  Insights on stellar surface large-scale magnetic field topologies are usually
drawn by applying Zeeman-Doppler-Imaging (ZDI) to the observed
spectropolarimetric time series. However, ZDI requires experience for reliable
results to be reached and is based on a number of prior assumptions that may
not be valid, e.g., when the magnetic topology is evolving on timescales
comparable to or shorter than the time span over which observations are
collected. In this paper, we present a method based on Principal Component
Analysis (PCA) applied to circularly polarised (Stokes~$V$) line profiles of
magnetic stars to retrieve the main characteristics of the parent large-scale
magnetic topologies, like for instance, the relative strength of the poloidal
and toroidal components, and the degree of axisymmetry of the dominant field
component and its complexity (dipolar or more complex). We show that this
method can also be used to diagnose the temporal variability of the large-scale
magnetic field. Performing best for stars with moderate projected equatorial
velocities hosting relatively simple magnetic field topologies, this new method
is simpler than ZDI, making it convenient to rapidly diagnose the main
characteristics of the large-scale fields of non-degenerate stars and to
provide insights into the temporal evolution of the field topology.
