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This paper introduces a new paradigm for unsupervised audiovisual document structuring. In this paradigm, a novel Nonnegative Matrix Factorization (NMF) algorithm is applied on histograms of counts (relating to a bag of features representation of the content) to jointly discover latent structuring patterns and their activations in time. Our NMF variant employs the Kullback-Leibler divergence as a cost function and imposes a temporal smoothness constraint to the activations. It is solved by a majorization-minimization technique. The approach proposed is meant to be generic and is particularly well suited to applications where the structuring patterns may overlap in time. As such, it is evaluated on two person-oriented video structuring tasks (one using the visual modality and the second the audio). This is done using a challenging database of political debate videos. Our results outperform reference results obtained by a method using Hidden Markov Models. Further, we show the potential that our general approach has for audio speaker diarization.