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Linear discriminant analysis for multiple functional data analysis.

Sugnet Gardner-Lubbe1

  • 1Department of Statistics and Actuarial Science, Stellenbosch University, Stellenbosch, South Africa.

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Summary
This summary is machine-generated.

This study introduces a new method for discriminant analysis with infinite dimensional functions. It finds optimal linear combinations of functions for better class separation in functional data analysis.

Keywords:
Functional data analysisclassificationlinear discriminant analysis

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Area of Science:

  • Statistics
  • Data Analysis

Background:

  • Fisher linear discriminant analysis optimally separates two classes in multivariate data using linear combinations of variables.
  • Functional data analysis extends multivariate analysis to infinite dimensions, analyzing continuous functions.

Purpose of the Study:

  • To develop a methodology for discriminant analysis on infinite dimensional continuous functions.
  • To find a linear combination of p infinite dimensional functions for optimal class separation.

Main Methods:

  • Extends Fisher linear discriminant analysis to the infinite-dimensional setting of functional data.
  • Develops a method to identify a linear combination of p continuous functions.

Main Results:

  • Introduces a novel approach for discriminant analysis in functional data.
  • Generates a set of continuous canonical functions that are optimally separated.

Conclusions:

  • The proposed methodology enables discriminant analysis on infinite dimensional functions.
  • Achieves optimal separation of classes in the canonical space for functional data.