Compressed Spectral Clustering

Compressed sensing has received much attention in both data mining and signal processing communities. In this paper, we provide theoretical results to show that compressed spectral clustering, separating data samples into different clusters directly in the compressed measurement domain, is possible. Specifically, we provide theoretical bounds guaranteeing that if the data is measured directly in the compressed domain, spectral clustering on the compressed data works almost as well as that in the data domain. Moreover, we show that for a family of well-known compressed sensing matrices, compressed spectral clustering is universal, i. e., clustering in the measurement domain works provided that the data are sparse in some, even unknown, basis. Finally, experimental results on both toy and real world data sets demonstrate that compressed spectral clustering achieves comparable clustering performance with traditional spectral clustering that works directly in the data domain, with much less computational time.