Adaptive Template Matching with Shift-Invariant Semi-NMF

How does one extract unknown but stereotypical events that are linearly superimposed within a signal with variable latencies and variable amplitudes? One could think of using template matching or matching pursuit to find the arbitrarily shifted linear components. However, traditional matching approaches require that the templates be known a priori. To overcome this restriction we use instead semi Non-Negative Matrix Factorization (semi-NMF) that we extend to allow for time shifts when matching the templates to the signal. The algorithm estimates templates directly from the data along with their non-negative amplitudes.