Convex Hull Convolutive Non-Negative Matrix Factorization for Uncovering Temporal Patterns in Multivariate Time-Series Data

We propose the Convex Hull Convolutive Non-negative Matrix Factorization (CH-CNMF) algorithm to learn temporal patterns in multivariate time-series data. The algorithm factors a data matrix into a basis tensor that contains temporal patterns and an activation matrix that indicates the time instants when the temporal patterns occurred in the data. Importantly, the temporal patterns correspond closely to the observed data and represent a wide range of dynamics. Experiments with synthetic data show that the temporal patterns found by CH-CNMF match the data better and provide more meaningful information than the temporal patterns found by Convolutive Non-negative Matrix Factorization with sparsity constraints (CNMF-SC). Additionally, CH-CNMF applied on vocal tract constriction data yields a wider range of articulatory gestures compared to CNMF-SC. Moreover, we find that the gestures comprising the CH-CNMF basis generalize better to unseen data and capture vocal tract structure and dynamics significantly better than those comprising the CNMF-SC basis.