Generalized Minkowski Distance-Based Local Mean k-Nearest Neighbor Classifier

This research focuses on comparing the classification performance of Local Mean-based K Nearest Neighbors (LMKNN) using different distance metrics. Specifically, we examine different value of close neighbors and 10 distance metrics within the
$L_{p}$
Norm ranging from 1 to 10, such as Euclidean distance, Minkowski distance and Manhattan distance. The KNN algorithm is a powerful tool for classification and regression tasks. Unlike many other algorithms, KNN is non-parametric, meaning it can adapt to complex models without making any assumptions about the data distribution. This makes it a popular choice for researchers who prefer simple classification model rather than complex one. However, calculating the distance between each test data point and all training data points can be computationally expensive, particularly when working with a large data set. To address this issue, we have consulted an improved KNN algorithm based on the local mean, which significantly reduces the calculation complexity without sacrificing accuracy. We have applied our algorithm to several commonly used data sets on UCI and observed promising classification performance. Furthermore, we have extended the Euclidean distance measurement in the original algorithm to the level of vector norm. This expands the classification index of KNN beyond just Euclidean distance and provides more accurate and robust results.