  Spectral clustering approaches have led to well-accepted algorithms for
finding accurate clusters in a given dataset. However, their application to
large-scale datasets has been hindered by computational complexity of
eigenvalue decompositions. Several algorithms have been proposed in the recent
past to accelerate spectral clustering, however they compromise on the accuracy
of the spectral clustering to achieve faster speed. In this paper, we propose a
novel spectral clustering algorithm based on a mixing process on a graph.
Unlike the existing spectral clustering algorithms, our algorithm does not
require computing eigenvectors. Specifically, it finds the equivalent of a
linear combination of eigenvectors of the normalized similarity matrix weighted
with corresponding eigenvalues. This linear combination is then used to
partition the dataset into meaningful clusters. Simulations on real datasets
show that partitioning datasets based on such linear combinations of
eigenvectors achieves better accuracy than standard spectral clustering methods
as the number of clusters increase. Our algorithm can easily be implemented in
a distributed setting.
