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Functional Analysis of Variance, Discriminant Analysis, and Clustering in a Manifold of Elastic Curves

2011; Taylor & Francis; Volume: 40; Issue: 14 Linguagem: Inglês

10.1080/03610926.2010.484159

1532-415X

David Kaziska,

Statistical Methods and Applications

Abstract We develop functional data analysis techniques using the differential geometry of a manifold of smooth elastic functions on an interval in which the functions are represented by a log-speed function and an angle function. The manifold's geometry provides a method for computing a sample mean function and principal components on tangent spaces. Using tangent principal component analysis, we estimate probability models for functional data and apply them to functional analysis of variance, discriminant analysis, and clustering. We demonstrate these tasks using a collection of growth curves from children from ages 1–18. Keywords: Functional analysis of varianceFunctional clusteringFunctional data analysisFunctional discriminant analysisMathematics Subject Classification: Primary 62HSecondary 62P Notes For Ramsay and Silverman's method, this table shows the number of correctly classified functions from the test set of 39 girls and 26 boys. For the indicated discrimination method, this table shows the number of correctly classified functions from the test set of 39 girls and 26 boys. For the Mahalanobis method using separate tangent planes, this table shows the number of correctly classified functions from the test set of 39 girls and 26 boys.