Novel Algorithm for Computing Mahalanobis Distance

This document introduces a novel algorithm for computing Mahalanobis distance. The algorithm utilizes quadratic covariance matrix operations to incorporate relative factors into distance calculations. This development addresses the limitation of existing algorithms that fail to account for relative factors during distance computation. The implementation involves performing quadratic operations on the covariance matrix, typically through matrix decomposition and reconstruction techniques like Cholesky factorization or eigenvalue decomposition to handle covariance matrix transformations. The algorithm finds broad applications across various domains; in machine learning, it can calculate distances between different features within datasets, aiding in better understanding dataset structures and characteristics through enhanced similarity measurements. Additionally, it proves valuable for research in image processing, speech recognition, and other pattern recognition tasks where relative distance relationships play a crucial role.