The Maximum Euclidean Distance in a Class Defines the Boundary of Neighborhood and Leads to a New Machine Learning Algorithm

Classification occurs when we are given a data set in which each data point is assigned a class based on the values and or characteristics of attributes. The k-Nearest Neighbor (kNN) algorithm in machine learning is a very simple and powerful tool for doing this. It is based on the idea that data points of a certain class are neighbours to one another. To find the class to which a given test data or unknown data belongs, one measures the Euclidean distances of the test data or unknown data from all the data points of all the classes in the training data in kNN. Then, out of the k nearest distances, where k is any number greater or equal to 1, the class to which test data or unknown data is closest its most number of times is the class assigned to the test data or unidentified data. In this chapter, I propose a variation of kNN, which I call the ANN method (Alternative Nearest Neighbor) to distinguish it from kNN. The definition of neighbour is the distinguishing feature of ANN that distinguishes it from kNN. In ANN, the class to which the unknown data is neighbour is the class whose maximum Euclidean distance from its data points is less than or equal to the maximum Euclidean distance between all of the class's training data points.As a result, ANN will always provide a unique solution to each unknown data. In contrast, the solution in kNN may vary depending on the value of the number of nearest neighbours k. So, in kNN, as k is varied the performance may vary too. However, this is not the case with ANN; its performance for a specific training dataset is unique.

The main motivation behind finding the ANN machine learning method has been to modify the conventional kNN method in such a way that it is independent of the parameter k and the user of the method need not make a choice of k neighbors based on experience or other criteria.