Featured research · IEEE MLSP 2026
A local bandwidth-selection criterion for Gaussian-kernel graphs that matches spectral complexity to the intrinsic complexity of the data manifold.
Visual summary
The key idea: very small bandwidths make the local kernel nearly identity-like, while very large bandwidths collapse it toward rank one. The target is the intermediate regime where the effective rank is consistent with local manifold complexity.
The problem
Gaussian-kernel graph methods depend strongly on bandwidth. At one extreme, the graph fragments because the kernel resolves spurious directions. At the other, distinct directions become indistinguishable. The challenge is to select the useful scale locally.
The idea
For each node, the method compares the kernel's effective rank with an MST-based local intrinsic-dimension estimate, while restricting the search to the manifold-consistent log-log scaling regime.
Method
Measures how many meaningful spectral directions the local kernel operator resolves. The target is not raw rank, but a continuous effective complexity.
An MST-based estimate captures manifold complexity in the high-dimensional regime where pairwise distance ratios can become unreliable.
The search favors bandwidths inside the scaling region where kernel mass follows the expected manifold law.
Evidence
Across CIFAR-100 embeddings from six self-supervised encoders, the selected bandwidth produces an effective-rank signal that aligns substantially better with dimMST than with the Levina–Bickel estimator. The paper reports Spearman correlations of 0.88–0.91 for dimMST versus 0.43–0.63 for LB across the evaluated encoders.
The adaptive bandwidth improves leave-one-out classification and label propagation over fixed-bandwidth and competing adaptive baselines, for both dense and sparse graph constructions.
Supporting visual
The paper's second figure compares effective rank at the selected bandwidth against per-node intrinsic dimension for three encoders. The site graphic above is a visual placeholder for the published multi-panel result; the source figure and full details remain in the paper.
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