Example of KNN overfitting with k=1 I know that with k=1 a KNN lead to overfitting, this is because it follows the noisy data of the training sample and not generalize well on new input sample. But I am confused on how this happens, I understand the graphics but cant't figure out an example. For instance, why in the training data noise are followed and in test data not ? if someone can please give me an example, I'll be grateful.
Thanks to all :).

In the training data, each observation is its own 1-nearest neighbor and thus, the model predicts without error. Out-of-sample, this logic (fortunately) fails because the nearest neighbor is again selected from the training data.
