The Mahalanobis distance for functional data with applications to classification
| Autor: | Pedro Galeano, Esdras Joseph, Rosa E. Lillo |
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| Rok vydání: | 2013 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Functional observations Multivariate statistics Monte Carlo method Machine Learning (stat.ML) Mathematics - Statistics Theory Statistics Theory (math.ST) Functional Mahalanobis semi-distance Statistics - Computation Measure (mathematics) Methodology (stat.ME) Functional principal components Statistics - Machine Learning Statistics FOS: Mathematics Computation (stat.CO) Statistics - Methodology Mathematics Mahalanobis distance business.industry Applied Mathematics Functional data analysis Pattern recognition Modeling and Simulation Classification methods Artificial intelligence business |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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