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2020 High dimensional classification for spatially dependent data with application to neuroimaging
Yingjie Li, Liangliang Zhang, Tapabrata Maiti
Electron. J. Statist. 14(2): 3429-3486 (2020). DOI: 10.1214/20-EJS1743

Abstract

Discriminating patients with Alzheimer’s disease (AD) from healthy subjects is a crucial task in the research of Alzheimer’s disease. The task can be potentially achieved by linear discriminant analysis (LDA), which is one of the most classical and popular classification techniques. However, the classification problem becomes challenging for LDA because of the high-dimensionality and the spatial dependency of the brain imaging data. To address the challenges, researchers have proposed various ways to generalize LDA into high-dimensional context in recent years. However, these existing methods did not reach any consensus on how to incorporate spatially dependent structure. In light of the current needs and limitations, we propose a new classification method, named as Penalized Maximum Likelihood Estimation LDA (PMLE-LDA). The proposed method uses Matérn covariance function to describe the spatial correlation of brain regions. Additionally, PMLE is designed to model the sparsity of high-dimensional features. The spatial location information is used to address the singularity of the covariance. Tapering technique is introduced to reduce computational burden. We show in theory that the proposed method can not only provide consistent results of parameter estimation and feature selection, but also generate an asymptotically optimal classifier driven by high dimensional data with specific spatially dependent structure. Finally, the method is validated through simulations and an application into ADNI data for classifying Alzheimer’s patients.

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Yingjie Li. Liangliang Zhang. Tapabrata Maiti. "High dimensional classification for spatially dependent data with application to neuroimaging." Electron. J. Statist. 14 (2) 3429 - 3486, 2020. https://doi.org/10.1214/20-EJS1743

Information

Received: 1 February 2019; Published: 2020
First available in Project Euclid: 26 September 2020

zbMATH: 07270268
MathSciNet: MR4154844
Digital Object Identifier: 10.1214/20-EJS1743

Subjects:
Primary: 62H30
Secondary: 62H35

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Vol.14 • No. 2 • 2020
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