  Graph is a highly generic and diverse representation, suitable for almost any
data processing problem. Spectral graph theory has been shown to provide
powerful algorithms, backed by solid linear algebra theory. It thus can be
extremely instrumental to design deep network building blocks with spectral
graph characteristics. For instance, such a network allows the design of
optimal graphs for certain tasks or obtaining a canonical orthogonal
low-dimensional embedding of the data. Recent attempts to solve this problem
were based on minimizing Rayleigh-quotient type losses. We propose a different
approach of directly learning the eigensapce. A severe problem of the direct
approach, applied in batch-learning, is the inconsistent mapping of features to
eigenspace coordinates in different batches. We analyze the degrees of freedom
of learning this task using batches and propose a stable alignment mechanism
that can work both with batch changes and with graph-metric changes. We show
that our learnt spectral embedding is better in terms of NMI, ACC, Grassman
distance, orthogonality and classification accuracy, compared to SOTA. In
addition, the learning is more stable.
