The Mahalanobis Distance for Functional Data With Applications to Classification

This article presents a new semidistance for functional observations that generalizes the Mahalanobis distance for multivariate datasets. The main characteristics of the functional Mahalanobis semidistance are shown. To illustrate the applicability of this measure of proximity between functional observations, new versions of several well-known functional classification procedures are developed using the functional Mahalanobis semidistance. A Monte Carlo study and the analysis of two real examples indicate that the classification methods used in conjunction with the functional Mahalanobis semidistance give better results than other well-known functional classification procedures. This article has supplementary material online.

本文提出一种面向函数型观测的新型半距离，该方法针对多元数据集场景下的马氏距离（Mahalanobis distance）进行了推广。本文阐明了函数型马氏半距离（functional Mahalanobis semidistance）的核心特性。为说明该函数型观测间邻近性度量的适用性，本文基于函数型马氏半距离构建了多款经典函数型分类方法的改进版本。经蒙特卡洛（Monte Carlo）实验与两个真实案例分析验证，结合函数型马氏半距离的分类方法，其性能表现优于其他经典函数型分类方法。本文附带在线补充材料。