2013/04/17 by Esdras Joseph, Joseph, Esdras, Pedro Galeano +3
Computer Science · Decision Sciences · Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Fuzzy Systems and Optimization #Machine Learning (stat.ML) #Methodology (stat.ME) #Multi-Criteria Decision Making #Rough Sets and Fuzzy Logic #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.CO #stat.ME #stat.ML #stat.TH
paper · pdf · doi:10.48550/arxiv.1304.4786
arxiv created 2013/04/17 · openalex publication_date 2013/04/17 · arxiv updated 2013/04/18 · openalex created_date 2025/10/24 · openalex updated_date 2026/08/04
This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More precisely, a new semi-distance for functional observations that generalize the usual Mahalanobis distance for multivariate datasets is introduced. For that, the development uses a regularized square root inverse operator in Hilbert spaces. Some of the main characteristics of the functional Mahalanobis semi-distance are shown. Afterwards, new versions of several well known functional classification procedures are developed using the Mahalanobis distance for functional data as a measure of proximity between functional observations. The performance of several well known functional classification procedures are compared with those methods used in conjunction with the Mahalanobis distance for functional data, with positive results, through a Monte Carlo study and the analysis of two real data examples.