Let's start our classification adventure with the simplest task — binary classification. Suppose we want to classify sweets as cookies/not cookies based on a single feature: their weight.

A simple way to predict the class of a new instance is to look at its closest neighbor. In our example, we must find a sweet that weighs most similarly to the new instance.

That is the idea behind k-Nearest Neighbors(k-NN) - we just look at the neighbors. The k-NN algorithm assumes that similar things exist in close proximity. In other words, similar things are near each other. k in the k-NN stands for the number of neighbors we consider when making a prediction.

In the example above, we considered only 1 neighbor, so it was 1-Nearest Neighbor. But usually, k is set to a bigger number, as looking only at one neighbor can be unreliable:

If k (number of neighbors) is greater than one, we choose the most frequent class in the neighborhood as a prediction. Here is an example of predicting two new instances with k=3:

As you can see, changing the k may cause different predictions.