Balancing Geometry and Density: Path Distances on High-Dimensional Data
From MaRDI portal
Publication:5037564
DOI10.1137/20M1386657zbMath1493.62391arXiv2012.09385OpenAlexW4226462355MaRDI QIDQ5037564
James M. Murphy, Daniel McKenzie, Anna V. Little
Publication date: 1 March 2022
Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.09385
Classification and discrimination; cluster analysis (statistical aspects) (62H30) Computational aspects of data analysis and big data (68T09)
Related Items
Clustering Dynamics on Graphs: From Spectral Clustering to Mean Shift Through Fokker–Planck Interpolation ⋮ Geometric scattering on measure spaces
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Local kernels and the geometric structure of data
- Shortest path through random points
- Density-sensitive semisupervised inference
- Generalized density clustering
- On energy, discrepancy and group invariant measures on measurable subsets of Euclidean space
- Entropy reduction in Euclidean first-passage percolation
- Variable bandwidth diffusion kernels
- A note on some rates of convergence in first-passage percolation
- The strong uniform consistency of nearest neighbor density estimates
- Euclidean models of first-passage percolation
- A distribution-free theory of nonparametric regression
- Geodesics and spanning trees for Euclidean first-passage percolation.
- Manifold learning with arbitrary norms
- Fractional diffusion maps
- Nonhomogeneous Euclidean first-passage percolation and distance learning
- Connecting dots: from local covariance to empirical intrinsic geometry and locally linear embedding
- The reach, metric distortion, geodesic convexity and the variation of tangent spaces
- The geometry of kernelized spectral clustering
- Robust path-based spectral clustering
- Estimating the reach of a manifold
- Finding the homology of submanifolds with high confidence from random samples
- Diffusion maps
- 50 Years of First-Passage Percolation
- Curvature Measures
- Efficient Algorithms for Shortest Paths in Sparse Networks
- Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
- Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
- Exact computation of a manifold metric, via Lipschitz Embeddings and Shortest Paths on a Graph
- Clustering Based on Pairwise Distances When the Data is of Mixed Dimensions
- A Nonparametric Estimate of a Multivariate Density Function
- Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data