Efficient Coding of Time-Relative Structure Using Spikes
Neural Computation
Comparing measures of sparsity
IEEE Transactions on Information Theory
Basis Decomposition of Motion Trajectories Using Spatio-temporal NMF
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
Sparse and shift-Invariant representations of music
IEEE Transactions on Audio, Speech, and Language Processing
A generative model for music transcription
IEEE Transactions on Audio, Speech, and Language Processing
On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization
IEEE Transactions on Neural Networks
Recovery of Sparse Translation-Invariant Signals With Continuous Basis Pursuit
IEEE Transactions on Signal Processing
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We use shift-invariant Non-negative Matrix Factorization (NMF) for decomposing continuous-valued time series into a number of characteristic primitives, i.e. the basis vectors, and their activations, which results in a model-independent and fully data driven parts-based representation. We interpret the basis vectors as short parts of motion that are shared between all trajectories in the data set, and the activations as onset times of those parts. The extension of the shift-invariant NMF by a new competition term between adjacent activations allows to gain temporally isolated activation events, which further supports this interpretation. We show that the resulting sparse and compact representation can be used for the prediction of motion trajectories, and that it can be beneficial for classification, because it allows the application of simple standard classification models with few parameters. In this paper we show that basis vectors can be extracted, which can be interpreted as short motion segments. We present results on trajectory prediction, and show that the sparse representation can be used for classification of trajectories of a single joint, like the one of a hand, obtained by motion capturing.