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This paper develops a new way of analyzing k-Nearest Neighbor prediction for classification problems. Nearest Neighbor prediction is a simple and well studied classification method that, although the first results date decades back, has recently seen some renewed interest and new development. This paper provides a new angle on Nearest Neighbor analysis by incorporating that the behavior of NN classifiers actually automatically adapt to local scaling (with respect to the probability distribution) of the input space. This aspect has not been taken into account in previous studies on NN. Previous analysis of NN has been in terms of smoothness parameters and bounds provided reflect some sort of worst case over the data space of this smoothness parameters.