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Article

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

1
Department of Mathematics, Statistics and Computer Science, University of Cantabria, 39005 Santander, Spain
2
Department of Mathematics, Imperial College London, London SW7 2BX, UK
3
Department of Mathematics, University of Trento, 38122 Trento, Italy
*
Author to whom correspondence should be addressed.
Current address: Faculty of Science, Avd. Los Castros s/n, 39005 Santander, Spain.
Academic Editors: Carmen Lacave and Ana Isabel Molina
Mathematics 2021, 9(8), 820; https://doi.org/10.3390/math9080820
Received: 3 March 2021 / Revised: 30 March 2021 / Accepted: 6 April 2021 / Published: 9 April 2021
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. View Full-Text
Keywords: Alzheimer’s disease; dementia; functional data analysis; functional depth; statistical data depth; symmetry Alzheimer’s disease; dementia; functional data analysis; functional depth; statistical data depth; symmetry
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MDPI and ACS Style

Nieto-Reyes, A.; Battey, H.; Francisci, G. Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients. Mathematics 2021, 9, 820. https://doi.org/10.3390/math9080820

AMA Style

Nieto-Reyes A, Battey H, Francisci G. Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients. Mathematics. 2021; 9(8):820. https://doi.org/10.3390/math9080820

Chicago/Turabian Style

Nieto-Reyes, Alicia, Heather Battey, and Giacomo Francisci. 2021. "Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients" Mathematics 9, no. 8: 820. https://doi.org/10.3390/math9080820

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