15 citations · 34 across the 26 of their papers we have counts for
32 papers
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…
The Null Is the Hard Part: Exact Tests for Memorization in Generative Models
Sushovan Majhi, Pramita Bagchi
Memorization audits of generative models read similarity scores against thresholds, with no null distribution, and the conclusions they support can be wrong. By MemBench's rule, th…
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…
Certified Topological Interaction in Neural Representations: Exact Tests and the Statistic They Require
Sushovan Majhi
Class disentanglement--the separation of a representation's class-conditional point clouds along depth and over training--is measured by descriptive curves: the sentence such a stu…
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 constant-factor approximation of the Gromov-Hausdorff distance in the plane
Sushovan Majhi
We give the first polynomial-time constant-factor approximation of the Gromov-Hausdorff distance d_GH between finite point sets in the Euclidean plane; in fixed Euclidean dimension…
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…
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…
Vietoris--Rips Shadow for Euclidean Graph Reconstruction
Rafal Komendarczyk, Sushovan Majhi, Atish Mitra
The shadow of an abstract simplicial complex with vertices in is a subset of defined as the union of the convex hulls of simplices of . The Vie…
Topology of The Polar Vortex and Montana Weather
Joshua Dorrington, Sushovan Majhi, Atish Mitra +4
This paper explores the use of Topological Data Analysis (TDA) to investigate patterns in zonal-mean zonal winds of the Arctic, which make up the polar vortex, in order to better e…
Detecting the Indian Monsoon using Topological Data Analysis
Enrique Alvarado, Daniela Beckelhymer, Joshua Dorrington +5
A monsoon is a wind system that seasonally reverses its direction, accompanied by corresponding changes in precipitation. The Indian monsoon is the most prominent monsoon system, p…
Lower Bounding the Gromov--Hausdorff distance in Metric Graphs
Henry Adams, Sushovan Majhi, Fedor Manin +2
Let be a finite, connected metric graph and let be a subset. If is sufficiently dense in , we show that the Gromov--Hausdorff distance matches the Hausdor…
Faithful Reeb Graph Reconstruction of a Tectonic Subduction Zone from Earthquake Hypocenters
Halley Fritze, Sushovan Majhi, Marissa Masden +2
An important problem in topological data analysis (TDA)$\unicode{x2014}$of both theoretical and practical interest$\unicode{x2014}$is to reconstruct the topology and geometry of an…
Topological Stability and Latschev-type Reconstruction Theorems for Spaces of Curvature Bounded Above
Rafal Komendarczyk, Sushovan Majhi, Will Tran
We consider the problem of homotopy-type reconstruction of compact subsets that have the Alexandrov curvature bounded above ( ) in the intrinsic length metr…
Identifying Extreme Events in the Stock Market: A Topological Data Analysis
Anish Rai, Buddha Nath Sharma, Salam Rabindrajit Luwang +2
This paper employs Topological Data Analysis (TDA) to detect extreme events (EEs) in the stock market at a continental level. Previous approaches, which analyzed stock indices sepa…
Complex network analysis of cryptocurrency market during crashes
Kundan Mukhia, Anish Rai, SR Luwang +3
This paper identifies the cryptocurrency market crashes and analyses its dynamics using the complex network. We identify three distinct crashes during 2017-20, and the analysis is…
Hausdorff vs Gromov-Hausdorff distances
Henry Adams, Florian Frick, Sushovan Majhi +1
Let be a closed Riemannian manifold and let . If the sample is sufficiently dense relative to the curvature of , then the Gromov-Hausdorff distance between…
Metric and Path-Connectedness Properties of the Frechet Distance for Paths and Graphs
Erin Chambers, Brittany Fasy, Benjamin Holmgren +2
The Frechet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to handwriting recognition. M…
Graph Mover's Distance: An Efficiently Computable Distance Measure for Geometric Graphs
Sushovan Majhi
Many applications in pattern recognition represent patterns as a geometric graph. The geometric graph distance (GGD) has recently been studied as a meaningful measure of similarity…