Reproduce “Geometry-Aware Graph Construction via Adaptive Spectral Bandwidth Control” on OpenResearch
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About this paper
Ecem Bozkurt, Antonio Ortega
Researchers at the University of Southern California developed a per-node adaptive Gaussian bandwidth selection criterion for kernelized graph construction, which aligns the kernel's effective rank with the local intrinsic dimension of the data manifold. This method consistently improves Leave-One-Out classification and Label Propagation accuracy on CIFAR-100 across various self-supervised learning embeddings.
Key insights
- A kernel operates at the correct scale when its spectral complexity (quantified by effective rank) is comparable to the intrinsic complexity of the local data manifold.
- The Minimum Spanning Tree (MST)-based intrinsic dimension estimator is suitable for robustly characterizing local geometric complexity in high-dimensional, ℓ2-normalized self-supervised embeddings.
- Optimizing for both the alignment of effective rank with intrinsic dimension and manifold scaling consistency is crucial for constructing geometrically faithful and effective graphs.
Summary by alphaXiv.
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