Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/8/820 |
| _version_ | 1797538287821258752 |
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| author | Alicia Nieto-Reyes Heather Battey Giacomo Francisci |
| author_facet | Alicia Nieto-Reyes Heather Battey Giacomo Francisci |
| author_sort | Alicia Nieto-Reyes |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T12:28:26Z |
| format | Article |
| id | doaj.art-dd7f80722f71472ea43fc36d7c5d4654 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T12:28:26Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-dd7f80722f71472ea43fc36d7c5d46542023-11-21T14:50:52ZengMDPI AGMathematics2227-73902021-04-019882010.3390/math9080820Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s PatientsAlicia Nieto-Reyes0Heather Battey1Giacomo Francisci2Department of Mathematics, Statistics and Computer Science, University of Cantabria, 39005 Santander, SpainDepartment of Mathematics, Imperial College London, London SW7 2BX, UKDepartment of Mathematics, Statistics and Computer Science, University of Cantabria, 39005 Santander, SpainBlack-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.https://www.mdpi.com/2227-7390/9/8/820Alzheimer’s diseasedementiafunctional data analysisfunctional depthstatistical data depthsymmetry |
| spellingShingle | Alicia Nieto-Reyes Heather Battey Giacomo Francisci Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients Mathematics Alzheimer’s disease dementia functional data analysis functional depth statistical data depth symmetry |
| title | Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients |
| title_full | Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients |
| title_fullStr | Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients |
| title_full_unstemmed | Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients |
| title_short | Functional Symmetry and Statistical Depth for the Analysis of Movement Patterns in Alzheimer’s Patients |
| title_sort | functional symmetry and statistical depth for the analysis of movement patterns in alzheimer s patients |
| topic | Alzheimer’s disease dementia functional data analysis functional depth statistical data depth symmetry |
| url | https://www.mdpi.com/2227-7390/9/8/820 |
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