Title: Regularized classification of incomplete functions

Presenting author: David Kraus (Masaryk University, Brno, Czech
Republic)

Co-author: Marco Stefanucci (Sapienza University of Rome, Italy)

Abstract: We consider classification of functional data into two
groups by linear classifiers based on one-dimensional projections of
functions. We reformulate the task to find the best classifier as an
optimization problem and solve it by regularization techniques, namely
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 non-convergent empirical regularization path.
Being able to work with fragmentary training data 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 methodology is illustrated on a
medical data set, where we observe a substantial improvement of
classification accuracy due to domain extension.