Gardner-Lubbe Sugnet
Department of Statistics and Actuarial Science, Stellenbosch University, Stellenbosch, South Africa.
J Appl Stat. 2020 Jun 17;48(11):1917-1933. doi: 10.1080/02664763.2020.1780569. eCollection 2021.
In multivariate data analysis, Fisher linear discriminant analysis is useful to optimally separate two classes of observations by finding a linear combination of variables. Functional data analysis deals with the analysis of continuous functions and thus can be seen as a generalisation of multivariate analysis where the dimension of the analysis space strives to infinity. Several authors propose methods to perform discriminant analysis in this infinite dimensional space. Here, the methodology is introduced to perform discriminant analysis, not on single infinite dimensional functions, but to find a linear combination of infinite dimensional continuous functions, providing a set of continuous canonical functions which are optimally separated in the canonical space.
在多变量数据分析中，Fisher线性判别分析通过寻找变量的线性组合来最优地分离两类观测值，十分有用。函数数据分析处理连续函数的分析，因此可被视为多变量分析的一种推广，其中分析空间的维度趋向于无穷大。几位作者提出了在这个无限维空间中进行判别分析的方法。在此，引入一种方法来进行判别分析，不是对单个无限维函数进行，而是寻找无限维连续函数的线性组合，从而提供一组在规范空间中最优分离的连续规范函数。
