Spectral clustering is one of the most popular unsupervised machine learning methods. Constructing similarity matrix is crucial to this type of method. In most existing works, the similarity matrix is computed once for all or is updated alternatively. However, the former is difficult to reflect comprehensive relationships among data points, and the latter is time-consuming and is even infeasible for large-scale problems. In this work, we propose a restarted clustering framework with self-guiding and block diagonal representation. An advantage of the strategy is that some useful clustering information obtained from previous cycles could be preserved as much as possible. To the best of our knowledge, this is the first work that applies restarting strategy to spectral clustering. The key difference is that we reclassify the samples in each cycle of our method, while they are classified only once in existing methods. To further release the overhead, we introduce a block diagonal representation with Nystr\"{o}m approximation for constructing the similarity matrix. Theoretical results are established to show the rationality of inexact computations in spectral clustering. Comprehensive experiments are performed on some benchmark databases, which show the superiority of our proposed algorithms over many state-of-the-art algorithms for large-scale problems. Specifically, our framework has a potential boost for clustering algorithms and works well even using an initial guess chosen randomly.

翻译：谱聚类是最流行的无监督机器学习方法之一。构建相似矩阵对此类方法至关重要。现有工作中，相似矩阵要么一次性计算完毕，要么交替更新。然而，前者难以反映数据点之间的全面关系，后者则耗时且对于大规模问题甚至不可行。本文提出了一种具有自引导与块对角表示的重启式聚类框架。该策略的一个优势是能够尽可能保留之前循环中获得的有用聚类信息。据我们所知，这是首次将重启策略应用于谱聚类的研究。关键区别在于，我们的方法在每个循环中对样本进行重新分类，而现有方法仅分类一次。为进一步降低开销，我们引入了基于Nyström近似的块对角表示来构建相似矩阵。建立了理论结果以证明谱聚类中非精确计算的合理性。在多个基准数据库上进行了全面实验，结果表明我们提出的算法在大规模问题上优于许多最先进的算法。具体来说，我们的框架对聚类算法具有潜在提升作用，即使使用随机选择的初始猜测也能很好地工作。