K-Nearest Neighbors

KNN is a simple model for regression and classification tasks. It is so simple that its name describes most of its learning algorithm. The titular neighbors are representations of training instances in a metric space. A metric space is a feature space in which the distances between all members of a set are defined. In the previous chapter's pizza problem, our training instances were represented in a metric space because the distances between all the pizza diameters was defined. These neighbors are used to estimate the value of the response variable for a test instance. The hyperparameter k specifies how many neighbors can be used in the estimation. A hyperparameter is a parameter that controls how the algorithm learns; hyperparameters are not estimated from the training data and are sometimes set manually. Finally, the k neighbors that are selected are those that are nearest to the test instance, as measured by some distance function.

For classification tasks, a set of tuples of feature vectors and class labels comprise the training set. KNN is a capable of binary, multi-class, and multi-label classification; we will define these tasks later, and we will focus on binary classification in this chapter. The simplest KNN classifiers use the mode of the KNN labels to classify test instances, but other strategies can be used. The k is often set to an odd number to prevent ties. In regression tasks, the feature vectors are each associated with a response variable that takes a real-valued scalar instead of a label. The prediction is the mean or weighted mean of the KNN response variables.