  SVD serves as an exploratory tool in identifying the dominant features in the
form of top rank-r singular factors corresponding to the largest singular
values. For Big Data applications it is well known that Singular Value
Decomposition (SVD) is restrictive due to main memory requirements. However, a
number of applications such as community detection, clustering, or bottleneck
identification in large scale graph data-sets rely upon identifying the lowest
singular values and the singular corresponding vectors. For example, the lowest
singular values of a graph Laplacian reveal the number of isolated clusters
(zero singular values) or bottlenecks (lowest non-zero singular values) for
undirected, acyclic graphs. A naive approach here would be to perform a full
SVD however, this quickly becomes infeasible for practical big data
applications due to the enormous memory requirements. Furthermore, for such
applications only a few lowest singular factors are desired making a full
decomposition computationally exorbitant. In this work, we trivially extend the
previously proposed Range-Net to \textbf{Tail-Net} for a memory and compute
efficient extraction of lowest singular factors of a given big dataset and a
specified rank-r. We present a number of numerical experiments on both
synthetic and practical data-sets for verification and bench-marking using
conventional SVD as the baseline.

Machine Learning;Artificial Intelligence