Constrained variable clustering and the best basis problem in functional data analysis
This work addresses the need for efficient data reduction in functional data analysis, offering a domain-specific incremental improvement.
The paper tackles the problem of simplifying functional data by proposing a constrained variable clustering method to design piecewise constant representations, resulting in a polynomial complexity algorithm that provides optimal solutions.
Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained from a fine grid sampling of functional data, all methods benefit from a prior simplification of the functions that reduces the redundancy induced by the regularity. In this paper we propose to use a clustering approach that targets variables rather than individual to design a piecewise constant representation of a set of functions. The contiguity constraint induced by the functional nature of the variables allows a polynomial complexity algorithm to give the optimal solution.