Majhi, Atish Mitra
The Vietoris-Rips complex, denoted , of a metric space at scale is an abstract simplicial complex where each -simplex corresponds to points of wi…