Shifted Non-Negative Matrix Factorization

Non-negative matrix factorization (NMF) has become a widely used blind source separation technique due to its part based representation and ease of interpretability. We currently extend the NMF model to allow for delays between sources and sensors. This is a natural extension for spectrometry data where a shift in onset of frequency profile can be induced by the Doppler effect. However, the model is also relevant for biomedical data analysis where the sources are given by compound intensities over time and the onset of the profiles have different delays to the sensors. A simple algorithm based on multiplicative updates is derived and it is demonstrated how the algorithm correctly identifies the components of a synthetic data set. Matlab implementation of the algorithm and a demonstration data set is available.