Using path signatures to predict a diagnosis of Alzheimer's disease

The path signature is a means of feature generation that can encode nonlinear interactions in the data as well as the usual linear features. It can distinguish the ordering of time-sequenced changes: for example whether or not the hippocampus shrinks fast, then slowly or the converse. It provides interpretable features and its output is a fixed length vector irrespective of the number of input points so it can encode longitudinal data of varying length and with missing data points. In this paper we demonstrate the path signature in providing features to distinguish a set of people with Alzheimer's disease from a matched set of healthy individuals. The data used are volume measurements of the whole brain, ventricles and hippocampus from the Alzheimer's Disease Neuroimaging Initiative (ADNI). The path signature method is shown to be a useful tool for the processing of sequential data which is becoming increasingly available as monitoring technologies are applied.