If a K-NN ($ k $ Nearest Neighbors) Algorithm Performs Very Well for Low $ k $, Can Something Be Inferred About the Data Set? I am running kNN  on a very small data set for binary classification. Each class has 100 samples. 
I am getting the best performances for $k=1$ and $k=3$. Can I deduce information about my data set from kNN performing very well for small values of $k$?
If the result is consistent with a large test set than it means your training data is dense and well define the degrees of freedom of the problem.

If the training set was small it means there is a good separation between your classes in space.