Spectral Clustering Based on Local PCA
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Abstract (arXiv)
We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weighted according to a discrepancy between the principal subspaces in the neighborhoods, and then applies spectral clustering. As opposed to standard spectral methods based solely on pairwise distances between points, our algorithm is able to resolve intersections. We establish theoretical guarantees for simpler variants within a prototypical mathematical framework for multi-manifold clustering, and evaluate our algorithm on various simulated data sets.
Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Jan 2013.
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Citing papers per year: 2021: 4; 2022: 2; 2023: 3; 2024: 1; 2025: 2; 2026: 3.
15 papers.
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- 2021Tangent Space and Dimension Estimation with the Wasserstein Distancecited by 10
- 2021A Multiscale Environment for Learning by Diffusioncited by 8
- 2021Large sample spectral analysis of graph-based multi-manifold clusteringcited by 8
- 2022Enhancing cluster analysis via topological manifold learningcited by 6
- 2023CA-PCA: Manifold Dimension Estimation, Adapted for Curvaturecited by 4
- 2023CAMEL: Curvature-Augmented Manifold Embedding and Learningcited by 3
- 2021Measuring inter-cluster similarities with Alpha Shape TRIangulation in loCal Subspaces (ASTRICS) facilitates visualization and clustering of high-dimensional datacited by 0
- 2022Tensor Robust PCA with Nonconvex and Nonlocal Regularizationcited by 0
- 2023On Linear Separation Capacity of Self-Supervised Representation Learningcited by 0
- 2024LINSCAN -- A Linearity Based Clustering Algorithmcited by 0
- 2025A Graph-Partitioning Based Continuous Optimization Approach to Semi-supervised Clustering Problemscited by 0
- 2025Robust Multi-Manifold Clustering via Simplex Pathscited by 0
3 more
- 2026Harnessing Data Asymmetry: Manifold Learning in the Finsler Worldcited by 0
- 2026Uncovering Locally Low-dimensional Structure in Networks by Locally Optimal Spectral Embeddingcited by 0
- 2026TNF based Spectral Embedding for Effective Application of Supervised Machine Learning Techniques in Automobile Insurance Fraud Detectioncited by 0
- 2026TNF based Spectral Embedding for Effective Application of Supervised Machine Learning Techniques in Automobile Insurance Fraud Detection27 Sep 2026
- 2026Uncovering Locally Low-dimensional Structure in Networks by Locally Optimal Spectral Embedding12 Mar 2026
- 2026Harnessing Data Asymmetry: Manifold Learning in the Finsler World12 Mar 2026
- 2025Robust Multi-Manifold Clustering via Simplex Paths14 Jul 2025
- 2025A Graph-Partitioning Based Continuous Optimization Approach to Semi-supervised Clustering Problems6 Mar 2025
- 2024LINSCAN -- A Linearity Based Clustering Algorithm25 Jun 2024
- 2023On Linear Separation Capacity of Self-Supervised Representation Learning29 Oct 2023
- 2023CA-PCA: Manifold Dimension Estimation, Adapted for Curvature23 Sep 2023
- 2023CAMEL: Curvature-Augmented Manifold Embedding and Learning5 Mar 2023
- 2022Tensor Robust PCA with Nonconvex and Nonlocal Regularization4 Nov 2022
- 2022Enhancing cluster analysis via topological manifold learning1 Jul 2022
- 2021Tangent Space and Dimension Estimation with the Wasserstein Distance12 Oct 2021
3 more
- 2021Large sample spectral analysis of graph-based multi-manifold clustering28 Jul 2021
- 2021Measuring inter-cluster similarities with Alpha Shape TRIangulation in loCal Subspaces (ASTRICS) facilitates visualization and clustering of high-dimensional data15 Jul 2021
- 2021A Multiscale Environment for Learning by Diffusion31 Jan 2021
- 2021Tangent Space and Dimension Estimation with the Wasserstein Distancecited by 10
- 2021A Multiscale Environment for Learning by Diffusioncited by 8
- 2021Large sample spectral analysis of graph-based multi-manifold clusteringcited by 8
- 2022Enhancing cluster analysis via topological manifold learningcited by 6
- 2023CA-PCA: Manifold Dimension Estimation, Adapted for Curvaturecited by 4
- 2023CAMEL: Curvature-Augmented Manifold Embedding and Learningcited by 3
- 2021Measuring inter-cluster similarities with Alpha Shape TRIangulation in loCal Subspaces (ASTRICS) facilitates visualization and clustering of high-dimensional datacited by 0
- 2022Tensor Robust PCA with Nonconvex and Nonlocal Regularizationcited by 0
- 2023On Linear Separation Capacity of Self-Supervised Representation Learningcited by 0
- 2024LINSCAN -- A Linearity Based Clustering Algorithmcited by 0
- 2025A Graph-Partitioning Based Continuous Optimization Approach to Semi-supervised Clustering Problemscited by 0
- 2025Robust Multi-Manifold Clustering via Simplex Pathscited by 0
12 most cited of 15 All 15 (JSON)
- 2026TNF based Spectral Embedding for Effective Application of Supervised Machine Learning Techniques in Automobile Insurance Fraud Detection27 Sep 2026
- 2026Uncovering Locally Low-dimensional Structure in Networks by Locally Optimal Spectral Embedding12 Mar 2026
- 2026Harnessing Data Asymmetry: Manifold Learning in the Finsler World12 Mar 2026
- 2025Robust Multi-Manifold Clustering via Simplex Paths14 Jul 2025
- 2025A Graph-Partitioning Based Continuous Optimization Approach to Semi-supervised Clustering Problems6 Mar 2025
- 2024LINSCAN -- A Linearity Based Clustering Algorithm25 Jun 2024
- 2023On Linear Separation Capacity of Self-Supervised Representation Learning29 Oct 2023
- 2023CA-PCA: Manifold Dimension Estimation, Adapted for Curvature23 Sep 2023
- 2023CAMEL: Curvature-Augmented Manifold Embedding and Learning5 Mar 2023
- 2022Tensor Robust PCA with Nonconvex and Nonlocal Regularization4 Nov 2022
- 2022Enhancing cluster analysis via topological manifold learning1 Jul 2022
- 2021Tangent Space and Dimension Estimation with the Wasserstein Distance12 Oct 2021
12 newest of 15 All 15 (JSON)