The Joint Distance Measure: A Measure of Similarity Accounting for Spatial and Angular Distances (2504.21005v1)

Abstract: Vector similarity measures play a fundamental role in various fields, including machine learning, natural language processing, information retrieval, and data mining. These measures quantify the closeness between two vectors in a high-dimensional space and are vital for tasks such as document similarity, recommendation systems, and clustering. While several vector similarity measures exist, each similarity measure is suited to specific purposes. In addition, some of these measures lack robustness to certain data types and/or probability distributions. This article presents a measure of vector similarity, known as the Joint Distance Measure (JDM). The JDM combines the Minkowski distance measure and the cosine similarity measure to establish a distance measure that captures the advantages of both measures.