Fast Large-Scale Spectral Clustering by Sequential Shrinkage Optimization

Abstract

In many applications, we need to cluster large-scale data objects. However, some recently proposed clustering algorithms such as spectral clustering can hardly handle large-scale applications due to the complexity issue, although their effectiveness has been demonstrated in previous work. In this paper, we propose a fast solver for spectral clustering. In contrast to traditional spectral clustering algorithms that first solve an eigenvalue decomposition problem, and then employ a clustering heuristic to obtain labels for the data points, our new approach sequentially decides the labels of relatively well-separated data points. Because the scale of the problem shrinks quickly during this process, it can be much faster than the traditional methods. Experiments on both synthetic data and a large collection of product records show that our algorithm can achieve significant improvement in speed as compared to traditional spectral clustering algorithms.