  A profile from the Argo ocean observation array is a sequence of
three-dimensional vectors composed of pressure, salinity, and temperature,
appearing as a continuous curve in three-dimensional space. The shape of this
curve is faithfully represented by a path signature, which is a collection of
all the iterated integrals. Moreover, the product of two terms of the signature
of a path can be expressed as the sum of higher-order terms. Thanks to this
algebraic property, a nonlinear function of profile shape can always be
represented by a weighted linear combination of the iterated integrals, which
enables machine learning of a complicated function of the profile shape. In
this study, we performed supervised learning for existing Argo data with
quality control flags by using the signature method, and demonstrated the
estimation performance by cross-validation. Unlike rule-based approaches, which
require several complicated and possibly subjective rules, this method is
simple and objective in nature because it relies only on past knowledge
regarding the shape of profiles. This technique should be critical to realizing
automatic quality control for Argo profile data.
