Title: Linear classification for functional data with direct estimation
Authors: Juhyun Park - ENSIIE (France) [presenting]
Jeongyoun Ahn - University of Georgia (United States)
Yongho Jeon - Yonsei University (Korea, South)
Abstract: Functional data are inherently infinite-dimensional and, thus, dimension reduction is crucial to solve many inverse problems arising in statistical analysis. Functional PCA has been popular as a key technique to find an efficient finite dimensional representation. Many regression and clustering solutions are based on that, as essentially the inverse of the covariance operator is well defined. However, it is known that functional classification can achieve a perfect classification, if high dimensionality is well exploited. Hence, for the purpose of classification, it is not necessarily advantageous to have a well-defined finite-dimensional representation. An alternative method such as partial least squares method may find a better representation to exploit the dimensionality. Nevertheless, selecting the truncation order to define a finite representation in general is not a trivial issue. Based on these observations, we seek an alternative approach to classification with a direct estimation method. We consider the problem in linear methods and formulate it as a regularization problem with appropriate penalty. An added advantage of using penalty formulation is the possibility of incorporating some structural constraints in functional data such as sparsity or smoothness as we desire. We study the performance of the new method and develop an efficient algorithm.