Using signatures to summarize time series data

Signatures are a mathematical construction that arises from rough path theory – a branch of mathematics established by Terry Lyons in the 1990s. The signature of a path is an abstract description of the variability of the path and, up to “tree-like equivalence,” the signature of a path is unique (for instance, two paths that are related by a translation will have the same signature). The signature is independent of parametrization and, consequently, signatures handle irregularly sampled data effectively.

Recently, signatures have found their way into the data science world as a means of summarizing time series data to be passed into machine learning pipelines (and for other applications). One of the reasons this is effective is because the signature of a path (truncated to a particular level) is always a fixed size, regardless of how many samples are used to compute the signature. One of the easiest applications...