Fast Large-Scale Spectral Clustering by Sequential Shrinkage Optimization

In many applications, we need to cluster largescale 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 many 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.