We present our follow-up observations to search for an electromagnetic
counterpart of the IceCube high-energy neutrino, IceCube-170922A. Monitoring
observations of a likely counterpart, TXS 0506+056, are also described. First,
we quickly took optical and near-infrared images of 7 flat-spectrum radio
sources within the IceCube error region right after the neutrino detection and
found a rapid flux decline of TXS 0506+056 in Kanata/HONIR J-band data.
Motivated by this discovery, intensive follow-up observations of TXS 0506+056
are continuously done, including our monitoring imaging observations,
spectroscopic observations, and polarimetric observations in optical and
near-infrared wavelengths. TXS 0506+056 shows a large amplitude (~1.0 mag)
variability in a time scale of several days or longer, although no significant
variability is detected in a time scale of a day or shorter. TXS 0506+056 also
shows a bluer-when-brighter trend in optical and near-infrared wavelengths.
Structure functions of variabilities are examined and indicate that TXS
0506+056 is not a special blazar in terms of optical variability. Polarization
measurement results of TXS 0506+056 are also discussed.