A method and system for spectrum data analysis. The method comprises the steps of collecting a spectrum of an unknown material; providing a set of data templates; calculating weighting factors for the element data templates to minimize error in approximating the spectrum; removing one or more of the templates having negative weights in approximating the spectrum; and re-calculating an approximation of the spectrum with said one or more templates removed. Embodiments of the invention are suitable for analyzing noisy spectra having relatively few data points.