Spectral clustering (SC) is a widely used technique to perform group unsupervised classification of graph signals. However, SC is sometimes computationally intensive due to the need to calculate the graph similarity matrices on large high-dimensional data sets. This paper proposes an efficient SC method that rapidly calculates the similarity matrix using a matrix completion algorithm. First, a portion of the elements in the similarity matrix are selected by a blue noise sampling mask, and their similarity values are calculated directly from the original dataset. After that, a split Bregman algorithm based on the Schatten capped p norm is developed to rapidly retrieve the rest of the matrix elements. Finally, spectral clustering is performed based on the completed similarity matrix. A set of simulations based on different data sets are used to assess the performance of the proposed method. It is shown that for a sufficiently large sampling rate, the proposed method can accurately calculate the completed similarity matrix, and attain good clustering results while improving on computational efficiency.

谱聚类 (SC) 是一种广泛使用的技术，用于执行图信号的组无监督分类。然而，由于需要在大型高维数据集上计算图相似性矩阵，SC 有时是计算密集型的。本文提出了一种高效的 SC 方法，该方法使用矩阵完成算法快速计算相似度矩阵。首先，通过蓝噪声采样掩码选择相似矩阵中的一部分元素，直接从原始数据集计算它们的相似值。之后，基于 Schatten 上限p的分裂 Bregman 算法norm 被开发用于快速检索其余的矩阵元素。最后，基于完成的相似度矩阵进行谱聚类。一组基于不同数据集的模拟用于评估所提出方法的性能。结果表明，对于足够大的采样率，所提出的方法可以准确地计算完整的相似矩阵，并在提高计算效率的同时获得良好的聚类结果。