通过噪声谱嵌入方法，无贪婪搜索地选出高维数据中关键特征。
Diffusion-Guided Feature Selection via Nishimori Temperature: Noise-Based Spectral Embedding
- 基于物理启发的谱嵌入框架，利用贝斯海森矩阵奇异点确定关键温度。
- 仅保留30%特征时，ImageNet分类准确率下降低于1%，优于传统方法。
- 适合需要高压缩比且保持精度的特征选择场景，如模型轻量化。
我们提出噪声基谱嵌入（NBSE），一种无需贪婪搜索即可从高维数据中选择信息特征的物理启发框架。NBSE在样本上构建稀疏相似性图，并识别贝蒂海森矩阵奇异时的奈须茂温度β_N。对应最小特征向量捕捉内在度修正扩散过程的主导模式，自然重加权节点以避免中心节点主导。通过转置数据矩阵并在特征空间应用NBSE，获得一维谱嵌入，揭示冗余或语义相关的维度群；均衡分箱后每组选取一个代表。我们证明彩色高斯扰动对β_N的影响不超过O(σ̄²)，保证对测量噪声的鲁棒性。在MobileNetV2和EfficientNet-B4的ImageNet嵌入上实验显示，即使在激进压缩下NBSE仍保持分类准确率：保留30%特征时，EfficientNet-B4准确率下降低于1%，优于ANOVA F检验和随机选择最多6.8%。
原文摘要 · Abstract (English)
We propose Noise-Based Spectral Embedding (NBSE), a physics-informed framework for selecting informative features from high-dimensional data without greedy search. NBSE constructs a sparse similarity graph on the samples and identifies the Nishimori temperature $β_N$ the critical inverse temperature at which the Bethe Hessian becomes singular. The corresponding smallest eigenvector captures the dominant mode of an intrinsically degree-corrected diffusion process, naturally reweighting nodes to prevent hub dominance. By transposing the data matrix and applying NBSE in feature space, we obtain a one-dimensional spectral embedding that reveals groups of redundant or semantically related dimensions; balanced binning then selects one representative per group. We prove that coloured Gaussian perturbations shift $β_N$ by at most $O(\barσ^2)$, guaranteeing robustness to measurement noise. Experiments on ImageNet embeddings from MobileNetV2 and EfficientNet-B4 show that NBSE preserves classification accuracy even under aggressive compression: on EfficientNet-B4 the accuracy drop is below $1\%$ when retaining only $30\%$ of features, outperforming ANOVA $F$-test and random selection by up to $6.8\%$.
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