Finding the Homology of Submanifolds with High Confidence from Random Samples

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The Complexity of Some Topological Inference Problems

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Manifold Adaptive Kernelized Low‐Rank Representation for Semisupervised Image Classification

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Graph Laplacians on Singular Manifolds: Toward understanding complex spaces: graph Laplacians on manifolds with singularities and boundariesPreprint

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Maximum leave-one-out likelihood for kernel density estimation

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Expressivity of expand-and-sparsify representationsPreprint

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Outlier-robust subsampling techniques for persistent homologyPreprint

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The Impact of Changes in Resolution on the Persistent Homology of Images

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A Sheaf-Theoretic Construction of Shape Space

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Topological data analysis of noise: Uniform unimodal distributions

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A Sheaf-Theoretic Perspective on Sampling

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Cone Fields and Topological Sampling in Manifolds with Bounded Curvature

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Optimal Reconstruction Might be Hard

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Only distances are required to reconstruct submanifoldsPreprint

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Minimax adaptive estimation in manifold inference

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Some Geometrical and Topological Aspects of Dimensionality Reduction in Signal Analysis

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Geometric models with weigthed topology

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Statistical Learning on Manifold-Valued Data

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Geometric and probabilistic limit theorems in topological data analysis

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Manifold Modeling in Machine Learning

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The Normalized Graph Cut and Cheeger Constant: From Discrete to Continuous

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The critical curvature degree of an algebraic variety

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Generalized Morse theory of distance functions to surfaces for persistent homology

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Stratification Learning through Homology Inference

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Recognizing Shrinkable Complexes Is NP-Complete

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Fitting an immersed submanifold to data via Sussmann’s orbit theorem

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Homotopy types of random cubical complexes

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Spherical coordinates from persistent cohomology

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Computable Bounds for the Reach and r-Convexity of Subsets of $${{\mathbb {R}}}^d$$

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Computational differential topology

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Regularization for DesignPreprint

Matni, N., & Chandrasekaran, V. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1404.1972 · Cited by 3

Tight Lower Bounds for Homology InferencePreprint

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On the apparent failure of the topological theory of phase transitionsPreprint

Gori, M., Franzosi, R., & Pettini, M. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1602.01240 · Cited by 3

Limit Theorems for the Sum of Persistence BarcodesPreprint

Owada, T. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1604.04058 · Cited by 3

Visualizing data in high-dimensional spaces

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Manifold Fitting under Unbounded NoisePreprint

Yao, Z., & Xia, Y. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1909.10228 · Cited by 3

Curvature of point clouds through principal component analysisPreprint

Asao, Y., & Ike, Y. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2106.09972 · Cited by 3

Unraveling cell differentiation mechanisms through topological exploration of single-cell developmental trajectoriesPreprint

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Finding the homology of manifolds using ellipsoids

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Topological and geometric characterization of synthetic aperture sonar collections

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Curvature analysis of pattern transformation manifolds

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Regression on High-Dimensional Inputs

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Reconstruction of manifold embeddings into Euclidean spaces via intrinsic distances

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Complex Links and Hilbert–Samuel Multiplicities

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On the Error of Random Sampling

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Characterization of stability of dynamic particle ensemble systems using topological data analysis

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Effective homology and periods of complex projective hypersurfaces

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Optimal reconstruction might be hard

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Hyper Neural Network as the Diffeomorphic Domain for Short Code Soft Decision Beyound Belief Propagation Decoding Problem

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Intrinsic persistent homology via density-based metric learning

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$$A_\infty $$ Persistent Homology Estimates Detailed Topology from Pointcloud Datasets

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The reach of subsets of manifolds

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Random Geometric Complexes and Graphs on Riemannian Manifolds in the Thermodynamic Limit

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An algorithm for learning representations of models with scarce data

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Measuring and Localing Homology ClassesPreprint

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Persistent Homology meets Statistical Inference - A Case Study: Detecting Modes of One-Dimensional SignalsPreprint

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Random \v{C}ech Complexes on Riemannian ManifoldsPreprint

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$A_\infty$ persistent homology estimates the topology from pointcloud datasetsPreprint

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Singular persistent homology with geometrically parallelizable computationPreprint

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Intrinsic Dimension Estimation.Preprint

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Denario Project: Deep Knowledge Artificial Intelligence Agents for Scientific Discovery

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Measure estimation on a manifold explored by a diffusion process

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HADES: Fast Singularity Detection with Local Measure Comparison

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Estimating Multidimensional Persistent Homology Through a Finite Sampling

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Restricted Isometry Property of Subspace Projection Matrix Under Random Compression

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Manifold Homotopy via the Flow Complex

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The DTM-signature for a geometric comparison of metric-measure spaces from samples

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Metric Reconstruction Via Optimal Transport

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Restricted isometry property of subspace projection matrix under random compression

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Adversarial Manifold Estimation

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Probability estimates for manifold learning from random samples

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Fitting a manifold of large reach to noisy data

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On topology estimation of submanifolds in Riemannian manifolds by random pointsPreprint

Mirzaie, R. (2025) · arXiv (Cornell University) · doi:10.48550/arxiv.2512.23225

On the sample complexity of learning smooth cuts on a manifold

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