  We investigate the relation between the radio (F_r) and optical (F_o) flux
densities of a variety of classes of radio transients and variables, with the
aim of analysing whether this information can be used, in the future, to
classify such events. Using flux density values between 1-10 GHz and the
optical bands V and R, we build a sample with a total of 12,441 F_r and F_o
measurements. The sample contains both Galactic objects, such as stellar
sources and X-ray binaries, and extragalactic objects, such as gamma-ray bursts
and quasars. By directly comparing the two parameters, it is already possible
to distinguish between the Galactic and extragalactic populations. Although
individual classes are harder to separate from the F_r-F_o parameter space to a
high accuracy, and can only provide approximations, the basic approach provides
an already useful foundation to develop a more accurate classification
technique. In addition, we illustrate how example objects from different
classes move in the parameter space as they evolve over time, offering a
feature that could be used to reduce the confusion between classes. A small,
blind test of the classification performance is also undertaken using a
catalogue of FIRST transient and variable sources, to demonstrate the
advantages and current limitations of the approach. With more multi-wavelength
data becoming available in the future, we discuss other classification
techniques which the F_r-F_o method could be combined with and potentially
become an important part of an automatic radio transient classification system.
