Classification of functional fragments by regularized linear classifiers with domain selection

We consider classification of functional data into two groups by linear classifiers based on one-dimensional projections of functions. We reformulate the task of finding the best classifier as an optimization problem and solve it by the conjugate gradient method with early stopping, the principal component method, and the ridge method. We study the empirical version with finite training samples consisting of incomplete functions observed on different subsets of the domain and show that the optimal, possibly zero, misclassification probability can be achieved in the limit along a possibly nonconvergent empirical regularization path. We propose a domain extension and selection procedure that finds the best domain beyond the common observation domain of all curves. In a simulation study we compare the different regularization methods and investigate the performance of domain selection. Our method is illustrated on a medical dataset, where we observe a substantial improvement of classification accuracy due to domain extension.