Improved graph Laplacian via geometric self-consistency
arXiv:1406.0118v119 citations
Originality Incremental advance
AI Analysis
This addresses a specific technical bottleneck in manifold learning algorithms, though it appears incremental in scope.
The paper tackles the problem of setting kernel bandwidth for graph Laplacian construction in manifold learning by optimizing geometric self-consistency, resulting in an effective and robust approach.
We address the problem of setting the kernel bandwidth 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 the bandwidth by optimizing the Laplacian's ability to preserve the geometry of the data. Experiments show that this principled approach is effective and robust.