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 data in addition to the usual linear terms. It provides interpretable features and its output is a fixed length vector irrespective of the number of input points or their sample times. In this paper we use the path signature to provide features for identifying people whose diagnosis subsequently converts to Alzheimer's disease. In two separate classification tasks we distinguish converters from 1) healthy individuals, and 2) individuals with mild cognitive impairment. The data used are time-ordered measurements of the whole brain, ventricles and hippocampus from the Alzheimer's Disease Neuroimaging Initiative (ADNI). We find two nonlinear interactions which are predictive in both cases. The first interaction is change of hippocampal volume with time, and the second is a change of hippocampal volume relative to the volume of the whole brain. While hippocampal and brain volume changes are well known in Alzheimer's disease, we demonstrate the power of the path signature in their identification and analysis without manual feature selection. Sequential data is becoming increasingly available as monitoring technology is applied, and the path signature method is shown to be a useful tool in the processing of this data.