Human Activities as Stochastic Kronecker Graphs

A human activity can be viewed as a space-time repetition of activity primitives. Both instances of the primitives, and their repetition are stochastic. They can be modeled by a generative model-graph, where nodes correspond to the primitives, and the graph’s adjacency matrix encodes their affinities for probabilistic grouping into observable video features. When a video of the activity is represented by a graph capturing the space-time layout of video features, such a video graph can be viewed as probabilistically sampled from the activity’s model-graph. This sampling is formulated as a successive Kronecker multiplication of the model’s affinity matrix. The resulting Kronecker-power matrix is taken as a noisy permutation of the adjacency matrix of the video graph. The paper presents our: 1) model-graph; 2) memory- and time-efficient, weakly supervised learning of activity primitives and their affinities; and 3) inference aimed at finding the best expected correspondences between the primitives and observed video features. Our results demonstrate good scalability on UCF50, and superior performance to that of the state of the art on individual, structured, and collective activities of UCF YouTube, Olympic, and Collective datasets.