Semantic learning and understanding of multi-vehicle interaction patterns in a cluttered driving environment are essential but challenging for autonomous vehicles to make proper decisions. This paper presents a general framework to gain insights into intricate multi-vehicle interaction patterns from bird's-eye view traffic videos. We adopt a Gaussian velocity field to describe the time-varying multi-vehicle interaction behaviors and then use deep autoencoders to learn associated latent representations for each temporal frame. Then, we utilize a hidden semi-Markov model with a hierarchical Dirichlet process as a prior to segment these sequential representations into granular components, also called traffic primitives, corresponding to interaction patterns. Experimental results demonstrate that our proposed framework can extract traffic primitives from videos, thus providing a semantic way to analyze multi-vehicle interaction patterns, even for cluttered driving scenarios that are far messier than human beings can cope with.