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In this paper, we extend the traditional few-shot learning (FSL) problem to the situation when the source-domain data is not accessible but only high-level information in the form of class prototypes is available. This limited information setup for the FSL problem deserves much attention due to its implication of privacy-preserving inaccessibility to the source-domain data but it has rarely been addressed before. Because of limited training data, we propose a non-parametric approach to this FSL problem by assuming that all the class prototypes are structurally arranged on a manifold. Accordingly, we estimate the novel-class prototype locations by projecting the few-shot samples onto the average of the subspaces on which the surrounding classes lie. During classification, we again exploit the structural arrangement of the categories by inducing a Markov chain on the graph constructed with the class prototypes. This manifold distance obtained using the Markov chain is expected to produce better results compared to a traditional nearest-neighbor-based Euclidean distance. To evaluate our proposed framework, we have tested it on two image datasets - the large-scale ImageNet and the small-scale but fine-grained CUB-200. We have also studied parameter sensitivity to better understand our framework.