Spectral clustering based on local linear approximations

DOI10.1214/11-EJS651zbMath1271.62132arXiv1001.1323WikidataQ29040379 ScholiaQ29040379MaRDI QIDQ1952238

Gilad Lerman, Guangliang Chen, Ery Arias-Castro

Publication date: 28 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1323

zbMATH Keywords

local polynomial approximationspectral clusteringlocal linear approximationdimension estimationnearest-neighbor searchdetection of clusters in point cloudshigher-order affinities

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Pattern recognition, speech recognition (68T10)

Related Items

Learning the geometric structure of manifolds with singularities using the tensor voting graph, Unnamed Item, Unnamed Item, A distributed framework for trimmed kernel \(k\)-means clustering, The Fiedler Vector of a Laplacian Tensor for Hypergraph Partitioning, A dynamic programming approach for distributing quantum circuits by bipartite graphs, Hybrid linear modeling via local best-fit flats, A new approach to two-view motion segmentation using global dimension minimization, Random walk distances in data clustering and applications, Robust recovery of multiple subspaces by geometric \(l_{p}\) minimization, \(l_p\)-recovery of the most significant subspace among multiple subspaces with outliers, Remember the curse of dimensionality: the case of goodness-of-fit testing in arbitrary dimension, Robust subspace clustering, The shape of data and probability measures, Laplacian and signless Laplacian spectra and energies of multi-step wheels, A Well-Tempered Landscape for Non-convex Robust Subspace Recovery, A multiscale environment for learning by diffusion, Statistical analysis of a hierarchical clustering algorithm with outliers, LEAST SQUARES APPROXIMATIONS OF MEASURES VIA GEOMETRIC CONDITION NUMBERS

Cites Work

• Unnamed Item
• Robust algebraic segmentation of mixed rigid-body and planar motions from two views
• Foundations of a multi-way spectral clustering framework for hybrid linear modeling
• A unified algebraic approach to 2-D and 3-D motion segmentation and estimation
• Optimal construction of \(k\)-nearest-neighbor graphs for identifying noisy clusters
• Measuring the strangeness of strange attractors
• Connectivity of the mutual \(k\)-nearest-neighbor graph in clustering and outlier detection
• Asymptotical minimax recovery of sets with smooth boundaries
• Metric entropy of some classes of sets with differentiable boundaries
• A survey of kernel and spectral methods for clustering
• Consistency of spectral clustering
• Finding the homology of submanifolds with high confidence from random samples
• Fast multiscale clustering and manifold identification
• Image manifolds which are isometric to Euclidean space
• Networks of polynomial pieces with application to the analysis of point clouds and images
• Curvature Measures
• Cluster Identification in Nearest-Neighbor Graphs
• Estimation of Subspace Arrangements with Applications in Modeling and Segmenting Mixed Data
• Detection of Abnormal Behavior Via Nonparametric Estimation of the Support
• Random Geometric Graphs
• Detection of non-random patterns in cosmological gravitational clustering
• The Generic Chaining
• Lanczos Algorithms for Large Symmetric Eigenvalue Computations
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Clustering Based on Pairwise Distances When the Data is of Mixed Dimensions
• Operator norm convergence of spectral clustering on level sets
• Connect the dots: how many random points can a regular curve pass through?
• On the Volume of Tubes