Reconfigurable intelligent surface (RIS) is a revolutionary technology for achieving high rate and large coverage in future wireless networks by smartly reflecting the signals with adjustable phase shifts. To design the reflection beamforming, accurate individual channel state information is required at the RIS, which is a challenge task due to the lack of signal processing ability in passive mode. In this paper, we add signal processing units for a few antennas at the RIS to partially acquire the channels and extrapolate them to the full channels, in which the active antenna selection is a key point but has not been addressed yet. We construct an active antenna selection network that utilizes the probabilistic sampling theory to select the optimal locations of these active antennas. With this active antenna selection network, we further design two deep learning-based schemes, i.e., the channel extrapolation scheme and the beam searching scheme. The former utilizes the selection network and a convolutional neural network to extrapolate the full channels from the partial channels, while the latter adopts a fully-connected neural network to achieve the direct mapping from the partial channels to the optimal beamforming vector with maximal transmission rate. Simulation results show that the proposed optimal antenna selection outperforms the trivial uniform antenna selection, and the performance of beam searching is more stable than that of channel extrapolation with fewer active antennas.