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. The resulting method can be thought of as an adaptive template matching procedure. We demonstrate the procedure on the task of extracting spikes from single channel extracellular recordings. On these data the algorithm essentially performs spike detection and unsupervised spike clustering. Results on simulated data and extracellular recordings indicate that the method performs well for signal-to-noise ratios of 6dB or higher and that spike templates are recovered accurately provided they are sufficiently different.