Sparse functional linear discriminant analysis

Summary Functional linear discriminant analysis provides a simple yet efficient method for classification, with the possibility of achieving perfect classification. Several methods have been proposed in literature that mostly address dimensionality problem. On other hand, there is growing interest interpretability analysis, which favours and sparse solution. In this paper we propose new approach incorporates type sparsity identifies nonzero subdomains functional setting, yielding solution easier to interpret without compromising performance. Given need embed additional constraints solution, reformulate as regularization problem an appropriate penalty. Inspired by success $\ell_1$-type at inducing zero coefficients scalar variables, develop $L^1$-type penalty, $\int |f|$, induce regions. We demonstrate our formulation has well-defined contains regions, sense domain selection. addition, misclassification probability regularized shown converge Bayes error if data are Gaussian. Our does not assume underlying function regions domain, but it produces estimator consistently estimates true whether or latter sparse. Using both simulated real examples, property finite samples through comparisons existing methods.