The k-Nearest Neighbors

K-Nearest Neighbors, or simply kNN, belongs to the class of instance-based learning, also known as lazy classifiers. It's one of the simplest classification methods because the classification is done by just looking at the K closest examples in the training set (in terms of Euclidean distance or some other kind of distance) in the case that we want to classify. Then, given the K similar examples, the most popular target (majority voting) is chosen as the classification label. Two parameters are mandatory for this algorithm: the neighborhood cardinality (K) and the measure to evaluate the similarity (although the Euclidean distance, or L2, is the most used and is the default parameter for most implementations).

Let's take a look at an example. We are going to use a pretty big dataset, the MNIST handwritten digits. We will later explain why we use this dataset. We're going to use only a small portion of it (1000 samples) to keep the computational time reasonable and...