发表机构
University of Southern California（南加州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出自适应谱带宽控制方法，使核化图方法的带宽与流形固有复杂度匹配，在CIFAR-100上验证其可提升自监督学习嵌入的分类与标签传播准确率。
AI 中文摘要
使用高斯核的核化图方法（包括谱聚类、扩散映射和稀疏核回归图）依赖于高斯带宽σ的选择，σ决定了局部核算子的谱特性。当σ过小时，核会高估局部复杂度，将每个样本视为独立方向；当σ过大时，核会将多个方向合并，条件数发散，所有几何判别性都会丧失。我们提出一种尺度选择方法，使核的谱复杂度与底层流形的固有复杂度一致。我们提出一种逐节点带宽准则，通过将核的有效秩与通过最小生成树估计的局部固有维数相匹配，在与流形一致的对数-对数缩放范围内锚定搜索，来实现这一原理。我们在CIFAR-100上评估了来自六个编码器的自监督学习（SSL）嵌入，结果显示，自适应带宽在留一法（LOO）分类和标签传播（LP）准确率上，始终优于固定带宽方法和其他竞争自适应方法。
英文摘要
Kernelized graph methods - spectral clustering, diffusion maps, and sparse kernel -regression graphs - that use Gaussian kernels depend on the choice of Gaussian bandwidth sigma, which governs the spectral character of the local kernel operator. When sigma is too small, the kernel overestimates local complexity and treats each sample as an independent direction; when sigma is too large, the kernel collapses multiple directions together, the condition number diverges, and all geometric discrimination is lost. We propose a choice of scale to make the spectral complexity of the kernel consistent with the intrinsic complexity of the underlying manifold. We propose a per-node bandwidth criterion that operationalizes this principle by jointly matching the kernel's effective rank to the local intrinsic dimension estimated via minimum spanning tree, anchoring the search in the manifold-consistent log-log scaling regime. We evaluate SSL embeddings from six encoders on CIFAR-100, showing that adaptive bandwidth consistently improves leave-one-out (LOO) classification and label propagation (LP) accuracy over fixed-bandwidth methods and competing adaptive methods.
CommentsAccepted at IEEE MLSP 2026. 6 pages, 4 figures
