# Spectral Clustering Based on Local PCA

arXiv: https://arxiv.org/abs/1301.2007 · HTML: https://mlsanity.com/paper/1301.2007/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2013.

## Built on by (most cited first, 15 of 15)

- [Tangent Space and Dimension Estimation with the Wasserstein Distance](https://mlsanity.com/paper/2110.06357/) (2021)
- [A Multiscale Environment for Learning by Diffusion](https://mlsanity.com/paper/2102.00500/) (2021)
- [Large sample spectral analysis of graph-based multi-manifold clustering](https://mlsanity.com/paper/2107.13610/) (2021)
- [Enhancing cluster analysis via topological manifold learning](https://mlsanity.com/paper/2207.00510/) (2022)
- [CA-PCA: Manifold Dimension Estimation, Adapted for Curvature](https://mlsanity.com/paper/2309.13478/) (2023)
- [CAMEL: Curvature-Augmented Manifold Embedding and Learning](https://mlsanity.com/paper/2303.02561/) (2023)
- [Harnessing Data Asymmetry: Manifold Learning in the Finsler World](https://mlsanity.com/paper/2603.11396/) (2026)
- [Measuring inter-cluster similarities with Alpha Shape TRIangulation in loCal Subspaces (ASTRICS) facilitates visualization and clustering of high-dimensional data](https://mlsanity.com/paper/2107.07603/) (2021)
- [Tensor Robust PCA with Nonconvex and Nonlocal Regularization](https://mlsanity.com/paper/2211.02404/) (2022)
- [On Linear Separation Capacity of Self-Supervised Representation Learning](https://mlsanity.com/paper/2310.19041/) (2023)
- [LINSCAN -- A Linearity Based Clustering Algorithm](https://mlsanity.com/paper/2406.17952/) (2024)
- [A Graph-Partitioning Based Continuous Optimization Approach to Semi-supervised Clustering Problems](https://mlsanity.com/paper/2503.04447/) (2025)
- [Robust Multi-Manifold Clustering via Simplex Paths](https://mlsanity.com/paper/2507.10710/) (2025)
- [Uncovering Locally Low-dimensional Structure in Networks by Locally Optimal Spectral Embedding](https://mlsanity.com/paper/2603.11965/) (2026)
- [TNF based Spectral Embedding for Effective Application of Supervised Machine Learning Techniques in Automobile Insurance Fraud Detection](https://mlsanity.com/paper/2609.33376/) (2026)

## 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.