• Corpus ID: 236318489

The decomposition of the higher-order homology embedding constructed from the k-Laplacian

  title={The decomposition of the higher-order homology embedding constructed from the k-Laplacian},
  author={Yu-Chia Chen and Marina Meilă},
The null space of the k-th order Laplacian Lk, known as the k-th homology vector space, encodes the non-trivial topology of a manifold or a network. Understanding the structure of the homology embedding can thus disclose geometric or topological information from the data. The study of the null space embedding of the graph Laplacian L0 has spurred new research and applications, such as spectral clustering algorithms with theoretical guarantees and estimators of the Stochastic Block Model. In… 

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