Animals living in groups collectively produce social structure. In this context individuals make strategic decisions about when to cooperate and compete. This requires that individuals can perceive patterns in collective dynamics, but how this pattern extraction occurs is unclear. Our goal is to identify a model that extracts meaningful social patterns from a behavioral time series while remaining cognitively parsimonious by making the fewest demands on memory. Using fine-grained conflict data from macaques, we show that sparse coding, an important principle of neural compression, is an effective method for compressing collective behavior. The sparse code is shown to be efficient, predictive, and socially meaningful. In our monkey society, the sparse code of conflict is composed of related individuals, the policers, and the alpha female. Our results suggest that sparse coding is a natural technique for pattern extraction when cognitive constraints and small sample sizes limit the complexity of inferential models. Our approach highlights the need for cognitive experiments addressing how individuals perceive collective features of social organization.