, Volume 46, Issue 1, pp 147–162 | Cite as

Functional logistic discrimination with sparse PCA and its application to the structural MRI

  • Yuko ArakiEmail author
  • Atsushi Kawaguchi
Invited Paper


We propose a functional classification method with high-dimensional image predictors using a combination of logistic discrimination and basis expansions with sparse principal component analysis (PCA). Our model is an extension of the existing functional generalized linear models with image predictors using functional principal component regression to L1-regularized principal components. This extension enables us to create a more flexible prognostic region that does not depend on the shape of basis functions. Monte Carlo simulations were conducted to examine the method’s efficiency when compared with several possible classification techniques. Our method was shown to be the best in terms of both sensitivity and specificity for detecting the shape of interests and classifying groups. In addition, our model was applied to data on Alzheimer’s disease. Our model detected the prognostic brain region and was used to classify early-stage Alzheimer patients efficiently, based on three-dimensional structural magnetic resonance imaging (sMRI).


Functional data analysis Regularized logistic classification Sparse PCA Radial basis expansions 

Mathematics Subject Classification

62H30 62H25 62P10 



The authors would like to express their gratitude to the Editors and the Reviewers for their constructive suggestions and careful reading of our manuscript, which considerably improved the paper. This research was supported in part by Grants-in-Aid for Young Scientists (B) from the Ministry of Education, Culture, Sport, Science and Technology of Japan (26730023 to YA) and by Takayanagi Memorial Foundation for Science and Technology, Shizuoka University.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© The Behaviormetric Society 2019

Authors and Affiliations

  1. 1.Faculty of InformaticsShizuoka UniversityHamamatsuJapan
  2. 2.Faculty of MedicineSaga UniversitySagaJapan

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