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.