Optimal design for classification of functional data

Abstract

We study the design problem for the optimal classification of functional data. The goal is to select sampling time points so that functional data observed at these time points can be classified accurately. We propose optimal designs that are applicable to either dense or sparse functional data. Using linear discriminant analysis, we formulate our design objectives as explicit functions of the sampling points. We study the theoretical properties of the proposed design objectives and provide a practical implementation. The performance of the proposed design is evaluated through simulations and real data applications. The Canadian Journal of Statistics 48: 285–307; 2020 © 2019 Statistical Society of Canada

Review on functional data classification

“…For instance, results from functional data classification problems may benefit data collection and design. Given a pilot study with functional data that have known classes and may either densely or sparsely observed, C. Li and Xiao (2020) identified the optimal sampling time points to collect observations for a new subject using linear discriminant analysis. Despite progress being made in this field, existing methods often involve a single or finite number of random functions observed in the same domain.…”

“…See Galeano et al (2015) for a similar setup in conjunction with the functional Mahalanobis semidistance. C. Li and Xiao (2019) utilized FLDA to refine their design process by identifying the optimal sampling time points for accurately classifying functional data. Kraus and Stefanucci (2019) reformulated the centroid method as an optimization problem and searched the solution by the conjugate gradient method with early stopping.…”