  Most galaxies in the nearby Universe are gravitationally bound to a cluster
or group of galaxies. Their optical contents, such as optical richness, are
crucial for understanding the co-evolution of galaxies and large-scale
structures in modern astronomy and cosmology. The determination of optical
richness can be challenging. We propose a self-supervised approach for
estimating optical richness from multi-band optical images. The method uses the
data properties of the multi-band optical images for pre-training, which
enables learning feature representations from a large but unlabeled dataset. We
apply the proposed method to the Sloan Digital Sky Survey. The result shows our
estimate of optical richness lowers the mean absolute error and intrinsic
scatter by 11.84% and 20.78%, respectively, while reducing the need for labeled
training data by up to 60%. We believe the proposed method will benefit
astronomy and cosmology, where a large number of unlabeled multi-band images
are available, but acquiring image labels is costly.
