  Poincar\'e plots, also called Poincar\'e maps, are used by plasma physicists
to understand the behavior of magnetically confined plasma in numerical
simulations of a tokamak. These plots are created by the intersection of field
lines with a two-dimensional poloidal plane that is perpendicular to the axis
of the torus representing the tokamak. A plot is composed of multiple orbits,
each created by a different field line as it goes around the torus. Each orbit
can have one of four distinct shapes, or classes, that indicate changes in the
topology of the magnetic fields confining the plasma. Given the (x,y)
coordinates of the points that form an orbit, the analysis task is to assign a
class to the orbit, a task that appears ideally suited for a machine learning
approach. In this paper, we describe how we overcame two major challenges in
solving this problem - creating a high-quality training set, with few
mislabeled orbits, and converting the coordinates of the points into features
that are discriminating, despite the variation within the orbits of a class and
the apparent similarities between orbits of different classes. Our automated
approach is not only more objective and accurate than visual classification,
but is also less tedious, making it easier for plasma physicists to analyze the
topology of magnetic fields from numerical simulations of the tokamak.
