HEE

This python module offers a series of Spectral Learning techniques for Hypergraph embedding.

How to use HEE

The implementation of all methods are available in the python script hee.methods.spectral_methods.py.

New spectral embedding techniques must be implemented extending the base class SpectralEmbeddingFramework and the class must implement the methods:

• _laplacian(self) (private) that returns the hypergraph laplacian matrix;
• fit(self, dim, **kwargs) that returns the vertex embeddings matrix.

Quick look

We provide a python notebook when the implemented techniques are compared on a clustering task on the ZOO dataset.

List of supported methods

• Zhou D. Zhou, J. Huang, and B. Schölkopf. 2007. Learning with Hypergraphs: Clustering, Classification, and Embedding. In Proceedings of Neural Information Processing Systems. 1601–1608
• Ren P. Ren, R. C. Wilson, and E. R. Hancock. 2008. Spectral Embedding of Feature Hypergraphs. In Structural, Syntactic, and Statistical Pattern Recognition. 308–317
• Bolla M. Bolla. 1993. Spectra, Euclidean representations and clusterings of hypergraphs. Discrete Math. 117 (1993), 19–39. Issue 1-
• Zhu Y. Zhu, Z. Guan, T. Tan, H. Liu, D. Cai, and X. He. 2016. Heterogeneous hypergraph embedding for document recommendation. Neurocomputing 216 (2016), 150–162
• Luo F. Luo, B. Du, L. Zhang, L. Zhang, and D. Tao. 2019. Feature Learning Using Spatial-Spectral Hypergraph Discriminant Analysis for Hyperspectral Image. IEEE Trans. on Cybernetics 49, 7 (2019), 2406–2419
• Rodriguez J.A. Rodrìguez. 2002. On the Laplacian Eigenvalues and Metric Parameters of Hypergraphs. Linear and Multilinear Algebra 50, 1 (2002), 1–14.
• Saito S. Saito, D. P. Mandic, and H. Suzuki. 2018. Hypergraph p-Laplacian: A Differential Geometry View. Proceedings of the AAAI Conference on Artificial Intelligence 32, 1 (2018)

Requirements

• HypernetX
• Numpy
• Scipy
• sklearn