Sparse Functional Linear Discriminant Analysis

Park, Juhyun and Ahn, Jeongyoun and Jeon, Yongho (2021) Sparse Functional Linear Discriminant Analysis. Biometrika. ISSN 0006-3444

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Abstract

Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the dimensionality of the problem. On the other hand, there is a growing interest in interpretability of the analysis, which favors a simple and sparse solution. In this work, we propose a new approach that incorporates a type of sparsity that identifies nonzero sub-domains in the functional setting, offering a solution that is easier to interpret without compromising performance. With the need to embed additional constraints in the solution, we reformulate the functional linear discriminant analysis as a regularization problem with an appropriate penalty. Inspired by the success of ℓ1-type regularization at inducing zero coefficients for scalar variables, we develop a new regularization method for functional linear discriminant analysis that incorporates an L1-type penalty, ∫ |f|, to induce zero regions. We demonstrate that our formulation has a well-defined solution that contains zero regions, achieving a functional sparsity in the sense of domain selection. In addition, the misclassification probability of the regularized solution is shown to converge to the Bayes error if the data are Gaussian. Our method does not presume that the underlying function has zero regions in the domain, but produces a sparse estimator that consistently estimates the true function whether or not the latter is sparse. Numerical comparisons with existing methods demonstrate this property in finite samples with both simulated and real data examples.

Item Type:
Journal Article
Journal or Publication Title:
Biometrika
Additional Information:
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version uhyun Park, Jeongyoun Ahn, Yongho Jeon, Sparse Functional Linear Discriminant Analysis, Biometrika, , asaa107, is available online at: https://doi.org/10.1093/biomet/asaa107
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1100/1101
Subjects:
ID Code:
150070
Deposited By:
Deposited On:
17 Dec 2020 15:30
Refereed?:
Yes
Published?:
Published
Last Modified:
26 Jan 2021 12:48