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Keywords:

  • Classification;
  • Filtering;
  • Functional data;
  • Linear discriminant analysis;
  • Low dimensional representation;
  • Reduced rank;
  • Regularized discriminant analysis;
  • Sparse curves

We introduce a technique for extending the classical method of linear discriminant analysis (LDA) to data sets where the predictor variables are curves or functions. This procedure, which we call functional linear discriminant analysis (FLDA), is particularly useful when only fragments of the curves are observed. All the techniques associated with LDA can be extended for use with FLDA. In particular FLDA can be used to produce classifications on new (test) curves, give an estimate of the discriminant function between classes and provide a one- or two-dimensional pictorial representation of a set of curves. We also extend this procedure to provide generalizations of quadratic and regularized discriminant analysis.