How to find nearest neighbors in SMOTE

I am reading the original paper by Chawla and others for SMOTE. I am trying to understand how to generate these synthetic examples for over-sampling the minority class. The paper says:

“Synthetic samples are generated in the following way: Take the difference between the feature vector (sample) under consideration and its nearest neighbor. Multiply this difference by a random number between 0 and 1, and add it to the feature vector under consideration. This causes the selection of a random point along the line segment between two specific features”.

I understand the idea, take your sample, the nearest neighbor, pick a random point in between, what I don’t understand is how these nearest neighbors are defined.