Consider a random, symmetric perturbation of a symmetric, low rank matrix. The goal of this paper is to present entry-wise bounds on the perturbation of the singular vectors. In particular, our result shows that, under common incoherence assumptions, the entry-wise error is evenly dissipated. This improves a number of previous results and has algorithmic applications for many well known clustering problems, including the hidden clique, planted coloring, and planted bipartition.

翻译：考虑一个对称低秩矩阵的随机对称摄动。本文旨在给出奇异向量摄动的逐分量界。特别地，我们的结果表明，在常见的非相干性假设下，逐分量误差被均匀耗散。这改进了先前多项结果，并具有诸多知名聚类问题的算法应用，包括隐藏团问题、植入染色问题和植入二分划分问题。