论文标题
频谱群集的剩余单个子空间扰动分析
Leave-one-out Singular Subspace Perturbation Analysis for Spectral Clustering
论文作者
论文摘要
奇异子空间扰动理论在概率和统计中至关重要。它在不同领域具有各种应用。我们考虑两个任意的矩阵，其中一个是另一个列出的一个列出的子矩阵，并为两个相应的奇异子空间之间的距离建立了一种新型的扰动上限。它非常适合混合模型，并且与诸如韦丁定理之类的经典扰动范围相比，它具有更清晰，更精细的统计分析。在此保留的扰动理论的授权下，我们为混合模型下的光谱聚类的性能提供了确定性的进入分析。我们的分析导致了高斯混合模型光谱聚类的明确指数错误率。对于各向同性高斯人的混合物，在信号到噪声状态较弱的情况下，速率比l {Ö} ffler等人的速率是最佳的。 （2021）。
The singular subspaces perturbation theory is of fundamental importance in probability and statistics. It has various applications across different fields. We consider two arbitrary matrices where one is a leave-one-column-out submatrix of the other one and establish a novel perturbation upper bound for the distance between the two corresponding singular subspaces. It is well-suited for mixture models and results in a sharper and finer statistical analysis than classical perturbation bounds such as Wedin's Theorem. Empowered by this leave-one-out perturbation theory, we provide a deterministic entrywise analysis for the performance of spectral clustering under mixture models. Our analysis leads to an explicit exponential error rate for spectral clustering of sub-Gaussian mixture models. For the mixture of isotropic Gaussians, the rate is optimal under a weaker signal-to-noise condition than that of L{ö}ffler et al. (2021).
