  Recent observations have revealed an interesting active galactic nuclei (AGN)
subclass that shows strong activity at large scales ($\sim1$ kpc) but weaker at
small scales ($<10$ pc), suggesting a strong change in the mass accretion rate
of the central engine in the past $10^{3-4}$ yr. We systematically search for
such declining or fading AGN by cross-matching the SDSS type-1 AGN catalog at
$z<0.4$, covering the [OIII]$\lambda5007$ emission line which is a tracer for
the narrow-line region (NLR) emission, with the WISE mid-infrared (MIR) catalog
covering the emissions from the dusty tori. Out of the 7,653 sources, we found
57 AGN whose bolometric luminosities estimated from the MIR band are at least
one order of magnitude fainter than those estimated from the
[OIII]$\lambda5007$ emission line. This luminosity declining AGN candidate
population shows four important properties: 1) the past AGN activity estimated
from the [OIII]$\lambda5007$ line reaches around the Eddington-limit, 2) more
than 30% of the luminosity declining AGN candidates show a large absolute
variability of $\Delta W1 > 0.45$ mag in the previous $\sim10$ yr at the WISE
3.4 $\mu$m band, 3) the median ratio of $\log$([NII]$\lambda6584/
\mathrm{H}\alpha\lambda6563)=-0.52$, suggesting a lower gas metallicity and/or
higher ionization parameter compared to other AGN populations. 4) the second
epoch spectra of the population indicate a spectral type change for 15% of the
sources. This population provides insights on the possible connection between
the luminosity decline which started $\sim10^{3-4}$ yr ago and the decline in
the recent $10$ yr.
