# How k-NN (k-Nearest Neighbors) Works for Classification

We already know that classification problem is predicting given input data into certain class. The simplest and most naive method is nearest neighbor. Given data training with class label, nearest neighbor classifier will assign given input data to the nearest data label. It can be done by using euclidean distance. Here is the illustration.

See picture above in the left, decision boundary is the black line. We can just simply assign class of given data input to the nearest data training class. We can extend using more than 1 nearest neighbors, that’s why we call it k-nearest neighbors, because we can specify the number of $k$. Let’s say we set $k=5$, then we will find 5 nearest data training, and then do voting for the class prediction using that 5 nearest class labels.

The characteristic of k-NN, when we have bigger number of $k$, our decision boundary will be more general and regular, but less sensitive. As a contrast, when we have lower value of $k$, we will have decision boundary that is more sensitive but less general, so that it is more probe to be overfitting.