  Anchor-based techniques reduce the computational complexity of spectral
clustering algorithms. Although empirical tests have shown promising results,
there is currently a lack of theoretical support for the anchoring approach. We
define a specific anchor-based algorithm and show that it is amenable to
rigorous analysis, as well as being effective in practice. We establish the
theoretical consistency of the method in an asymptotic setting where data is
sampled from an underlying continuous probability distribution. In particular,
we provide sharp asymptotic conditions for the algorithm parameters which
ensure that the anchor-based method can recover with high probability disjoint
clusters that are mutually separated by a positive distance. We illustrate the
performance of the algorithm on synthetic data and explain how the theoretical
convergence analysis can be used to inform the practical choice of parameter
scalings. We also test the accuracy and efficiency of the algorithm on two
large scale real data sets. We find that the algorithm offers clear advantages
over standard spectral clustering. We also find that it is competitive with the
state-of-the-art LSC method of Chen and Cai (Twenty-Fifth AAAI Conference on
Artificial Intelligence, 2011), while having the added benefit of a consistency
guarantee.
