Fast Communication-Efficient Spectral Clustering over Distributed Data

Abstract

The last decades have seen a surge of interests in distributed computing thanks to advances in clustered computing and big data technology. Existing distributed algorithms typically assume all the data are already in one place, and divide the data and conquer on multiple machines. However, it is increasingly often that the data are located at a number of distributed sites, and one wishes to compute over all the data with low communication overhead. For spectral clustering, we propose a novel framework that enables its computation over such distributed data, with "minimal" communications while a major speedup in computation. The loss in accuracy is negligible compared to the non-distributed setting. Our approach allows local parallel computing at where the data are located, thus turns the distributed nature of the data into a blessing; the speedup is most substantial when the data are evenly distributed across sites. Experiments on synthetic and large UC Irvine datasets show almost no loss in accuracy with our approach while about 2x speedup under various settings with two distributed sites. As the transmitted data need not be in their original form, our framework readily addresses the privacy concern for data sharing in distributed computing.

DC2: A Divide-and-conquer Algorithm for Large-scale Kernel Learning with Application to Clustering

“…Another line of closely related work are those under the term "learning over inherently distributed data" [45,46]. Instead of dividing the data, these work deal with situations where the data are already distributed, i.e., stored at a number of distributed machines as a result of business operation or diverse data collection channels.…”

“…We will use recursive random projections [13,44] to produce a compressed signature for each partition. The idea of recursive random projections has been successfully applied in fast approximate spectral clustering [43], computing over distributed data [45,46], and other procedures. Since our approach is a divide-and-conquer method with a representation compression, we refer to it as divide-compress-and-conquer, or DC 2 in short.…”