Improved Graph Laplacian via Geometric Self-Consistency

Part of Advances in Neural Information Processing Systems 30 (NIPS 2017)

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Dominique Joncas, Marina Meila, James McQueen


We address the problem of setting the kernel bandwidth, epps, used by Manifold Learning algorithms to construct the graph Laplacian. Exploiting the connection between manifold geometry, represented by the Riemannian metric, and the Laplace-Beltrami operator, we set epps by optimizing the Laplacian's ability to preserve the geometry of the data. Experiments show that this principled approach is effective and robust