  Graph-based representations of images have recently acquired an important
role for classification purposes within the context of machine learning
approaches. The underlying idea is to consider that relevant information of an
image is implicitly encoded into the relationships between more basic entities
that compose by themselves the whole image. The classification problem is then
reformulated in terms of an optimization problem usually solved by a
gradient-based search procedure. Vario-eta through structure is an approximate
second order stochastic optimization technique that achieves a good trade-off
between speed of convergence and the computational effort required. However,
the robustness of this technique for large scale problems has not been yet
assessed. In this paper we firstly provide a theoretical justification of the
assumptions made by this optimization procedure. Secondly, a complexity
analysis of the algorithm is performed to prove its suitability for large scale
learning problems.
