Reachable Distance Function for KNN Classification

TL;DR

This paper introduces a new reachable distance function for KNN classification that considers class attributes, ensuring more accurate affinity measurement and improved classification performance.

Contribution

It proposes a novel Z-shaped distance function that incorporates class information, addressing limitations of traditional geometric distance measures.

Findings

Achieved better classification accuracy with the new distance function.

Ensured intraclass points are closer than interclass points.

Demonstrated improved affinity measurement in experiments.

Abstract

Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the affinity between data points. This paper proposes a reachable distance function for KNN classification. The reachable distance function is not a geometric direct-line distance between two data points. It gives a consideration to the class attribute of a training dataset when measuring the affinity between data points. Concretely speaking, the reachable distance between data points includes their class center distance and real distance. Its shape looks like "Z", and we also call it a Z distance function. In this way, the affinity between data points in the same class is always stronger than that in different classes. Or, the intraclass data points are always closer than those interclass data points. We evaluated the reachable distance with experiments, and demonstrated that the proposed distance function achieved better performance in KNN classification.