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.
Highlights
Alzheimer’s disease is a neurodegenerative condition that affects 15 million people worldwide [1]
The evolution of the patient passes through different stages of the disease, which, according to the Global Deterioration Scale (GDS) [2], are: (GDS 1)
We focus on symmetry in statistics, in this case, it is not the random objects themselves to which a notion of symmetry applies, but rather their distributions
Summary
Alzheimer’s disease is a neurodegenerative condition that affects 15 million people worldwide [1]. As an additional tool for the doctor to consider in taking that decision, [3,4] analyzed the movement patterns of Alzheimer’s sufferers when moving freely in a daycare facility. The objective of those papers was supervised classification, so that given the movement patterns of a set of patients and their disease stage, the stage of other patients could be predicted based on their movement patterns. The analysis used neural networks applied to multivariate time series data This is a black-box technique that results in high success rates, 83% in [4] and 91% in [3], but does not reveal which characteristics of the data helped with the classification.
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