Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients

Alicia Nieto-Reyes, Heather Battey and Giacomo Francisci
Additional contact information
Alicia Nieto-Reyes: Department of Mathematics, Statistics and Computer Science, University of Cantabria, 39005 Santander, Spain
Heather Battey: Department of Mathematics, Imperial College London, London SW7 2BX, UK
Giacomo Francisci: Department of Mathematics, Statistics and Computer Science, University of Cantabria, 39005 Santander, Spain

Mathematics, 2021, vol. 9, issue 8, 1-17

Abstract: Black-box techniques have been applied with outstanding results to classify, in a supervised manner, the movement patterns of Alzheimer’s patients according to their stage of the disease. However, these techniques do not provide information on the difference of the patterns among the stages. We make use of functional data analysis to provide insight on the nature of these differences. In particular, we calculate the center of symmetry of the underlying distribution at each stage and use it to compute the functional depth of the movements of each patient. This results in an ordering of the data to which we apply nonparametric permutation tests to check on the differences in the distribution, median and deviance from the median. We consistently obtain that the movement pattern at each stage is significantly different to that of the prior and posterior stage in terms of the deviance from the median applied to the depth. The approach is validated by simulation.

Keywords: Alzheimer’s disease; dementia; functional data analysis; functional depth; statistical data depth; symmetry (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/8/820/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/8/820/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:8:p:820-:d:533021

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().