Classification of functional fragments by regularized linear classifiers with domain selection

TL;DR

This paper introduces a regularized linear classification approach for functional data, incorporating domain selection to improve accuracy with fragmentary observations, demonstrated through simulations and a medical dataset.

Contribution

It proposes a novel domain extension and selection procedure for functional data classification using regularization techniques, handling incomplete observations effectively.

Findings

Regularization methods achieve optimal misclassification rates.

Domain extension improves classification accuracy.

Method outperforms traditional approaches in simulations and real data.

Abstract

We consider the problem of 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.