  The Kepler mission has provided high-accurate photometric data in a long time
span for more than two hundred thousands stars, looking for planetary transits.
Among the detected candidates, the planetary nature of around 15% has been
established or validated by different techniques. But additional data is needed
to characterize the rest of the candidates and reject other possible
configurations. We started a follow-up program to validate, confirm, and
characterize some of the planet candidates. In this paper we present the radial
velocity analysis (RV) of those presenting large variations, compatible with
being eclipsing binaries. We also study those showing large rotational
velocities, which prevents us from obtaining the necessary precision to detect
planetary-like objects. We present new RV results for 13 Kepler objects of
interest (KOIs) obtained with the CAFE spectrograph at the Calar Alto
Observatory, and analyze their high-spatial resolution images and the Kepler
light curves of some interesting cases. We have found five spectroscopic and
eclipsing binaries. Among them, the case of KOI-3853 is of particular interest.
This system is a new example of the so-called heartbeat stars, showing dynamic
tidal distortions in the Kepler light curve. We have also detected duration and
depth variations of the eclipse. We suggest possible scenarios to explain such
effect, including the presence of a third substellar body possibly detected in
our RV analysis. We also provide upper mass limits to the transiting companions
of other six KOIs with large rotational velocities. This property prevents the
RV method to obtain the necessary precision to detect planetary-like masses.
Finally, we analyze the large RV variations of other two KOIs, incompatible
with the presence of planetary-mass objects. These objects are likely to be
stellar binaries but a longer timespan is still needed.
