  With the advent of increasingly elaborate experimental techniques in physics,
chemistry and materials sciences, measured data are becoming bigger and more
complex. The observables are typically a function of several stimuli resulting
in multidimensional data sets spanning a range of experimental parameters. As
an example, a common approach to study ferroelectric switching is to observe
effects of applied electric field, but switching can also be enacted by
pressure and is influenced by strain fields, material composition, temperature,
time, etc. Moreover, the parameters are usually interdependent, so that their
decoupling toward univariate measurements or analysis may not be
straightforward. On the other hand, both explicit and hidden parameters provide
an opportunity to gain deeper insight into the measured properties, provided
there exists a well-defined path to capture and analyze such data. Here, we
introduce a new, two-dimensional approach to represent hysteretic response of a
material system to applied electric field. Utilizing ferroelectric polarization
as a model hysteretic property, we demonstrate how explicit consideration of
electromechanical response to two rather than one control voltages enables
significantly more transparent and robust interpretation of observed
hysteresis, such as differentiating between charge trapping and
ferroelectricity. Furthermore, we demonstrate how the new data representation
readily fits into a variety of machinelearning methodologies, from unsupervised
classification of the origins of hysteretic response via linear clustering
algorithms to neural-network-based inference of the sample temperature based on
the specific morphology of hysteresis.
