  (abridged) The overwhelming majority of diagnostic tools for galactic
activity are focused on active galaxies. Passive or dormant galaxies are often
excluded from these diagnostics which usually employ emission line features. In
this work, we use infrared and optical colors in order to build an
all-inclusive galactic activity diagnostic tool that can discriminate between
star-forming, AGN, LINER, composite, and passive galaxies, and which can be
used in local and low-redshift galaxies. We explore classification criteria
based on infrared colors from the 3 WISE bands supplemented with optical colors
from the u, g, and r SDSS bands. From these we aim to find the minimal
combination of colors for optimal results. Furthermore, to mitigate biases
related to aperture effects, we introduce a new WISE photometric scheme combing
different sized apertures. We develop a diagnostic tool using machine learning
methods that includes both active and passive galaxies under one unified scheme
using 3 colors. We find that the combination of W1-W2, W2-W3, and g-r colors
offers good performance while the broad availability of these colors for a
large number of galaxies ensures wide applicability on large galaxy samples.
The overall accuracy is $\sim$81% while the achieved completeness for each
class is $\sim$81% for star-forming, $\sim$56% for AGN, $\sim$68% for LINER,
$\sim$65% for composite, and $\sim$85% for passive galaxies. Our diagnostic
provides a significant improvement over existing IR diagnostics by including
all types of active, as well as passive galaxies, and extending them to the
local Universe. The inclusion of the optical colors improves their performance
in identifying low-luminosity AGN which are generally confused with
star-forming galaxies, and helps to identify cases of starbursts with extreme
mid-IR colors which mimic obscured AGN galaxies, a well-known problem for most
IR diagnostics.
