  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.
