Improved Graph Laplacian via Geometric Self-Consistency
Yu-Chia Chen, Dominique Perrault-Joncas, Marina Meilă, James McQueen
NIPS Workshop on NIPS Highlights (MLTrain), Learn How to code a paper with state of the art frameworks, 2017
Abstract
In all manifold learning algorithms and tasks setting the kernel bandwidth $\varepsilon$ used construct the graph Laplacian is critical. We address this problem by choosing a quality criterion for the Laplacian, that measures its ability to preserve the geometry of the data. For this, we exploit the connection between manifold geometry, represented by the Riemannian metric, and the Laplace-Beltrami operator. Experiments show that this principled approach is effective and robust.
Recommended citation
Yu-Chia Chen, Dominique Perrault-Joncas, Marina Meilă, and James McQueen. Improved Graph Laplacian via Geometric Self-Consistency. NIPS Workshop on NIPS Highlights (MLTrain), Learn How to code a paper with state of the art frameworks, Long Beach, CA, December 2017