A Sparsity Constraint for Topic Models - Application to Temporal Activity Mining

We address the mining of sequential activity patterns from document logs given as word-time occurrences. We achieve this using topics that models both the cooccurrence and the temporal order in which words occur within a temporal window. Discovering such topics, which is particularly hard when multiple activities can occur simultaneously, is conducted through the joint inference of the temporal topics and of their starting times, allowing the implicit alignment of the same activity occurences in the document. A current issue is that while we would like topic starting times to be represented by sparse distributions, this is not achieved in practice. Thus, in this paper, we propose a method that encourages sparsity, by adding regularization constraints on the searched distributions. The constraints can be used with most topic models (e.g. PLSA, LDA) and lead to a simple modified version of the EM standard optimization procedure. The effect of the sparsity constraint on our activity model and the robustness improvment in the presence of difference noises have been validated on synthetic data. Its effectiveness is also illustrated in video activity analysis, where the discovered topics capture frequent patterns that implicitly represent typical trajectories of scene objects.