Fast spectral clustering method based on graph similarity matrix completion

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.