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

@inproceedings{Chen2021TheDO, title={The decomposition of the higher-order homology embedding constructed from the k-Laplacian}, author={Yu-Chia Chen and Marina Meilă}, booktitle={NeurIPS}, year={2021} }

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…

## One Citation

Dist2Cycle: A Simplicial Neural Network for Homology Localization

- Computer Science, MathematicsArXiv
- 2021

The proposed model enables learning topological features of the underlying simplicial complexes, specifically, the distance of each k-simplex from the nearest “optimal” kth homology generator, effectively providing an alternative to homology localization.

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